Ling Xue

A Network-Based Meta-Population Approach to Model Rift Valley Fever Epidemics

Rift Valley fever virus (RVFV) has been expanding its geographical distribution with important implications for both human and animal health. The emergence of Rift Valley fever (RVF) in the Middle East, and its continuing presence in many areas of Africa, has negatively impacted both medical and veterinary infrastructures and human morbidity, mortality, and economic endpoints. Furthermore, worldwide attention should be directed towards the broader infection dynamics of RVFV, because suitable host, vector and environmental conditions for additional epidemics likely exist on other continents; including Asia, Europe and the Americas. We propose a new compartmentalized model of RVF and the related ordinary differential equations to assess disease spread in both time and space; with the latter driven as a function of contact networks. Humans and livestock hosts and two species of vector mosquitoes are included in the model. The model is based on weighted contact networks, where nodes of the networks represent geographical regions and the weights represent the level of contact between regional pairings for each set of species. The inclusion of human, animal, and vector movements among regions is new to RVF modeling. The movement of the infected individuals is not only treated as a possibility, but also an actuality that can be incorporated into the model. We have tested, calibrated, and evaluated the model using data from the recent 2010 RVF outbreak in South Africa as a case study; mapping the epidemic spread within and among three South African provinces. An extensive set of simulation results shows the potential of the proposed approach for accurately modeling the RVF spreading process in additional regions of the world. The benefits of the proposed model are twofold: not only can the model differentiate the maximum number of infected individuals among different provinces, but also it can reproduce the different starting times of the outbreak in multiple locations. Finally, the exact value of the reproduction number is numerically computed and upper and lower bounds for the reproduction number are analytically derived in the case of homogeneous populations.

A hierarchical network approach for modeling Rift Valley fever epidemics with applications in North America

Rift Valley fever is a vector-borne zoonotic disease which causes high morbidity and mortality in livestock. In the event Rift Valley fever virus is introduced to the United States or other non-endemic areas, understanding the potential patterns of spread and the areas at risk based on disease vectors and hosts will be vital for developing mitigation strategies. Presented here is a general network-based mathematical model of Rift Valley fever. Given a lack of empirical data on disease vector species and their vector competence, this discrete time epidemic model uses stochastic parameters following several PERT distributions to model the dynamic interactions between hosts and likely North American mosquito vectors in dispersed geographic areas. Spatial effects and climate factors are also addressed in the model. The model is applied to a large directed asymmetric network of 3,621 nodes based on actual farms to examine a hypothetical introduction to some counties of Texas, an important ranching area in the United States of America. The nodes of the networks represent livestock farms, livestock markets, and feedlots, and the links represent cattle movements and mosquito diffusion between different nodes. Cattle and mosquito (Aedes and Culex) populations are treated with different contact networks to assess virus propagation. Rift Valley fever virus spread is assessed under various initial infection conditions (infected mosquito eggs, adults or cattle). A surprising trend is fewer initial infectious organisms result in a longer delay before a larger and more prolonged outbreak. The delay is likely caused by a lack of herd immunity while the infection expands geographically before becoming an epidemic involving many dispersed farms and animals almost simultaneously. Cattle movement between farms is a large driver of virus expansion, thus quarantines can be efficient mitigation strategy to prevent further geographic spread.

The network level reproduction number for infectious diseases with both vertical and horizontal transmission

A wide range of infectious diseases are both vertically and horizontally transmitted. Such diseases are spatially transmitted via multiple species in heterogeneous environments, typically described by complex meta-population models. The reproduction number, R0, is a critical metric predicting whether the disease can invade the meta-population system. This paper presents the reproduction number for a generic disease vertically and horizontally transmitted among multiple species in heterogeneous networks, where nodes are locations, and links reflect outgoing or incoming movement flows. The metapopulation model for vertically and horizontally transmitted diseases is gradually formulated from two species, two-node network models. We derived an explicit expression of R0, which is the spectral radius of a matrix reduced in size with respect to the original next generation matrix. The reproduction number is shown to be a function of vertical and horizontal transmission parameters, and the lower bound is the reproduction number for horizontal transmission. As an application, the reproduction number and its bounds for the Rift Valley fever zoonosis, where livestock, mosquitoes, and humans are the involved species are derived. By computing the reproduction number for different scenarios through numerical simulations, we found the reproduction number is affected by livestock movement rates only when parameters are heterogeneous across nodes. To summarize, our study contributes the reproduction number for vertically and horizontally transmitted diseases in heterogeneous networks. This explicit expression is easily adaptable to specific infectious diseases, affording insights into disease evolution.

Spatial-temporal distribution of dengue and climate characteristics for two clusters in Sri Lanka from 2012 to 2016

Dengue is a vector-borne disease causing high morbidity and mortality in tropical and subtropical countries. Urbanization, globalization, and lack of effective mosquito control have lead to dramatically increased frequency and magnitude of dengue epidemic in the past 40 years. The virus and the mosquito vectors keep expanding geographically in the tropical regions of the world. Using the hot spot analysis and the spatial-temporal clustering method, we investigated the spatial-temporal distribution of dengue in Sri Lanka from 2012 to 2016 to identify spatial-temporal clusters and elucidate the association of climatic factors with dengue incidence. We detected two important spatial-temporal clusters in Sri Lanka. Dengue incidences were predicted by combining historical dengue incidence data with climate data, and hot and cold spots were forecasted using the predicted dengue incidences to identify areas at high risks. Targeting the hot spots during outbreaks instead of all the regions can save resources and time for public health authorities. Our study helps better understand how climatic factors impact spatial and temporal spread of dengue virus. Hot spot prediction helps public health authorities forecast future high risk areas and direct control measures to minimize cost on health, time, and economy.

Two-sex mosquito model for the persistence of Wolbachia

ABSTRACT We develop and analyse an ordinary differential equation model to investigate the transmission dynamics of releasing Wolbachia-infected mosquitoes to establish an endemic infection in a population of wild uninfected mosquitoes. Wolbachia is a genus of endosymbiotic bacteria that can infect mosquitoes and reduce their ability to transmit some viral mosquito-transmitted diseases, including dengue fever, chikungunya, and Zika. Although the bacterium is transmitted vertically from infected mothers to their offspring, it can be difficult to establish an endemic infection in a wild mosquito population. Our transmission model for the adult and aquatic-stage mosquitoes takes into account Wolbachia-induced fitness change and cytoplasmic incompatibility. We show that, for a wide range of realistic parameter values, the basic reproduction number, , is less than one. Hence, the epidemic will die out if only a few Wolbachia-infected mosquitoes are introduced into the wild population. Even though the basic reproduction number is less than one, an endemic Wolbachia infection can be established if a sufficient number of infected mosquitoes are released. This threshold effect is created by a backward bifurcation with three coexisting equilibria: a stable zero-infection equilibrium, an intermediate-infection unstable endemic equilibrium, and a high-infection stable endemic equilibrium. We analyse the impact of reducing the wild mosquito population before introducing the infected mosquitoes and observed that the most effective approach to establish the infection in the wild is based on reducing mosquitoes in both the adult and aquatic stages.

A Multi-risk Model for Understanding the Spread of Chlamydia

Chlamydia trachomatis, CT, infection is the most frequently reported sexually transmitted infection in the United States. To better understand the recent increase in disease prevalence, and help guide in mitigation efforts, we created and analyzed a multi-risk model for the spread of chlamydia in the heterosexual community. The model incorporates the heterogeneous mixing between men and women with different number of partners and the parameters are defined to approximate the disease transmission in the 15–25 year-old New Orleans African American community. We use sensitivity analysis to assess the relative impact of different levels of screening interventions and behavior changes on the basic reproduction number. Our results quantify, and validate, the impact that reducing the probability of transmission per sexual contact, such as using prophylactic condoms, can have on CT prevalence.

Two Introductions of Lyme Disease into Connecticut: A Geospatial Analysis of Human Cases from 1984 to 2012

Lyme disease has become the most prevalent vector-borne disease in the United States and results in morbidity in humans, especially children. We used historical case distributions to explain vector-borne disease introductions and subsequent geographic expansion in the absence of disease vector data. We used geographic information system analysis of publicly available Connecticut Department of Public Health case data from 1984, 1985, and 1991 to 2012 for the 169 towns in Connecticut to identify the yearly clusters of Lyme disease cases. Our analysis identified the spatial and temporal origins of two separate introductions of Lyme disease into Connecticut and identified the subsequent direction and rate of spread. We defined both epidemic clusters of cases using significant long-term spatial autocorrelation. The incidence-weighted geographic mean analysis indicates a northern trend of geographic expansion for both epidemic clusters. In eastern Connecticut, as the epidemic progressed, the yearly shift in the geographic mean (rate of epidemic expansion) decreased each year until spatial equilibrium was reached in 2007. The equilibrium indicates a transition from epidemic Lyme disease spread to stable endemic transmission, and we associate this with a reduction in incidence. In western Connecticut, the parabolic distribution of the yearly geographic mean indicates that following the establishment of Lyme disease (1988) the epidemic quickly expanded northward and established equilibrium in 2009.

Modeling the Transmission of Wolbachia in Mosquitoes for Controlling Mosquito-Borne Diseases

We develop and analyze an ordinary differential equation model to assess the potential effectiveness of infecting mosquitoes with the Wolbachia bacteria to control the ongoing mosquito-borne epidemics, such as dengue fever, chikungunya, and Zika. Wolbachia is a natural parasitic microbe that stops the proliferation of the harmful viruses inside the mosquito and reduces disease transmission. It is difficult to sustain an infection of the maternal transmitted Wolbachia in a wild mosquito population because of the reduced fitness of the Wolbachia-infected mosquitoes and cytoplasmic incompatibility limiting maternal transmission. The infection will only persist if the fraction of the infected mosquitoes exceeds a minimum threshold. Our two-sex mosquito model captures the complex transmission-cycle by accounting for heterosexual transmission, multiple pregnant states for female mosquitoes, and the aquatic-life stage. We identify important dimensionless numbers and analyze the critical threshold condition for obtaining a sustained Wolbachia infection in the natural population. This threshold effect is characterized by a backward bifurcation with three coexisting equilibria of the system of differential equations: a stable disease-free equilibrium, an unstable intermediate-infection endemic equilibrium and a stable high-infection endemic equilibrium. We perform sensitivity analysis on epidemiological and environmental parameters to determine their relative importance to Wolbachia transmission and prevalence. We also compare the effectiveness of different integrated mitigation strategies and observe that the most efficient approach to establish the Wolbachia infection is to first reduce the natural mosquitoes and then release both infected males and pregnant females. The initial reduction of natural population could be accomplished by either residual spraying or ovitraps.

Modeling the Impact of Behavior Change on the Spread of Ebola

We create a compartmental mathematical model to analyze the role of behavior change in slowing the spread of the Ebola virus disease (EVD) in the 2014–2015 Western Africa epidemic. Our model incorporates behavior change, modeled as decreased contact rates between susceptible and infectious individuals, the prevention of traditional funerals, and/or increased access to medical facilities. We derived the basic reproductive number for the model, and approximated the parameter values for the spread of the EVD in Monrovia. We used sensitivity analysis to quantify the relative importance of the timing, and magnitude, of the population reducing their contact rates, avoiding the traditional burial practices, and having access to medical treatment facilities. We found that reducing the number of contacts made by infectious individuals in the general population is the most effective intervention method for mitigating an EVD epidemic. While healthcare interventions delayed the onset of the epidemic, healthcare alone is insufficient to stop the epidemic in the model.

Network-level reproduction number and extinction threshold for vector-borne diseases.

The basic reproduction number of deterministic models is an essential quantity to predict whether an epidemic will spread or not. Thresholds for disease extinction contribute crucial knowledge of disease control, elimination, and mitigation of infectious diseases. Relationships between basic reproduction numbers of two deterministic network-based ordinary differential equation vector-host models, and extinction thresholds of corresponding stochastic continuous-time Markov chain models are derived under some assumptions. Numerical simulation results for malaria and Rift Valley fever transmission on heterogeneous networks are in agreement with analytical results without any assumptions, reinforcing that the relationships may always exist and proposing a mathematical problem for proving existence of the relationships in general. Moreover, numerical simulations show that the basic reproduction number does not monotonically increase or decrease with the extinction threshold. Consistent trends of extinction probability observed through numerical simulations provide novel insights into mitigation strategies to increase the disease extinction probability. Research findings may improve understandings of thresholds for disease persistence in order to control vector-borne diseases.