Ticks on the run: A mathematical model of Crimean-Congo Haemorrhagic Fever (CCHF)-key factors for transmission
Suman Bhowmick, Khushal Khan Kasi, Jörn Gethmann, Susanne Fischer, Franz J. Conraths, Igor M. Sokolov, Hartmut H. K. Lentz
TTicks on the run: A mathematical model ofCrimean-Congo Haemorrhagic Fever (CCHF) – keyfactors for transmission
Suman Bhowmick b , Khushal Khan Kasi a , J¨orn Gethmann a , Susanne Fischer c ,Franz J. Conraths a , Igor M. Sokolov b,d , Hartmut H. K. Lentz a,1 a Friedrich-Loeffler-Institut, Institute of Epidemiology, S¨udufer 10, 17493 Greifswald,Germany b Institute for Physics, Humboldt-University of Berlin, Newtonstraße 15, 12489 Berlin,Germany c Friedrich-Loeffler-Institut, Institute of Infectology, S¨udufer 10, 17493 Greifswald, Germany d IRIS Adlershof, Zum Großen Windkanal 6, 12489 Berlin, Germany
Abstract
Crimean-Congo haemorrhagic fever (CCHF) is a tick-borne zoonotic diseasecaused by the Crimean-Congo hemorrhagic fever virus (CCHFV). Ticks belong-ing to the genus
Hyalomma are the main vectors and reservoir for the virus. It ismaintained in nature in an endemic vertebrate-tick-vertebrate cycle. CCHFV isprevalent in wide geographical areas including Asia, Africa, South-Eastern Eu-rope and the Middle East. Over the last decade, several outbreaks of CCHFVhave been observed in Europe, mainly in Mediterranean countries. Due to thehigh case/fatality ratio of CCHFV in human sometimes, it is of great impor-tance for public health. Climate change and the invasion of CCHFV vectors inCentral Europe suggest that the establishment of the transmission in CentralEurope may be possible in future.We developed a compartment-based nonlinear Ordinary Differential Equa-tion (ODE) system to model the disease transmission cycle including bloodsucking ticks, livestock and human. Sensitivity analysis of the basic reproduc-tion number R shows that decreasing in the tick survival time is an efficientmethod to eradicate the disease. The model supports us in understanding the Corresponding author
Preprint submitted to Journal of L A TEX Templates January 28, 2021 a r X i v : . [ phy s i c s . b i o - ph ] J a n nfluence of different model parameters on the spread of CCHFV. Tick to ticktransmission through co-feeding and the CCHFV circulation through trasstadialand transovarial stages are important factors to sustain the disease cycle. Theproposed model dynamics are calibrated through an empirical multi-countryanalysis and multidimensional scaling reveals the disease-parameter sets of dif-ferent countries burdened with CCHF are different. This necessary informationmay help us to select most efficient control strategies. Keywords:
CCHFV, ODE, Tick Borne Disease, Targeted Control,
Hyalomma
1. Introduction
Crimean-Congo haemorrhagic fever (CCHF) is a tick-borne viral zoonoticdisease widely distributed in Asia, Africa, Southeast Europe and the MiddleEast [1, 2]. CCHF was first identified in an outbreak during World War II onthe Crimean Peninsula in 1944–1945, when 200 Soviet military personnel gothemorrhagic fever with a case/fatality ratio of 10% [3]. The virus is antigenicallyidentical to a virus that was isolated from the blood of a patient in DemocraticRepublic of the Congo in 1956. The association of these two places resulted inthe name of the disease and the virus [4, 5].The etiological agent responsible for the disease, i.e. Crimean-Congo hemor-rhagic fever virus (CCHFV), belongs to the genus
Orthonairovirus in the family
Nairoviridae [6].CCHFV is transmitted between vertebrates and ticks but can also be trans-mitted horizontally and vertically within the tick population [7, 8]. Ticks maybe born infected as some fraction of infected female ticks transmit the disease totheir offspring. Depending on the developmental stage of the ticks, i.e. larvae,nymphs and adults, the vertebrate hosts range from small (birds, hares, rabbits)to large vertebrates (cattle, sheep, humans). Animals act as viral amplifyinghosts with transient viremia, but they do not develop clinical signs [2]. CCHFVpersists in the tick for its whole lifespan [2]. Within the tick population, it istransstadially transmitted, venereal transmission among ticks and transmission2hrough co-feeding may also occur [9, 10]. The route of transmission throughwhich an infected tick transfer tick-borne pathogens to a susceptible host andvice versa, is described as systemic transmission and another transmission path-way that helps the pathogens to persist in the ticks through co-feeding, is termedas non-systemic transmission.Hard ticks of the genus
Hyalomma are considered the main reservoir andvector for CCHFV ([9, 10, 7]). They are mainly present in the Afrotropicaland in parts of the Palaearctic regions [11, 12, 13, 14]. CCHFV has been alsodetected in other tick genera, including
Rhipicephalus, Amblyomma, Ixodes and
Dermacentor , but their role in CCHFV maintenance and their vector capacityis not yet clear [2].CCHF virus is transmitted to people either by tick bites, contact with bloodof infected animals or humans, body fluids or tissues. Hence, persons involved inthe livestock industry, such as agricultural workers, slaughterhouse workers andveterinarians are more vulnerable to CCHFV. Human-to-human transmissioncan also happen through contact with bodily fluids of patients comprising virusduring the first 7–10 days of illness [15]. Health workers including physicians,nurses and laboratory personnel are therefore at an increased risk of contractingCCHF vectors. There are several reported cases of nosocomial spread of thedisease [16, 17, 18, 19, 20] and possibly through sexual transmission [21, 22].Infections acquired in hospitals can also happen due to improper sterilisationof medical equipment or re-use of needles. CCHFV represents a potential riskfor humans who have unprotected contact with other body fluids [23]. Becauseof severe illness and a high case fatality rate in humans, CCHF is consideredas an important vector-borne disease in humans [24]. CCHF causes sporadiccases or outbreaks of severe scale across a huge geographical area extending fromChina to the Middle East, Southeastern Europe and Africa [25, 5, 1]. It is ahighly infectious disease in human with a case fatality rate from 5% to 80% [26].Human cases are seasonal and associated with an increased population of
H.marginatum under optimal weather conditions and habitat fragmentation [27].According to [15], the antibody positivity of CCHFV in livestock correlates3ith the manifestation of human cases and the occurrence of CCHF can happendue to contact with the blood of infected animals. The authors in [15] mentionthat repeated outbreaks and sporadic cases have been found in persons handlingor slaughtering livestock. The study conducted in [28] has shown the infection ofa single
H. m. rufipes that took a blood meal from a viraemic calf. The authorsin [29] demonstrated that adult ixodid ticks of several species can get CCHFvirus infection by feeding on viraemic cattle. In the same study, it was shownthat cattle can act as amplifying hosts of CCHFV by viraemic transmission ofCCHFV to ticks. [29] assert that the adult ticks, which get the infection afterfeeding, conceivably are a crucial source of infection in humans, if pull out byhands or crushed. The review in [30] features the role of livestock in the main-tenance and transmission of CCHFV. The conducted studies in [31] highlightthe fact that the transmission of CCHFV can occur to those who are involvedin livestock and animal husbandry in Pakistan, as well as the risk of transmis-sion is higher during the time of Eid-ul-Azha, when Muslims slaughter animals.According to [32], high prevalence values in ruminants in Turkey depicts therole of these species to identify the high-risk areas. Additionally, according tothe sensitivity analysis of R performed in [33], the input of total host densityacquires 28% of the total variability and the contribution of hare density is 16%and for the same for the cattle population is 12%.Figure 1 shows reported cases and deaths in humans over time for differentcountries. Although the number of cases appears to have stabilised or evendecreased in recent years, an increasing trend of fatal cases is shown in Figure1b. 4 Year H u m a n cases Country
AfghanistanIranPakistanTurkey
Asia
Year H u m a n cases Country
BulgariaGermanyKosovoSpainUK
Europe (a) l l l l l l l l l lll l ll l l l l l N u m b e r o f D ea t h Country lllll
BulgariaIranKosovoPakistanTurkey (b)Figure 1: (a) Reported cases of CCHFV in Asia and Europe. (b) Reported death cases ofCCHFV. Data from [14, 34, 31, 35].
CCHFV can spread over long distances through transportation of vectorsattached to migratory birds that fly through endemic areas such as Turkey orGreece [36, 37], or through imported livestock [38]. It has been estimated thatevery year hundreds of thousands of immature
Hyalomma ticks are transportedvia migratory birds into or over Central Europe during the spring migration ofbirds from southern Europe and Africa [11]. The virus has a wide range of hostsand vectors and therefore the potential to establish in a new region, if enoughsusceptible hosts and vectors are available [39]. There are several factors likeclimate change, social and anthropogenic factors that may have contributed tothe spread of CCHFV into new regions and to the increase of reported cases [40].Since several years, adult stages
Hyalomma marginatum ticks have occasionallybeen found in Germany [41, 42, 11]. They may have been introduced by birdsas nymphs and continued to develop to the adult stage [11]. The authors of thisstudy [11] point out that there is a lack of information about the transportationof
H. marginatum into Germany and how the tick succeeded to develop intothe adult stage in this country. In September 2018, successful moulting of a
Hyalomma nymph removed from a horse in Dorset, England, was reported.This horse had no history of overseas travel [43]. The environmental suitability5f CCHFV across Southern and Central Europe has been postulated [44]. Thelife cycle of CCHFV is complex and the influence of climate and environmentfactors has not been fully understand so far.Mathematical modelling provides a tool to test different scenarios and toanalyse the factors influencing the spread of CCHF. While the number of math-ematical models for vector-borne diseases has generally increased, the numberof mathematical models for CCHFV in particular is still limited [45, 46, 47, 33].We refine existing models by including human infection. Humans are an inte-gral part of the transmission cycle and they play a major role in detecting thedisease due to the high case fatality ratio in humans. This will help us to fitthe model. Our current modelling efforts are aiming to provide answers to thefollowing questions:1. What are the sensitive parameters responsible for the CCHF transmission?2. What are possible control measures to curb the infection spread in differentgeographical areas?3. What is the critical density of ticks necessary for a potential spread4. How to quantify the nature of dissemination of CCHFV in the endemicareas?Beside the above mentioned objectives, we utilise the basic reproduction numberas a measure of CCHFV transmission potential within the enzootic cycle andthis exhibits a crucial feature of risk of human infection.
2. Model Formulation
In this section first we describe the modelling assumptions and we then in-troduce the important model parameters with their meanings. We set forth ourpreference is to keep our compartment based Ordinary Differential Equation(ODE) model of three interacting populations, i.e. ticks, livestock and humansas shown in Figure 2 as simple as possible in order to provide general theoreti-cal results and concurrently to abstain from the issue of hyper-parameterisation6hile taking account of transstadial and transovarial transmissions. The cou-pled infection-population model, presented in Figure 2, concisely presents thefollowing mechanisms: transmission (from tick population to host) and acqui-sition (from livestock to tick population) of the CCHFV pathogen, transstadialpersistence of CCHFV amongst the tick life cycle, transovarial transmission fromthe female adult ticks to eggs and CCHFV transmission from infected livestockto human population along with the net growth of the interacting populations.After following [48], we summate together all tick stages to reach the equationsfor the total tick dynamics and admeasure as effective tick population ⇡ T
We assume that there is a fixed proportion of ticks that mature within eachdevelopmental stage and the developmental stages of the vectors would functionas a delay in the potential infection spread after following the authors in [49].Being parsimonious in nature, in our model we club together the differentadult tick activity phases together as it paves the way to postulate an abridgedmodel but flexible enough to incorporate further details in the future for possibleexplorations. We conveniently attempt to describe the certain biological mech-anism involving transstadial transmission, transovarial transmission. We alsoassume that systemic infection occurs at the beginning of the blood meal afterfollowing the authors in [48]. To accommodate the systemic and non-systemic7nfection we pursue the efforts done in [48, 47, 33]. In order to include theCCHFV transmission through co-feeding, we adhere to the following assump-tions: (i) It is proportional to the number of infected ticks, (ii) It is proportionalto the number of susceptible ticks, (iii) Constant number of rodents or the smallmammals are being bitten for the blood meals.Additionally, we make the following assumptions to model the dynamics ofCCHFV infection among ticks, livestock, and human: (i) Homogenous mixingamong all the interacting populations at all stages and that CCHFV infectiondoes not alter their movements, (ii) Livestock has more contact with adult ticksthan with other life-stages, (iii) Infection of
Hyalomma ticks does not affectthe birth or death rates of these ticks, (iv) Livestock will not die of CCHFVinfection [2] while CCHF-induced deaths in humans are taken into account [26].So we en route to construct a mechanistic ODE model including the aboveknowledge of CCHFV transmission in the human population and to analysethe burden of primary transmission routes undertaking a significant role of dis-semination of CCHFV primarily on the effective tick population to simplify themodelling effort. For the effective tick population, we consider an SEI dynam-ics as the tick remains infected for life [2], while for the livestock and humanpopulations we take an SEIR type of dynamics in to account.Considering the mentioned assumptions, we end up with the following modelsystem: For the tick population we have dT S dt = π T − σ T S L I L − σ T S T I T − µ T T S + (1 − ε ) π T T S (1) dT E dt = σ T S L I L + σ T S T I T − µ T T E − e T T E dT I dt = e T T E − µ T T I + επ T T I . We model the birth rate π T = σ T ω T exp (cid:16) − ν T T S + T E + T I Roω + Lω (cid:17) after following[49, 33], where T S , T E , T I are susceptible, exposed and infected ticks respec-tively, ν T is the strength of density-dependence in birth rate, ω and ω are theweightage of contributions of rodent and livestock populations on the growthof ticks, σ T is detachment rate of tick and ω T is mean no of eggs laid by an8dult female tick, Ro is the constant number of total rodents and L is the totalnumber of livestock. We incorporate the rodent-tick transmission cycle with-out explicitly deriving the equations of different stages of ticks. In order toinclude the transovarial transmission from adult female ticks to eggs, we in-troduce a parameter ε that measures the proportion of infected eggs laid byan infected female adult tick as mentioned in [49]. We have also opted for adensity-dependent mortality rate ( µ T ) according to [33]. The transmission pa-rameters of tick related model system are as follows: Livestock to tick infectiontransmission rate has been modelled according to [50, 47] as σ = p T γ T N T f S d T ,where p T is defined as transmission efficiency from livestock to tick, γ T is theduration of infective period, N T is the rate of average no of feeding ticks onlivestock, f S is defined as the fraction of blood meal per tick and d T is durationof attachment. Non-systemic transmission term σ is defined according to [48]as following: σ = [1 − exp {− ( n Ro + l Ro ) θ } ] σ Ro Ro , where n Ro is the fractionof nymphs against the total number of ticks feeding on the rodents, l Ro is thefraction of larvae against the total number of ticks feeding on the rodents, θ isthe transmission probability, σ Ro is encounter rate between the ticks and ro-dents. The domestic livestock population is described by the following systemof equations: dL S dt = π L − σ L S T I L − µ L L S (2) dL E dt = σ L S T I L − e L L E − µ L L E dL I dt = e L L E − α L L I − µ L L I dL R dt = α L L I − µ L L R . dH S dt = π H − σ H S T I H − σ H S L I H − µ H H S (3) dH E dt = σ H S T I H + σ H S L I H − e H H E − µ H H E dH I dt = e H H E − α H H I − µ H H I − δ H H I dH R dt = α H H I − µ H H R . Here L S , L E , L I and L R represent susceptible, exposed, infected and re-covered livestock and similarly H S , H E , H I and H R do the same for humanpopulation. We also have assumed a density-dependent birth rate ( π L ) for thelivestock and the linear growth rate ( π H ) for human. We model the acquisitionrate σ = [1 − exp {− ( N Ro κ N + L Ro κ L + A L κ A ) } ] σ L L after following [47, 33] toinclude the propagation of infection acquired during the transstadial stages. κ i is the transmission rate from larvae, nymphs and adult ticks, where i = L, N, A . N Ro is the ratio between the infectious nymphs and constant rodents density, L Ro is the ratio between the infectious larvae and constant rodents density, A L is the ratio between the infectious adult ticks and livestock density and κ i = 1 − (1 − T i ) dfeedi , with T i is the over all efficiency of transmission and d feed i is the feeding duration and σ L is encounter rate between the ticks andlivestock. σ is the transmission rate from an infected tick to a susceptible hu-man and σ is the transmission rate from an infected livestock to a susceptiblehuman. A full list of model parameters, variables and their biological meaningsare given in Tables 1, 2 and 3 as well as in Supplementary Information (SI).10 ariable Description of Model Variables (1), (2), (3), (17) TS Susceptible ticks TE Exposed ticks TI Infected ticks LS Susceptible livestocks LE Exposed livestocks LI Infected livestocks LR Recovered livestocks HS Susceptible humans HE Exposed humans HI Infected humans HR Recovered humans T Total tick population L Total livestock population Ro Total rodent population H Total human population σ σ σ σ σ σ ε proportion of the newborn infected ticks Table 1: Variables used in the model (1), (2), (3), (17). arameter Description Range References πL Birth term of livestock population [0 . , .
5] [51] πH Birth term of human population [0 . , .
5] [51] µL Death term of livestock population [1 / , / µH Death term of human population [1 / × , / ×
40] [51]1 /eT
Incubation period in tick [1 ,
3] [50, 52]1 /eL
Incubation period in livestock [3 ,
5] [50]1 /eH
Incubation period in human [1 ,
9] [52] σ . , .
04] [50] σ . , . σ . , . βH Effective contact rate: human to human [0 . , .
75] [54] ηH Proportion of quarantined [0 . , . λH Surveillance coverage 0 .
85 [54] τH Availability of isolation centres 0 .
65 [54] γH Enhanced personal hygiene [0 , . σH Rate of public enlightenment 0 .
90 [54]1 /αL
Recovery period of livestock [14 ,
21] [33]1 /αH
Recovery period of human population [15 ,
21] [55, 52] δH Disease induced death [0 . , .
8] [56, 52]
Table 2: Variables used in the model (1), (2), (3), (11), (17). arameter Description Range References ωT Mean no of eggs [4258 , νT Strength of density-dependence in birth rate 0 .
025 [48, 49] σT Detachment rate of tick 0 .
256 [50] ω . ω .
04 [49] pT Transmission efficiency: livestock to tick [0 . , .
33] [50] γT Duration of infective period [2 ,
6] [50] dT Duration of attachment [6 ,
8] [50] NT Rate of average no of feeding ticks on livestock [5 . , .
5] [50] µ .
28 [33] α . Table 3: Variables used in the model (1), (2), (3), (11), (17).
3. Basic Reproduction Number R In the course of epidemiology, the spread of epidemics often described by anepidemiological metric called as basic reproduction number ( R ). Elementarily,it characterises the expected number of secondary cases produced by a singleprimary case in a completely susceptible population. To illustrate the spread ofpathogens that infect multiple hosts, [57] incepted a formal mathematical frame-work named as Next Generation Matrix (NGM). The elements of NGM ( K ij )are the expected number of infected of type i produced by a single infectiousindividual of type j . Mathematically speaking, the matrix NGM depicts thelinearisation of the nonlinear model system when all the hosts are of susceptibletype. The largest eigenvalue of the NGM is defined as the basic reproductionnumber.For the tick-borne disease the definition of R is slightly different. In thiscase, R is described as number of new female parasites produced by a female13arasites without considering the density-dependent constraints governing thelife cycle of parasites [49]. First, we address the question, under which conditionsthe virus can spread in an initially susceptible population, if a single infectedindividual is introduced. Mathematically, we analyse the stability of the disease-free equilibrium E , which is a fixed point of the system (1), (2), (3). It is givenby: E = ( T ∗ S , , , L ∗ S , , , , H ∗ S , , ,
0) = (cid:16) π T µ T , , , π L µ L , , , , , π H µ H , , , , (cid:17) . Information regarding E , the mathematical properties of behaviour of themodel solution and the stability analysis are appended in the SupplementaryInformation (SI). If the disease-free equilibrium E is stable, the disease diesout before it can infect individuals, and it can spread over the population if E is instable. The stability condition for E can be expressed in terms of R ,where the outbreak condition is R > K = T ∗ S e T σ T ( e T + µ T )( µ T − επ T ) T ∗ S e L σ L ( α L + µ L )( e L + µ L ) L ∗ S e T σ L ( e T + µ T )( µ T − επ T ) . (4)The matrix K (4) can be biologically interpreted as K = T ick (cid:44) → T ick Livestock (cid:44) → T ickT ick (cid:44) → Livestock , (5)where X (cid:44) → Y means population X is infecting population Y .The basic reproduction number is defined as the spectral radius of the NGM(4). In our model we decompose the total basic reproduction number R intodifferent contributions. These are (i) infection from tick to tick via co-feedingand vertical transmission ( R T ) and (ii) infection from tick to livestock modelsystem R LA . For the whole model we get R = R T (cid:115)(cid:18) R T (cid:19) + R LA (6)= ⇒ (cid:20) R T + (cid:113) R T + 4 R LA (cid:21) R T = (cid:20) π T T e T ( e T + µ T ) σ επ T − µ T − ε ) π T − µ T (cid:21) (7)is the contribution of tick-to-tick transmission due to co-feeding and transovarialtransmission and R LA = (cid:20)(cid:18) π T L e L ( e L + µ L ) 1( α L + µ L ) σ µ L (cid:19) (cid:18) π L L e T ( e T + µ T ) σ επ T − µ T − ε ) π T − µ T (cid:19)(cid:21) (8) is the contribution of tick-to-livestock and livestock-to-tick transmission. Theequation (6) can also be represented as : R = T ick (cid:44) → T ick (cid:115)(cid:18)
T ick (cid:44) → T ick (cid:19) + ( Livestock (cid:44) → T ick )( T ick (cid:44) → Livestock ) , (9) If we exclude the transmission through co-feeding then the basic reproductionnumber is simply R w0 = √ R LA , where the index w stands for without co-feeding.The epidemic threshold is the critical point, where R = 1, R w0 can biologi-cally be described as R w0 = (cid:112) ( Livestock (cid:44) → T ick )( T ick (cid:44) → Livestock ), It fol-lows from (6) that at the critical point the contributions of both transmissionways simply add up, i.e. R CT + R CLA = 1. The terms in (7) can be interpretedas follows: e T e T + µ T is the probability that a tick will survive the incubation pe-riod and become infectious after co-feeding, − ε ) π T − µ T is the natural growthof a susceptible tick, σ επ T − µ T is the probability of CCHFV transmission from atick to another tick through non-systemic and transstadial in its lifetime, π T T is the ratio between the birth rate of a tick and the total number of ticks. Inthe same way the terms in (8) can be explained as before. e L e L + µ L is the theproportion of livestock that will survive the incubation period and become in-fectious, α L + µ L is the infectious lifespan of this livestock, σ µ L is the probabilityof CCHFV transmission from the livestock to a tick in the lifespan of infectiouslivestocks, σ επ T − µ T is the probability of CCHFV transmission from an infectioustick to livestock during the span of its natural growth, π T L is the ratio betweenthe birth rate of tick and the total number of livestock and π L L is the ratiobetween the birth rate of livestock and the total number of livestock. Finally,using the parameter values provided in 2, we obtain the following figures for the15asic reproduction number (6) R = 3 . , (10)where the contributions are for the co-feeding R T = 1 .
6, and for the tick-to-livestock and livestock-to-tick infection R LA = 7 .
2. The chosen parametersare the minima of the respective parameter ranges. When we perform thesame calculations with the assumed maximum values of the parameters, we get R T = 2 . R LA = 10 .
75 and R = 4 . CCHFV is a viral zoonosis with cases of human-to-human transmission [60]and case/fatality ratios ranging between 5% to 80% [26]. To take account ofthe nosocomial spread of CCHFV and cases of human-to-human transmittal,we include another transmission route as human-human transmission ( σ ) [61]in the model as depicted in Figure 3. The description of σ is included in SI. ⇡ T
So, our model equation system described in (3) modifies into the following:16 H S dt = π H − σ H S T I H − σ H S L I H − σ H S H I H − µ H H S (11) dH E dt = σ H S T I H + σ H S L I H + σ H S H I H − e H H E − µ H H E dH I dt = e H H E − α H H I − µ H H I − δ H H I dH R dt = α H H I − µ H H R . This system has a next generation matrix that can be simplified to K = T ∗ S e T σ T ( e T + µ T ) µ T T ∗ S e L σ L ( α L + µ L )( e L + µ L ) L ∗ S e T σ L ( e T + µ T ) µ T H ∗ S e T σ L ( e T + µ T ) µ T H ∗ S e L σ H ( α L + µ L )( e L + µ L ) H ∗ S e H σ H ( α H + δ H + µ H )( e H + µ H ) (12)with spectral radius R = max [ R H , R LA ] (13)where R H = (cid:20) π H H σ µ H e H ( e H + µ H ) 1( α H + δ H + µ H ) (cid:21) (14)The matrix K (12) can be biologically interpreted as K = T ick (cid:44) → T ick Livestock (cid:44) → T ick T ick (cid:44) → Livestock
T ick (cid:44) → Human Livestock (cid:44) → Human Human (cid:44) → Human (15)
According to [15, 62, 45], many of the reported cases of CCHFV are dueto the bites by adult ticks. As reported in [15],
Hyalomma are ”hunting” ticksand they can chase up to 400 m to find their hosts (including humans). Asurvey conducted in Turkey reveals that among all reported cases, 68 .
9% had ahistory of tick-bites or the contact with ticks, while only 0 .
16% cases representednosocomial infections [63]. The authors in [64] mention that humans might alsobe infected due to occupational exposure to bites by infected ticks or crushing17nfected ticks with bare hands. The study in [65] reported a large number ofpatients who tested positive for CCHF due to potential exposure via tick bitesalong with asymptomatic cases of CCHF in Tajikistan. After following the edictof WHO, [66] it is often possible to reduce or to curtail the risk of animal-to-human transmission in the countries with better health care facilities, availabletechniques and hygiene practices in slaughtering, meat handling, quality controland the widespread awareness of the perils of CCHFV transmission, whereas forthe countries lacking such resources this can be a daunting task to follow [67]. Inorder to mimic CCHF transmission under ideal hygiene conditions (slaughteringand meat handling), we consider only the subsystem related to the humans andthe ticks of the model system while ignoring the livestock-to-human transmissionpath (1), (2), (11).We obtain the following ODE system: dT S dt = π T − σ T S T I T − µ T T S (16) dT E dt = σ T S T I T − µ T T E − e T T E dT I dt = e T T E − µ T T I .dH S dt = π H − σ H S T I H − σ H S H I H − µ H H S (17) dH E dt = σ H S T I H + σ H S H I H − e H H E − µ H H E dH I dt = e H H E − α H H I − µ H H I − δ H H I dH R dt = α H H I − µ H H R . Next generation matrix ( K T H ) associated with (16), (17) is given by K T H = T ∗ S e T σ T ( e T + µ T ) µ T T ∗ S σ T µ T H ∗ S e T σ H ( e T + µ T ) µ T H ∗ S σ Hµ T H ∗ S e H σ H ( α H + δ H + µ H )( e H + µ H ) H ∗ S σ H ( α H + δ H + µ H ) (18)18 T H = max [ R H , R T ] (19)When we include the whole model but exclude the livestock to humans transmis-sion then we can have the basic reproduction number of the decoupled system as R T H = max [ R H , R LA ]. Once again following ([68]), we replace the host-specifictransmission rate ( σ → ζσ , σ → ζσ ) and calculate the value of R H where ζ ∈ [0 , R H becomes less than one when ζ ≈ . .
4. Dynamics of the model
We carry out a systematic examination to understand the long-term diseasedynamics first in the model systems (1), (2), (11) and in that of section 3.2using the parameters given in Table 2 and Table 3. Figure 4 shows the infec-tion dynamics incorporating the nosocomial spread and demonstrates the modelsystem in section 3.2 without the transmission routes from livestock to human.19 .10.20.30.4 0 25 50 75
Time P r e v a l an c e Time P r e v a l an c e Time P r e v a l an c e Time P r e v a l an c e Time P r e v a l an c e T I L I H I Figure 4: Simulated infection dynamics of multi-vectors model what includes the nosocomialspread of CCHF. CCHFV prevalence in the effective tick population, livestock and humanpopulations while considering in this instance both infectious and removed host populationsat the equilibrium point according to [33]. CCHFV prevalence in the effective tick populationand human populations without considering the livestock to human transmission path asdescribed in section 3.2
To demonstrate the infection profiles of ticks ( T I ), livestock ( L I ) and humans( H I ) in our model (1), (2), (11) and that of section 3.2, the initial conditionsare mentioned in the Table 4. To represent our simulated data, we followedthe modelling hypothesis as mentioned in [33]. According to the the authors in[33], simulated proportion of the interacting populations that were infected atleast once are calculated as the summation of infected and recovered or removedparts of the respective populations.Few interesting things are observed in this simulation experiment. TheCCHFV prevalence in the ticks do not show variations with time and it sat-urates, and the time average of the simulated prevalence in the ticks saturatesaround 40%. Similarly, the simulated prevalence in the livestock and human20opulations show fluctuations. Simulated prevalence in livestock shows thehighest prevalence around 62% (bottom panel) and slowly it decreases. Wecan claim that the prevalence in the livestock strongly depends on the ticksfeeding on the host. Simulated prevalence in humans in both cases (Figure 4middle panel) reveals the importance of the dissemination of CCHFV from live-stock to humans. According to the modelling experiment, when we include theCCHFV transmission from the livestock to humans, the simulated prevalence ofCCHFV is around twice the same of the simulated prevalence of CCHFV with-out the inclusion of the disease transmission from livestock to humans. Thispossibly shows the need for the proper care in handling of the infected livestockin certain geographical locations. Variable Initial Value TS TE TI LS LE LI LR HS HE HI HR Table 4: Initial values for the simulations.
5. Persistence-extinction boundary of CCHF
After drawing the curve described by R LA = 1 in (8), we can observe fromthe Figure 5, the required combinations of expected livestock densities that willlead CCHF to persist and those that are not.21 LA >1R LA <1 Livestock density A du l t T i ck d e n s i t y Figure 5: Relationship between tick density and livestock density on the predicted area ofCCHF persistence.
The curve for R LA = 1 illustrates the possible expected cut-off point forCCHFV to persist. Above this curve, CCHFV will persist, while it will die outbelow the curve.
6. Control Strategies
We use our model to analyse different control measures that can be employedby policy makers to decrease the number of human cases and the duration ofoutbreak situations. With the presented multi-host model, the exploration ofall possible control strategies is difficult to undertake. This leaves us with thechoice of aiming at particular host types only, such as vectors control, socialdistancing among humans, vaccinating livestock species etc. A new epidemi-ological metric named as
Target reproduction number ( T S ) is characterised toquantify the control measurements for infectious diseases with multiple hosttypes. Therefore, in this situation the Target reproduction number ( T S ) is moreuseful compared to conventional R [69]. This metric can be applied to studyvarious control measures, when targeting subset of different types of hosts. Let22s denote K (12) as following for convenience. K = K K K K K K (20)There are several options, through which we can effort to curb the bite ofCCHFV-infected ticks. Keeping the same notations as in [70], the target re-production number T S with respect to the target set S is defined as T S = ρ (cid:16) K S ( I − K + K S ) − (cid:17) (21)where, K S is the target matrix and defined as in [70] i.e. [ K S ] ij = K ij if( i, j ) ∈ S and 0, otherwise. I is the identity matrix and ρ is the spectral radiusof the matrix. Different disease control strategies are described below: Livestock Sanitation:
The usage of acaricides is a common technique to lowerthe tick burden on the livestock. Then the target set is S = { (1 , , (2 , , (3 , } ,where the code types represent the index pairs in (20). The type reproductionnumber targeting the host type 1 after employing (21) is given by: ρ K K − K K = (cid:114) K K − K (22)provided K < Human Sanitation & Isolation:
It is always advisable to wear proper cloth-ing, while walking in the grazing field or to take precautionary measures whenslaughtering livestock as well as during taking care of CCHFV-affected or -suspect patients. Here the target set is S = { (3 , , (3 , , (3 , } . Target re-production number T S with respect to S (i.e., the type reproduction numbertargeting the host type 2) is ρ − K K − − K K K − (cid:18) K K K − (cid:19) − K K K − (cid:18) K K K − (cid:19) − K K K − (cid:18) K K K − (cid:19) + K K K K − K (23) K . Combined Control:
If we combine both the control options then our targetset is S = { (1 , , (2 , , (3 , , (3 , , (3 , } . Target reproduction number T S with respect to S is ρ K K − K K − K K K = max { K , (cid:114) K K − K } (24) Isolation:
It is difficult to prevent or control the CCHFV infection cycle inlivestock and ticks, as the tick–animal–tick cycle usually goes unnoticed, andCCHFV infection in livestock is not evident due to the lack of clinical signs ofinfection. Moreover, the abundance of tick vectors is widespread and large innumbers, which requires an efficient tick control strategy. This may be possiblemainly in structured livestock farms. In those farms, where tick control maynot be possible due to economic constraints [31, 71], only isolation could be arealistic option. In this situation the target set is S = { (3 , } . ρ K (cid:18) K (cid:16) K K K − − K (cid:17) ( K − (cid:16) K K k − +1 (cid:17) − k k − (cid:19) − (cid:16) K K K − − K (cid:17) K K K K − +1 K = K (25)It is interesting to notice from the mathematical perspective that the effortsrequired to eradicate the disease are same for both Human Sanitation & Isola-tion and only for
Isolation . This can be attributed to the fact that the lattercase is a subset of the former control method.A compelling choice to reduce the potential risk of CCHFV in the livestockis to keep also chickens as they pick the ticks that is responsible for the trans-mission of CCHFV [72].
7. Sensitivity Analysis
In this section we carry out a sensitivity analysis of the model parameters tothe model output to deduce the important parameters that may help to control24he CCHF infection. It can be defined as the treatise of how uncertainty in theoutput of a mathematical model can correspond to different sources of uncer-tainty in the model input parameters [73]. It is a technique that systemicallyvaries the model input parameters and thus helps to determine their effects onthe model output.
Given the large number of model parameters, it is instructive to obtain thosemodel parameters that have the greatest influence on CCHF transmission. Wetherefore perform the sensitivity analysis through computing the Partial RankCorrelation Coefficients (PRCC) with 1000 simulations per run for each of themodel input parameter values sampled by the Latin Hypercube Sampling (LHS)scheme. This method has an assumption that there is a monotonic relationshipbetween the model input parameters and the model outputs. Here, we considerthe cumulative human cases of CCHF occurring during a simulation experimentas the model output of interest without the human-to-human spread. Thisapproach has the advantage that it captures the effects of model parameters onboth, the persistence of CCHF and the overall impact of CCHF outbreaks overtime. The sign of the PRCC values depicts the qualitative relationship betweenthe model input parameters and the model output of interests. A positive PRCCvalues means that while the corresponding model input parameters increases,the model output will also increase and on the other hand, a negative PRCCvalue suggests a negative correlation between the model in- and output [74].Values near zero indicate little effect on the model output.25 π T σ σ µ T σ σ σ Figure 6: PRCC Analysis
We can observe in Figure 6 that the mortality of the infected ticks ( µ T )shows a strong negative correlations with the cumulative incidences of CCHF inhumans, whereas the effective transmission between tick and livestock ( σ , σ ),effective transmission amongst the ticks through co-feeding ( σ ), the ticks birthrate ( π T ), the effective transmission between ticks and humans ( σ ) and effec-tive contact rate between livestock and humans ( σ ) show the strong positivecorrelations with the model output.Therefore, after using the results of sensitivity analysis we can concludethat the parameters with the strongest influence on the cumulative incidencesof CCHF in humans are µ T , π T and σ i , where ( i = 1 , , , , π T and σ i , where( i = 1 , , , ,
5) and decrease with µ T . To perform the sensitivity analysis weuse the sensitivity [75] package and for the LHS scheme we utilise the lhs [76]package in R [77]. 26 .2. NGM Sensitivity Analysis While sensitivity analysis of the model parameters gives us insights into thedynamics of the model, we can also measure the impact of parameters on R directly. Therefore, we compute the sensitivity and elasticity of NGM directly.Sensitivities and elasticities are measures of how infinitesimal changes in indi-vidual entries of a stage-structured population matrix will affect the populationand the quantification of projection results on the parameters. After noticing R (13) as a function of K [ X, Y ] (5), we denote S X,Y = ∂R ∂ K [ X, Y ] (26)as the sensitivity of R and T X,Y = K [ X, Y ] ∂ [ln R ] ∂ K [ X, Y ] (27)as the elasticity of R .Following [78], we perform sensitivity and elasticity analyses of (5) in R [77]using the package popbio [79] which is an R version of the Matlab code for theanalysis of matrix population models illustrated in [80].27 .290.9120.003 1.310.0610.008 0.5440.9720.013 H u m a nL i ves t o ck T i ck H u m a n L i ves t o ck T i ck Sensitivity Matrix H u m a nL i ves t o ck T i ck H u m a n L i ves t o ck T i ck Elasticity Matrix
Figure 7: (a) Sensitivity and (b) elasticity matrices for (5) .From Figure 7, it is noticeable that the value of R (13) is sensitive to thechanges in K , K , K and K of the elements from the matrix K (5). Thesecorrespond to the numbers of CCHFV-infected ticks attached to an infectedlivestock animal and the numbers of infected livestock animals infested by aninfected tick, followed by the number of infected humans bitten by an infectedtick and the number of infected humans produced by a single infected livestockanimal. It is also interesting to note that the number of infected ticks producedby a single infected tick through co-feeding ( K ) is also a sensitive parameter28n the model.Elasticities are actually proportional sensitivities ([81]) which measure theproportional change in R (13), given an infinitesimal one-at-a-time proportionalchange in the elements of the matrix K (5) with the assumption that K is growingor decreasing at a constant rate ([80]). Figure 7 shows the elasticity of R withrespect to the matrix elements K [ X, Y ]. The elasticities of the matrix elements K , K , K and K adds up–to approximately 90 . K [ X, Y ] are assumed to be linear [80]. Theinteraction between the infected tick and livestock are the prime factor drivingthe CCHF cycle.
8. Model Fitting
Mathematical models of disease dynamics and control have ample applica-tions: to understand the hidden functioning of a mechanism, to simulate ex-periments prior to perform them etc. Some of the associated parameters canbe found by conducting experiments or in the literature. However, for our pro-posed model, we lack the values and the distributions of different parameters.To validate the robustness of our ODE model (16), (17), we have fitted it to theactual CCHFV incidence data from six different countries. To perform this datafitting process, we have used the MATLAB ® [82] differential equation solver ode45 to approximate the solution for a trial set of parameter values with thefixed initial condition. We use Matlab functions fminsearch and lsqcurvefit .Fitting (16), (17) to real incidence data is important for modelling, as well asto have certain basic parameters, around which we can vary and run simulationsto explore various disease spread scenarios. The numerical simulation of humanCCHFV cases in different countries is shown in Figure 8. The increased aware-29ess towards the perils of CCHFV may have helped to decrease the cases forcases in Bulgaria, Iran and Kosovo, but in other countries, it appears that thisis not the case. Moreover, our fitted model simulations (Figure 8a, 8d and 8e)demonstrate that, given the current trend of the CCHFV cases in Afghanistan,Pakistan and Turkey, the number of human CCHFV cases will keep on increas-ing in future. Therefore, if no further effective prevention and control measures SimulationData (a) Afghanistan
SimulationData (b) Bulgaria
SimulationData (c) Kosovo
SimulationData (d) Turkey
SimulationData (e) Pakistan
SimulationData (f) IranFigure 8: The comparison between the reported human CCHFV cases in Afghanistan, Bul-garia, Kosovo, Turkey, Pakistan and Iran and the simulation of H I ( t ) from the model. Datafrom [14, 34, 31, 35, 83, 84, 85, 86, 87, 88, 89, 90] .are taken, the disease will not vanish. Visualisations of the fitted parametersare included in the Supplementary Information (SI).
9. Multidimensional Scaling Analysis
A central question is: How much do the found parameters differ for thecountries of concern? In order to find an answer, we endeavour to find thecosine similarity index amongst the fitted transmission coefficients to inquireabout the circulation of CCHFV transmission. Cosine similarity index is a gauge30f similarity between two non-zero vectors that measures the cosine of the anglebetween them. Afterwards, we employ multidimensional scaling to visualisethe level of similarity or dissimilarity of the fitted transmission parameters ofconcerned countries. We then interpret the findings about the pairwise cosinesimilarity index among the set of countries of consideration mapped into anabstract Cartesian space. It yields a useful tool to quantify, how similar infectionprofiles of different countries will be in terms of transmission parameters. FromFigure 9a it is evident that the disease transmission parameters are not equal.We can clearly observe that Afghanistan is the most affected country and hasthe highest disease transmission coefficient (Figure 9a). Afghanistan, Pakistan,Iran and Turkey are closer to each other as compared to the Balkan countriesBulgaria and Kosovo. P a k i s t an B u l ga r i a K o s o v o I r an T u r k e y A f ghan i s t an PakistanBulgariaKosovoIranTurkeyAfghanistan (a)
BulgariaBulgariaBulgariaBulgariaBulgariaBulgariaKosovoKosovoKosovoKosovoKosovoKosovoIranIranIranIranIranIranTurkeyTurkeyTurkeyTurkeyTurkeyTurkey AfghanistanAfghanistanAfghanistanAfghanistanAfghanistanAfghanistanPakistanPakistanPakistanPakistanPakistanPakistan −0.20.00.20.4 −0.4 −0.2 0.0 0.2
Co−ordinate1 C o − o r d i n a t e2 (b)Figure 9: Differences among the parameter sets of the considered countries. (a) Cosine simi-larity of the distance matrix (b) Spatial embedding of distance matrix. We are also interested to learn about the infection profiles of different coun-tries of concern while quantifying the burden of CCHFV dissemination by dis-tinct transmission routes. With the above said purpose, we employ multidimen-sional scaling to infer about the high-dimensional parameter space of the fitted31ransmission parameters. Figure 9b depicts a 2 dimensional spatial embeddingreflects the cosine distances of the parameters. It is clear that infection profilesof South Asian countries differs significantly from the Balkan and Middle East-ern countries. Perhaps this information might be helpful to policy makers toadapt CCHFV control measures.
10. Discussion & Conclusion
In recent years, a surge in CCHF cases has been observed, with an expansionbeyond its historical spatial range [91, 92]. Several factors possibly influence thegeographic expansion of CCHFV, such as environmental change and movementof hosts carrying
Hyalomma ticks to new geographical areas. In past, studies ontick-borne diseases e.g. Lyme disease [93], Tick-borne encephalitis (TBE) [94]etc. have been conducted, however, limited studies have been reported on math-ematical emphasise on the CCHFV [45, 46, 47, 33], as to our knowledge. In ourstudy, we construct CCHF transmission dynamics models (deterministic ODEmodels), which include the interactions amongst the
Hyalomma ticks, livestocksand human. We further extend our basic multi-vectors model by including thenosocomial spread of CCHF to analyse the effects of human-human transmissionon the disease dynamics.We analyse a new mathematical model which includes multiple transmis-sion avenues of CCHFV and compare it with the model that only incorporatesthe transmission of the CCHFV virus through direct contact with livestock andticks. Our model shows the importance of including of CCHFV transmissionthrough co-feeding and its sustainability in tick population. Co-feeding escalatesthe value of the basic reproduction number R and (6) quantitatively depictsthe increased value. With the assumed parameter list, our model predicts thatthe reduction of 18% of the contact rate between the ticks and the livestock canreduce the value of the basic reproduction number. When we consider only thetick-human model in Section 3.2, we observe a reduction of 37% in the contactrates which can help in reducing the value of the basic reproduction below 1.32imulations show that livestock has a significant role in disease transmissioncompare to tick-human model in the multi-vectors model. There is an increaseof approximately 65% in human CCHF cases due to contact with infected ani-mal blood etc. We propose that these additional pathways do not only increasethe basic reproductive number of CCHF, along with influence in the infectionprofiles of the multi-vectors system, but have also a dominant role in CCHFcontrol measures. Computation of R gives us the necessary tool to investi-gate different strategies to control the spread of vectors-borne diseases. Resultsfrom our simulations suggest the importance of the birth rate into the suscep-tible adult tick population in the disease dynamics and hence the influence ofthe rodent density implicitly. Linear growth in the tick population is reflectedin the basic reproduction number (both in R LA and R T ) as it shows a linearrelationship Freshly recruited livestock provides the necessary number of sus-ceptible livestock which increases the value of the basic reproduction number.We also explore the influence of the effective transmission amongst ticks on thebasic reproduction number. We observe a linear trend among σ , R LA and R T .This may show that co-feeding of ticks alone may enable CCHFV transmissionand increase the risk of transmission to humans substantially. The transmis-sion rate of CCHFV from the tick to livestock is an important parameter andthe increase in effective contact between questing adult ticks and the livestockspecies increases the basic reproduction number in a nonlinear way.Our mathematical model is novel in the sense that it incorporates multipletransmission routes. Some of the results are in accordance with the findingsof previous studies. For example, the analytical expression of R in (3) is sim-ilar to the one in [45] including the stability conditions. Moreover the basicreproductive number for CCHF increased by the factor mention in (6) throughco-feeding, the threshold quantities are comparable in [45]. The numerical ap-proximations of R and in [50] are comparable. The magnitude of the fittedparameters are in accord with previous findings [46, 50]. Simulated CCHFVprevalence in the tick and the livestock populations are of similar magnitudethrough our static model is of [33] without the influence of meteorological fac-33ors.Some authors [47, 50, 33] perform also a sensitivity analysis by analysing theeffects of parameter values on R , but our study is different, as we analyse thesensitivity on another important epidemiological quantity, i.e. the total numberof infected humans. Furthermore, sensitivity analysis of this quantity has notbeen examined elsewhere. Similar to [47, 33], our findings show that host den-sity, duration of infection and the immune responses are sensitive parameters.While CCHFV has been studied in [45] with livestock as the primary host,the systematic exploration of the model parameters and the mathematical il-lustrations of different control measures have not yet been fully explored. Forthe tick-borne diseases, the use of acaricides is the primary treatment and itmainly target the tick population, but in some poor regions, this may not befeasible. However, we should bear in mind that the profuse usage of acaricidesmay have a detrimental effect on the environment. In [45], the authors explorethis option. However, alternatives to using acaricides have been proposed, e.g.keeping chickens together with other livestock, because chickens eat ticks andmay therefore reduce the risk of exposure to CCHFV [72].We also methodically explore all possible ways to curb CCHF cases in hu-mans. We find that the mechanism of CCHFV dissemination varies in differentendemic countries. Our results show that human sanitation and isolation areeffective ways to reduce the CCHF cases in humans along with the acaricidetreatment as mentioned in [95]. Spatially embedded multidimensional scalingalong with the cosine similarity index amongst the transmission parametersgive us the clue that, the burden of CCHFV transmission differs from countryto country. However, the control mechanisms need to be adapted to the specificsituation in a country. The potential effects of measures can first be simulatedusing our model and any measures adapted accordingly, if the outcome in themodel warrants this.Just like other modelling endeavours [45, 46] on CCHF, our model has sev-eral limitations. Our model, like many others is based on assumption, whereknowledge and parameters were missing. Variables were parametrised with val-34es from the literature, which may be accurate or not, generally applicableor not. Therefore, the simulations conducted with our model are only meantfor demonstration purposes. We recommend to parametrise the model for thespecific situation, if it is used to plan or evaluate control measures.Future studies with this model should include the proper investigation ofthe data related to CCHF and systematic explorations of the parameter spaceto find the necessary paths to reduce the disease prevalence effectively. Forsimplicity, we have not included transovarial CCHFV tranmission [52]. Otherinvestigators [96] observe seasonality in human incidence and a dependence onambient temperatures. These factors are not included in our approach. Ideally,our model may encompass such a barrier, if the effect of the seasonality and thedependence of environmental factors are included when transmission dynamicsare modelled. The movement of animals and the migration of humans arealso not included in this study, although these may be important variables.According to [31], even in urban areas of Pakistan, the risk of transmissionis higher during the time of Eid-ul-Azha, when Muslims slaughter livestockanimals. Periodic transmission risks may be included in our model, however, ifappropriate.Despite the limitations of our model, the analytical expression of R and themathematically sound exploration of control strategies may make it relevant inthe fields of epidemiology and public health. Our work highlights the potentialcauses of CCHF spread. The insights derived can pioneer the development ofdata-driven control measures modelling with scenarios and parameter valuesthat are more realistic and adapted to a specific country or region. We expectthat our work on CCHF spread and control measures may help to collect thenecessary data related to CCHF and to further developing this and similarmathematical models and analyses. 35 eferences [1] J. P. Messina, D. M. Pigott, N. Golding, K. A. Duda, J. S. Brownstein,D. J. Weiss, H. Gibson, T. P. Robinson, M. Gilbert, G. R. William Wint,P. A. Nuttall, P. W. Gething, M. F. Myers, D. B. George, S. I. Hay, Theglobal distribution of Crimean-Congo hemorrhagic fever, Transactions ofThe Royal Society of Tropical Medicine and Hygiene 109 (8) (2015) 503–513.[2] A. Gargili, A. Estrada-Pe˜na, J. R. Spengler, A. Lukashev, P. A. Nuttall,D. A. Bente, The role of ticks in the maintenance and transmission ofcrimean-congo hemorrhagic fever virus: A review of published field andlaboratory studies, Antiviral Research 144 (2017) 93–119.[3] M. Chumakov, A new tick-borne virus disease—Crimean hemorrhagic fever,Simferopol, Moscow: Izd Otd Primorskoi Armii, 1945.[4] J. Woodall, M. Williams, D. Simpson, P. Ardoin, M. Lule, R. West, Thecongo group of agents, Rep E Afr Virus Res Inst (1963-1964) 14 (1965)34–36.[5] S. Chinikar, S. Ghiasi, R. Hewson, M. Moradi, A. Haeri, Crimean-congohemorrhagic fever in iran and neighboring countries, Journal of ClinicalVirology 47 (2) (2010) 110 – 114.[6] International committee on taxonomy of viruses., https://talk.ictvonline.org/taxonomy/ (2018).[7] J. R. Spengler, A. Estrada-Pe˜na, Host preferences support the prominentrole of hyalomma ticks in the ecology of crimean-congo hemorrhagic fever,PLOS Neglected Tropical Diseases 12 (2) (2018) 1–17.[8] T. W. O. for Animal Health (OIE), The world organisation for animalhealth (oie).URL [15] D. A. Bente, N. L. Forrester, D. M. Watts, A. J. McAuley, C. A. White-house, M. Bray, Crimean-congo hemorrhagic fever: History, epidemiology,pathogenesis, clinical syndrome and genetic diversity, Antiviral Research100 (1) (2013) 159 – 189.[16] H. Naderi, F. Sheybani, A. Bojdi, N. Khosravi, I. Mostafavi, Fatal nosoco-mial spread of crimean-congo hemorrhagic fever with very short incubation37eriod, The American Journal of Tropical Medicine and Hygiene 88 (3)(2013) 469–471.[17] P. D. Yadav, D. Y. Patil, A. M. Shete, P. Kokate, P. Goyal, S. Jadhav,S. Sinha, D. Zawar, S. K. Sharma, A. Kapil, D. K. Sharma, K. J. Upadhyay,D. T. Mourya, Nosocomial infection of cchf among health care workers inrajasthan, india, BMC Infectious Diseases 16 (1) (2016) 624.[18] N. Y. Pshenichnaya, S. A. Nenadskaya, Probable crimean-congo hemor-rhagic fever virus transmission occurred after aerosol-generating medicalprocedures in russia: nosocomial cluster, International Journal of Infec-tious Diseases 33 (2015) 120–122.[19] N. G. Conger, K. M. Paolino, E. C. Osborn, J. M. Rusnak, S. G¨unther,J. Pool, P. E. Rollin, P. F. Allan, J. Schmidt-Chanasit, T. Rieger, M. G.Kortepeter, Health care response to cchf in us soldier and nosocomial trans-mission to health care providers, germany, 2009, Emerging Infectious Dis-eases 21 (1) (2015) 23.[20] Y. G¨urb¨uz, I. Sencan, B. ¨Ozt¨urk, E. T¨ut¨unc¨u, A case of nosocomial trans-mission of crimean& [25] Y. Zhang, S. Shen, Y. Fang, J. Liu, Z. Su, J. Liang, Z. Zhang, Q. Wu,C. Wang, A. Abudurexiti, Z. Hu, Y. Zhang, F. Deng, Isolation, character-ization, and phylogenetic analysis of two new crimean-congo hemorrhagicfever virus strains from the northern region of xinjiang province, china,Virologica Sinica 33 (1) (2018) 74–86.[26] M. A. Sas, A. Vina-Rodriguez, M. Mertens, M. Eiden, P. Emmerich, S. C.Chaintoutis, A. Mirazimi, M. H. Groschup, A one-step multiplex real-timert-pcr for the universal detection of all currently known cchfv genotypes,Journal of Virological Methods 255 (2018) 38 – 43.[27] A. Estrada-Pe˜na, Z. Vatansever, A. Gargili, ¨O. Erg¨onul, The trend towardshabitat fragmentation is the key factor driving the spread of crimean-congohaemorrhagic fever, Epidemiology and Infection 138 (8) (2010) 1194–1203.[28] O. Causey, G. Kemp, M. Madbouly, T. David-West, Congo virus from do-mestic livestock, african hedgehog, and arthropods in nigeria, The Ameri-can journal of tropical medicine and hygiene 19 (5) (1970) 846—850.[29] A. J. Shepherd, R. Swanepoel, S. P. Shepherd, P. A. Leman, O. Mathee,Viraemic transmission of crimean-congo haemorrhagic fever virus to ticks,Epidemiology and infection 106 (2) (1991) 373–382.[30] J. R. Spengler, ´E. Bergeron, P. E. Rollin, Seroepidemiological studies ofcrimean-congo hemorrhagic fever virus in domestic and wild animals, PLoSneglected tropical diseases 10 (1) (2016) e0004210–e0004210.[31] M. Atif, A. Saqib, R. Ikram, M. R. Sarwar, S. Scahill, The reasons whypakistan might be at high risk of crimean congo haemorrhagic fever epi-demic; a scoping review of the literature, Virology Journal 14 (1) (2017)63. 3932] I. Schuster, M. Mertens, S. Mrenoshki, C. Staubach, C. Mertens,F. Br¨uning, K. Wernike, S. Hechinger, K. Berxholi, D. Mitrov, M. H.Groschup, Sheep and goats as indicator animals for the circulation of cchfvin the environment, Experimental & applied acarology 68 (3) (2016) 337–346.[33] T. Hoch, E. Breton, Z. Vatansever, Dynamic Modeling of Crimean CongoHemorrhagic Fever Virus (CCHFV) Spread to Test Control Strategies,Journal of Medical Entomology 55 (5) (2018) 1124–1132.[34] L. Fajs, I. Humolli, A. Saksida, N. Knap, M. Jelovˇsek, M. Korva, I. De-dushaj, T. Avˇsiˇc, Prevalence of crimean-congo hemorrhagic fever virus inhealthy population, livestock and ticks in kosovo, PLOS ONE 9 (11) (2014)1–6.[35] WHO, Who.URL http://applications.emro.who.int/docs/epi/2018/Epi_Monitor_2018_11_26.pdf?ua=1 [36] A. Papa, H. C. Maltezou, S. Tsiodras, V. G. Dalla, T. Papadimitriou,I. Pierroutsakos, G. N. Kartalis, A. Antoniadis, A case of crimean-congohaemorrhagic fever in greece, june 2008, Eurosurveillance 13 (33).[37] I. Pascucci, M. D. Domenico, G. C. Dondona, A. D. Gennaro, A. Polci,A. C. Dondona, E. Mancuso, C. Camm`a, G. Savini, J. G. Cecere, F. Spina,F. Monaco, Assessing the role of migratory birds in the introduction of ticksand tick-borne pathogens from african countries: An italian experience,Ticks and Tick-borne Diseases 10 (6) (2019) 101272.[38] L. J. Jameson, J. M. Medlock, Results of hpa tick surveillance in greatbritain, Veterinary Record 165 (5) (2009) 154–154.[39] J. A. House, M. J. Turell, C. A. Mebis, Rift valley fever: Present statusand risk to the western hemisphere, Annals of the New York Academy ofSciences 653 (1) (1992) 233–242. 4040] J. R. Spengler, ´E. Bergeron, C. F. Spiropoulou, Crimean-congo hemor-rhagic fever and expansion from endemic regions, Current opinion in virol-ogy 34 (2019) 70–78.[41] H. Kampen, W. Poltz, K. Hartelt, R. W¨olfel, M. Faulde, Detection of aquesting hyalomma marginatummarginatum adult female (acari, ixodidae)in southern germany, Experimental and Applied Acarology 43 (3) (2007)227–231.[42] R. Oehme, M. Bestehorn, S. W¨olfel, L. Chitimia-Dobler, Hyalommamarginatum in t¨ubingen, germany, Systematic and Applied Acarology22 (1) (2017) 1–6.[43] K. M. Hansford, D. Carter, E. L. Gillingham, L. M. Hernandez-Triana,J. Chamberlain, B. Cull, L. McGinley, L. P. Phipps, J. M. Medlock,Hyalomma rufipes on an untraveled horse: Is this the first evidence ofhyalomma nymphs successfully moulting in the united kingdom?, Ticksand Tick-borne Diseases 10 (3) (2019) 704 – 708.[44] M. Okely, R. Anan, S. Gad-Allah, A. M. Samy, Mapping the environ-mental suitability of etiological agent and tick vectors of crimean-congohemorrhagic fever, Acta Tropica (2019) 105319.[45] J. Switkes, B. Nannyonga, J. Mugisha, J. Nakakawa, A mathematical modelfor crimean-congo haemorrhagic fever: tick-borne dynamics with conferredhost immunity, Journal of Biological Dynamics 10 (1) (2016) 59–70.[46] B. S. Cooper, Mathematical Modeling of Crimean-Congo HemorrhagicFever Transmission, Springer Netherlands, Dordrecht, 2007, Ch. 15, pp.187–203.[47] T. Hoch, E. Breton, M. Josse, A. Deniz, E. Guven, Z. Vatansever, Identi-fying main drivers and testing control strategies for cchfv spread, Experi-mental and Applied Acarology 68 (3) (2016) 347–359.4148] L. Bolzoni, R. Ros`a, F. Cagnacci, A. Rizzoli, Effect of deer density ontick infestation of rodents and the hazard of tick-borne encephalitis. ii:Population and infection models, International Journal for Parasitology42 (4) (2012) 373 – 381.[49] R. Ros`a, A. Pugliese, Effects of tick population dynamics and host densi-ties on the persistence of tick-borne infections, Mathematical Biosciences208 (1) (2007) 216 – 240.[50] A. Matser, N. Hartemink, H. Heesterbeek, A. Galvani, S. Davis, Elasticityanalysis in epidemiology: an application to tick-borne infections, EcologyLetters 12 (12) (2009) 1298–1305.[51] S. C. Mpeshe, H. Haario, J. M. Tchuenche, A mathematical model of riftvalley fever with human host, Acta Biotheoretica 59 (3) (2011) 231–250.[52] S. Shayan, M. Bokaean, M. R. Shahrivar, S. Chinikar, Crimean-CongoHemorrhagic Fever, Laboratory Medicine 46 (3) (2015) 180–189.[53] A. Kriesel, M. Meyer, G. Peterson, Mathematical modeling of tick-borneencephalitis in humans, Journal of Undergraduate Research at MinnesotaState University, Mankato 9 (2009) 9.[54] M. K. Mondal, M. Hanif, M. H. A. Biswas, A mathematical analysis forcontrolling the spread of nipah virus infection, International Journal ofModelling and Simulation 37 (3) (2017) 185–197.[55] A. Papa, S. Bino, A. Llagami, B. Brahimaj, E. Papadimitriou, V. Pavli-dou, E. Velo, G. Cahani, M. Hajdini, A. Pilaca, A. Harxhi, A. Antoniadis,Crimean-congo hemorrhagic fever in albania, 2001, European Journal ofClinical Microbiology and Infectious Diseases 21 (8) (2002) 603–606.[56] I. Schuster, M. Mertens, S. Mrenoshki, C. Staubach, C. Mertens,F. Br¨uning, K. Wernike, S. Hechinger, K. Berxholi, D. Mitrov, M. H.Groschup, Sheep and goats as indicator animals for the circulation of cchfv42n the environment, Experimental and Applied Acarology 68 (3) (2016)337–346.[57] O. Diekmann, J. A. P. Heesterbeek, J. A. J. Metz, On the definition andthe computation of the basic reproduction ratio r0 in models for infectiousdiseases in heterogeneous populations, Journal of Mathematical Biology28 (4) (1990) 365–382.[58] M. J. Keeling, P. Rohani, Modeling infectious diseases in humans and ani-mals, Princeton University Press, 2011.[59] P. van den Driessche, J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease trans-mission, Mathematical Biosciences 180 (1) (2002) 29 – 48.[60] ¨O. Erg¨on¨ul, Crimean-congo haemorrhagic fever, The Lancet Infectious Dis-eases 6 (4) (2006) 203–214.[61] A. R. Garrison, D. R. Smith, J. W. Golden, Animal models for crimean-congo hemorrhagic fever human disease, Viruses 11 (7) (2019) 590.[62] R. Vorou, Crimean-congo hemorrhagic fever in southeastern europe, Inter-national Journal of Infectious Diseases 13 (6) (2009) 659 – 662.[63] G. R. Yilmaz, T. Buzgan, H. Irmak, A. Safran, R. Uzun, M. A. Cevik,M. A. Torunoglu, The epidemiology of crimean-congo hemorrhagic feverin turkey, 2002& 2013;2007, International Journal of Infectious Diseases13 (3) (2009) 380–386.[64] D. T. Mourya, P. D. Yadav, Y. K. Gurav, P. G. Pardeshi, A. M. Shete,R. Jain, D. D. Raval, K. J. Upadhyay, D. Y. Patil, Crimean congo hem-orrhagic fever serosurvey in humans for identifying high-risk populationsand high-risk areas in the endemic state of gujarat, india, BMC InfectiousDiseases 19 (1) (2019) 104. 4365] B. Atkinson, J. Chamberlain, L. J. Jameson, C. H. Logue, J. Lewis, E. A.Belobrova, M. Valikhodzhaeva, M. Mullojonova, F. H. Tishkova, R. Hew-son, Identification and analysis of crimean-congo hemorrhagic fever virusfrom human sera in tajikistan, International Journal of Infectious Diseases17 (11) (2013) e1031 – e1037.[66] WHO, Who.URL [67] S. Aslam, M. S. Latif, M. Daud, Z. U. Rahman, B. Tabassum, M. S. Riaz,A. Khan, M. Tariq, T. Husnain, Crimean-congo hemorrhagic fever: Riskfactors and control measures for the infection abatement, Biomedical re-ports 4 (1) (2016) 15–20.[68] A. Nguyen, J. Mahaffy, N. K. Vaidya, Modeling transmission dynamics oflyme disease: Multiple vectors, seasonality, and vector mobility, InfectiousDisease Modelling 4 (2019) 28 – 43.[69] J. Heesterbeek, M. Roberts, The type-reproduction number t in models forinfectious disease control, Mathematical Biosciences 206 (1) (2007) 3 – 10.[70] Z. Shuai, J. A. P. Heesterbeek, P. van den Driessche, Extending the type re-production number to infectious disease control targeting contacts betweentypes, Journal of Mathematical Biology 67 (5) (2013) 1067–1082.[71] H. B. Baghi, M. Aghazadeh, Include crimean-congo haemorrhagic fevervirus prevention in pre-travel advice, Travel Medicine and Infectious Dis-ease 14 (6) (2016) 634 – 635.[72] K. K. Kasi, M. A. Sas, C. Sauter-Louis, F. von Arnim, J. M. Gethmann,A. Schulz, K. Wernike, M. H. Groschup, F. J. Conraths, Epidemiologicalinvestigations of crimean-congo haemorrhagic fever virus infection in sheepand goats in balochistan, pakistan, Ticks and Tick-borne Diseases 11 (2)(2020) 101324. 4473] B. Iooss, A. Saltelli, Introduction to Sensitivity Analysis, Springer Interna-tional Publishing, Cham, 2017, Ch. 26, pp. 1103–1122.[74] Z. Zi, Sensitivity analysis approaches applied to systems biology models,IET Systems Biology 5 (6) (2011) 336–346.[75] B. Iooss, A. Janon, G. Pujol, with contributions from Khalid Boumhaout,S. D. Veiga, T. Delage, J. Fruth, L. Gilquin, J. Guillaume, L. Le Gratiet,P. Lemaitre, B. L. Nelson, F. Monari, R. Oomen, O. Rakovec, B. Ramos,O. Roustant, E. Song, J. Staum, R. Sueur, T. Touati, F. Weber, sensitivity:Global Sensitivity Analysis of Model Outputs (2018).[76] R. Carnell, lhs: Latin Hypercube Samples (2019).[77] R Core Team, R: A Language and Environment for Statistical Computing,R Foundation for Statistical Computing, Vienna, Austria (2018).[78] G. Polo, M. B. Labruna, F. Ferreira, Basic reproduction number for thebrazilian spotted fever, Journal of Theoretical Biology 458 (2018) 119 –124.[79] C. J. Stubben, B. G. Milligan, Estimating and analyzing demographic mod-els using the popbio package in r, Journal of Statistical Software 22 (11).[80] H. Caswell, Matrix population models : Construction, Analysis, and Inter-pretation 255.[81] M. Lesnoff, P. Ezanno, H. Caswell, Sensitivity analysis in periodic matrixmodels: A postscript to caswell and trevisan, Mathematical and ComputerModelling 37 (9) (2003) 945 – 948.[82] MATLAB, version 9.6 (R2019a), The MathWorks Inc., Natick, Mas-sachusetts, 2019.[83] N. Hegde, Livestock development for sustainable livelihood of small farm-ers, Asian Journal of Research in Animal and Veterinary Sciences (2019)1–17. 4584] P. B. of Statistics, Pakistan bureau of statistics.URL [85] Food, A. O. of the United Nations, Food and agriculture organization ofthe united nations.URL [86] S. O. of Kosovo, Statistical office of kosovo.URL https://ask.rks-gov.net/media/3142/sok-fao-and-mafrd-2002-statistics-on-agriculture-in-kosovo-2001.pdf [87] U. F. A. Service, Usda foreign agricultural service.URL https://apps.fas.usda.gov/newgainapi/api/report/downloadreportbyfilename?filename=Livestock%20and%20Products%20Annual_Sofia_Bulgaria_7-30-2018.pdf [88] Food, A. O. of the United Nations, Food and agriculture organization ofthe united nations.URL [89] A. Kamalzadeh, M. Rajabbaigy, A. Kiasat, Livestock production systemsand trends in livestock industry in iran, J. Agric. Soc. Sci. 4 (2008) 1813–223504.[90] Food, A. O. of the United Nations, Food and agriculture organization ofthe united nations.URL