Mathieu Andraud

Dynamic Epidemiological Models for Dengue Transmission: A Systematic Review of Structural Approaches

Dengue is a vector-borne disease recognized as the major arbovirose with four immunologically distant dengue serotypes coexisting in many endemic areas. Several mathematical models have been developed to understand the transmission dynamics of dengue, including the role of cross-reactive antibodies for the four different dengue serotypes. We aimed to review deterministic models of dengue transmission, in order to summarize the evolution of insights for, and provided by, such models, and to identify important characteristics for future model development. We identified relevant publications using PubMed and ISI Web of Knowledge, focusing on mathematical deterministic models of dengue transmission. Model assumptions were systematically extracted from each reviewed model structure, and were linked with their underlying epidemiological concepts. After defining common terms in vector-borne disease modelling, we generally categorised fourty-two published models of interest into single serotype and multiserotype models. The multi-serotype models assumed either vector-host or direct host-to-host transmission (ignoring the vector component). For each approach, we discussed the underlying structural and parameter assumptions, threshold behaviour and the projected impact of interventions. In view of the expected availability of dengue vaccines, modelling approaches will increasingly focus on the effectiveness and cost-effectiveness of vaccination options. For this purpose, the level of representation of the vector and host populations seems pivotal. Since vector-host transmission models would be required for projections of combined vaccination and vector control interventions, we advocate their use as most relevant to advice health policy in the future. The limited understanding of the factors which influence dengue transmission as well as limited data availability remain important concerns when applying dengue models to real-world decision problems.

Quantification of porcine circovirus type 2 (PCV-2) within-and between-pen transmission in pigs

PCV-2 within- and between-pen transmission was quantified by estimating the daily transmission rate beta and the basic reproduction ratio (R(0)) using a stochastic SEIR (Susceptible, Exposed, Infectious, Removed) model fitted on experimental data. Within-pen transmission was quantified by using four groups of eight SPF (specific pathogen-free) pigs (four infected and four susceptible pigs having direct contact). Between-pen transmission was studied in two groups of 16 SPF pigs (eight infected and eight susceptible pigs having indirect contact (10 cm distance)). Pigs were monitored twice a week (blood samples) and were tested for PCV-2 antibodies (ELISA test) and viral genome load in sera (real-time PCR). Transmission parameters beta(within) and beta(between) were estimated using a maximum likelihood method and the duration of infectiousness, to compute R(0), was estimated with a parametric survival model. Different assumptions were made to determine the end of infectiousness (seroconversion, seroconversion and decline in viral genome load, permanent infectiousness). R(0[within]) (8.9 (5.1-15.4)) was greater when the end of infectiousness was assumed to be related to both seroconversion and a decline of PCV-2 genome load in sera (average duration of infectiousness = 32 days) compared with only seroconversion as the indicator of recovery (R(0[within]) = 5.5 (3.3-9.0)). Whatever the assumption, between-pen R(0) (0.58 (0.23-1.47)) was always significantly lower than within-pen R(0). Only beta(within) was sensitive to the assumption on end of infectiousness and decreased with increasing duration of infectiousness. These results showed that PCV-2 transmission is influenced by contact structure that appears worth being taken into account in an epidemic model.

From the epidemiology of hepatitis E virus (HEV) within the swine reservoir to public health risk mitigation strategies: a comprehensive review

Hepatitis E virus (HEV) is the causative agent of hepatitis E in humans, an emerging zoonosis mainly transmitted via food in developed countries and for which domestic pigs are recognised as the main reservoir. It therefore appears important to understand the features and drivers of HEV infection dynamics on pig farms in order to implement HEV surveillance programmes and to assess and manage public health risks. The authors have reviewed the international scientific literature on the epidemiological characteristics of HEV in swine populations. Although prevalence estimates differed greatly from one study to another, all consistently reported high variability between farms, suggesting the existence of multifactorial conditions related to infection and within-farm transmission of the virus. Longitudinal studies and experimental trials have provided estimates of epidemiological parameters governing the transmission process (e.g. age at infection, transmission parameters, shedding period duration or lag time before the onset of an immune response). Farming practices, passive immunity and co-infection with immunosuppressive agents were identified as the main factors influencing HEV infection dynamics, but further investigations are needed to clarify the different HEV infection patterns observed in pig herds as well as HEV transmission between farms. Relevant surveillance programmes and control measures from farm to fork also have to be fostered to reduce the prevalence of contaminated pork products entering the food chain.

Dynamics of influenza A virus infections in permanently infected pig farms: evidence of recurrent infections, circulation of several swine influenza viruses and reassortment events

Concomitant infections by different influenza A virus subtypes within pig farms increase the risk of new reassortant virus emergence. The aims of this study were to characterize the epidemiology of recurrent swine influenza virus infections and identify their main determinants. A follow-up study was carried out in 3 selected farms known to be affected by repeated influenza infections. Three batches of pigs were followed within each farm from birth to slaughter through a representative sample of 40 piglets per batch. Piglets were monitored individually on a monthly basis for serology and clinical parameters. When a flu outbreak occurred, daily virological and clinical investigations were carried out for two weeks. Influenza outbreaks, confirmed by influenza A virus detection, were reported at least once in each batch. These outbreaks occurred at a constant age within farms and were correlated with an increased frequency of sneezing and coughing fits. H1N1 and H1N2 viruses from European enzootic subtypes and reassortants between viruses from these lineages were consecutively and sometimes simultaneously identified depending on the batch, suggesting virus co-circulations at the farm, batch and sometimes individual levels. The estimated reproduction ratio R of influenza outbreaks ranged between 2.5 [1.9-2.9] and 6.9 [4.1-10.5] according to the age at infection-time and serological status of infected piglets. Duration of shedding was influenced by the age at infection time, the serological status of the dam and mingling practices. An impaired humoral response was identified in piglets infected at a time when they still presented maternally-derived antibodies.

Living on three time scales: the dynamics of plasma cell and antibody populations illustrated for hepatitis a virus.

Understanding the mechanisms involved in long-term persistence of humoral immunity after natural infection or vaccination is challenging and crucial for further research in immunology, vaccine development as well as health policy. Long-lived plasma cells, which have recently been shown to reside in survival niches in the bone marrow, are instrumental in the process of immunity induction and persistence. We developed a mathematical model, assuming two antibody-secreting cell subpopulations (short- and long-lived plasma cells), to analyze the antibody kinetics after HAV-vaccination using data from two long-term follow-up studies. Model parameters were estimated through a hierarchical nonlinear mixed-effects model analysis. Long-term individual predictions were derived from the individual empirical parameters and were used to estimate the mean time to immunity waning. We show that three life spans are essential to explain the observed antibody kinetics: that of the antibodies (around one month), the short-lived plasma cells (several months) and the long-lived plasma cells (decades). Although our model is a simplified representation of the actual mechanisms that govern individual immune responses, the level of agreement between long-term individual predictions and observed kinetics is reassuringly close. The quantitative assessment of the time scales over which plasma cells and antibodies live and interact provides a basis for further quantitative research on immunology, with direct consequences for understanding the epidemiology of infectious diseases, and for timing serum sampling in clinical trials of vaccines.

Influence of husbandry and control measures on porcine circovirus type 2 (PCV-2) dynamics within a farrow-to-finish pig farm: A modelling approach

We assessed, using a modelling approach, the influence of several management practices within a farrow-to-finish farm on the age of PCV-2 infection. The impact of PCV-2 vaccination with different vaccination schemes on infection dynamics, was also tested. A stochastic individual-based model describing the population dynamics in a typical French farrow-to-finish pig farm was built and coupled with an epidemiological model of PCV-2 infection. The parameters of the infectious model were mainly obtained from previous transmission experiments. Results were subjected to a survival analysis of time-to-infection. For each comparison, the reference situation was no vaccination followed by random mixing of piglets after birth and after weaning. The risk of early infection was significantly reduced when mixing of piglets was reduced at different stages (avoiding cross-fostering and grouping piglets by litters in small pens after weaning, hazard ratio (HR)=0.52 [0.46; 0.59]). Sow-targeted vaccination delayed the infectious process until the waning of passive immunity and piglet-targeted vaccination considerably decreased the force of infection leading to a dramatic decrease of the total number of infections (HR=0.44 [0.37; 0.54]). The effect was even more pronounced when strict management measures were applied (HR=0.24 [0.19; 0.31]). Changing from a low (3%) prevalence of PCV-2-infected semen to a higher one (18%) significantly increased the risk of early infections (HR=1.36 [1.2; 1.53]), whereas reducing replacement rate or changing sow housing from individual crates to group housing had a limited impact on PCV-2 dynamics.

Modelling the time-dependent transmission rate for porcine circovirus type 2 (PCV2) in pigs using data from serial transmission experiments

Six successive transmission trials were carried out from 4 to 39 days post inoculation (DPI) to determine the features of the infectious period for PCV2-infected pigs. The infectiousness of inoculated pigs, assessed from the frequency of occurrence of infected pigs in susceptible groups in each contact trial, increased from 4 to 18 DPI (0, 7 and 8 infected pigs at 4, 11 and 18 DPI, respectively) and then decreased slowly until 39 days post infection (4, 2 and 1 pigs infected at 25, 32 and 39 DPI, respectively). The estimated time-dependent infectiousness was fitted to three unimodal function shapes (gamma, Weibull and lognormal) for comparison. The absence of infected pigs at 4 DPI revealed a latency period between 4 and 10 DPI. A sensitivity analysis was performed to test whether the parametric shape of the transmission function influenced the estimations. The estimated time-dependent transmission rate was implemented in a deterministic SEIR model and validated by comparing the model prediction with external data. The lognormal-like function shape evidenced the best quality of fit, leading to a latency period of 8 days, an estimated basic reproduction ratio of 5.9 [1.8,10.1] and a mean disease generation time of 18.4 days [18.2, 18.5].

Pharmacodynamic Modeling of In Vitro Activity of Marbofloxacin against Escherichia coli Strains

ABSTRACT A mathematical pharmacodynamic model was developed to describe the bactericidal activity of marbofloxacin against Escherichia coli strains with reduced susceptibility levels (determined using MICs) under optimal and intestinal growth conditions. Model parameters were estimated using nonlinear least-square curve-fitting procedures for each E. coli strain. Parameters related to bactericidal activity were subsequently analyzed using a maximum-effect (E max) model adapted to account for a direct and a delayed effect. While net growth rates did not vary significantly with strain susceptibility, culture medium had a major effect. The bactericidal activity of marbofloxacin was closely associated with the concentration and the duration of exposure of the bacteria to the antimicrobial agent. The value of the concentration inducing a half-maximum effect (C 50) was highly correlated with MIC values (R 2 = 0.87 and R 2 = 0.94 under intestinal and optimal conditions, respectively). Our model reproduced the time-kill kinetics with good accuracy (R 2 of >0.90) and helped explain observed regrowth.

A simple periodic-forced model for dengue fitted to incidence data in Singapore.

Dengue is the worlds major arbovirosis and therefore an important public health concern in endemic areas. The availability of weekly reports of dengue cases in Singapore offers the opportunity to analyze the transmission dynamics and the impact of vector control strategies. Based on a previous model studying the impact of vector control strategies in Singapore during the 2005 outbreak, a simple vector-host model accounting for seasonal fluctuation in vector density was developed to estimate the parameters governing the vector population dynamics using dengue fever incidence data from August 2003 to December 2007. The impact of vector control, which consisted principally of a systematic removal of actual and potential breeding sites during a six-week period in 2005, was also investigated. Although our approach does not account for the complex life cycle of the vector, the good fit between data and model outputs showed that the impact of seasonality on the transmission dynamics is highly important. Moreover, the periodic fluctuations of the vector population were found in phase with temperature variations, suggesting a strong climate effect on the vector density and, in turn, on the transmission dynamics.

Estimation of transmission parameters of a fluoroquinolone-resistant Escherichia coli strain between pigs in experimental conditions

Antimicrobial resistance is of primary importance regarding public and animal health issues. Persistence and spread of resistant strains within a population contribute to the maintenance of a reservoir and lead to treatment failure. An experimental trial was carried out to study the horizontal transmission of a fluoroquinolone-resistant Escherichia coli strain from inoculated to naïve pigs. All naïve contact pigs had positive counts of fluoroquinolone-resistant E. coli after only two days of contact. Moreover, re-infections of inoculated pigs caused by newly contaminated animals were suspected. A maximum likelihood method, based on a susceptible-infectious-susceptible (SIS) model, was used to determine the transmission parameters. Two transmission levels were identified depending on the quantity of bacteria shed by infected individuals: (i) low-shedders with bacterial counts of resistant E. coli in the faeces between 5*103 and 106 CFU/g (βL= 0.41 [0.27; 0.62]), (ii) high shedders with bacterial counts above 106 CFU/g (βH= 0.98 [0.59; 1.62]). Hence, transmission between animals could be pivotal in explaining the persistence of resistant bacteria within pig herds.