A diffusion model of Zika virus with human-vector transmission dynamics and control strategy including social distancing study

Abstract

Zika virus infection is caused by the Zika Virus belonging to the Flaviviridae family. The virus is transmitted to people through the bite of an infected Aedes mosquito. However, although rare, sexual and mother-to-child are also other modes of transmission. The incubation time in infected humans is a few days to a week. The spread of the disease still presents in some developing countries and remote areas that cannot afford basic public health intervention and vaccine, hence, investigating other options are necessary. In this study, we formulate a diffusion mathematical model of the Zika virus with controls (personal protection, medical treatment, and insecticide). In this model, we will be able to observe the spatial movement of individuals and investigate if the disease can be controlled by performing social distancing combined with other control strategies. Further, we investigate the essential dynamics of the model through equilibrium analyses. The basic reproduction number with the spatial movement of the model is derived. Meanwhile, a time-dependent optimal control study is applied to the model to seek a cost-effective strategy to eradicate Zika virus outbreaks. Numerical results show that strategically deployed personal protection, treatment, and insecticide can significantly reduce the number of infectious individuals and mosquitoes. Also, applying a social connection program can additionally reduce the spread from one place to another, and thus the number of infections in total is reduced.