A mathematical model for Zika virus transmission dynamics with a time-dependent mosquito biting rate

Abstract

BackgroundMathematical modeling has become a tool used to address many emerging diseases. One of the most basic and popular modeling frameworks is the compartmental model. Unfortunately, most of the available compartmental models developed for Zika virus (ZIKV) transmission were designed to describe and reconstruct only past, short-time ZIKV outbreaks in which the effects of seasonal change to entomological parameters can be ignored. To make an accurate long-term prediction of ZIKV transmission, the inclusion of seasonal effects into an epidemic model is unavoidable.MethodsWe developed a vector-borne compartmental model to analyze the spread of the ZIKV during the 2015–2016 outbreaks in Bahia, Brazil and to investigate the impact of two vector control strategies, namely, reducing mosquito biting rates and reducing mosquito population size. The model considered the influences of seasonal change on the ZIKV transmission dynamics via the time-varying mosquito biting rate. The model was also validated by comparing the model prediction with reported data that were not used to calibrate the model.ResultsWe found that the model can give a very good fit between the simulation results and the reported Zika cases in Bahia (R-square = 0.9989). At the end of 2016, the total number of ZIKV infected people was predicted to be 1.2087 million. The model also predicted that there would not be a large outbreak from May 2016 to December 2016 due to the decrease of the susceptible pool. Implementing disease mitigation by reducing the mosquito biting rates was found to be more effective than reducing the mosquito population size. Finally, the correlation between the time series of estimated mosquito biting rates and the average temperature was also suggested.ConclusionsThe proposed ZIKV transmission model together with the estimated weekly biting rates can reconstruct the past long-time multi-peak ZIKV outbreaks in Bahia.Electronic supplementary materialThe online version of this article (10.1186/s12976-018-0083-z) contains supplementary material, which is available to authorized users.

Winter is coming: pathogen emergence in seasonal environments

“…More precisely, a parameter µ i , λ i,j is periodic iff it is a function of temperature T , which is periodic (with period one year). The parameter values infered from observed epidemiological dynamics agree very well among the three studies we used Lourenço et al [2017], Suparit et al [2018], . All the parameter values used in our models are summed up in Table 1.…”

“…We want to determine the probability of emergence of Zika Virus, a newly emerging vector borne disease of humans. Our starting point is the epidemioloical model of Zika used in previous studies Lourenço et al [2017], Suparit et al [2018], . The epidemiological dynamics in the human population is described by an SEIR model : susceptible individuals S H , exposed indivuals E H , infected individuals I H and recovered/removed individuals R H .…”

“…Model I In this simple model, as in Suparit et al [2018], there is a single rate that varies with time. We assume that seasonality affects only the population size of vectors and, consequently, the only rate that varies with time is λ I H ,E V = β N V N H .…”

Computer-Assisted and Data Driven Approaches for Surveillance, Drug Discovery, and Vaccine Design for the Zika Virus

“…vector-borne and sexual, as well as seasonal and geographic variations need to be accounted for while calculating R 0 . To this end, [30] incorporated seasonal patterns in mosquito populations, [31] separately computed R 0 for different geographical regions, and [32][33][34] extended the basic SIR model to incorporate the sexual transmission as a second mode of infection. A few other approaches can be found in [35] and Table 1 of [36].…”

“…One example of Zika-specific extended SIR models is the SEIR model of [30] with separate populations for humans (h) and mosquito vectors (v) with time-varying transition rates. They define a separate exposed (E) category for humans and mosquitos separately, and assume the differential equations for humans and mosquitos:…”