A Particle System Model for Dengue Transmission

Abstract

Dengue disease has been known for decades as a vector-borne disease which is rapidly spreading in many tropical and subtropical countries. The disease is transmitted mostly by female Aedes aegypty mosquitoes. Although detailed biological properties of the infection process are already known, in the field applications the disease transmission of dengue is still far from being successfully controlled. The complexity surrounding the transmission is contributed by various factors such as climate, mobility and human-mosquito behavior. Many deterministic models have been developed to investigate the spread of dengue. However, in a deterministic model, spatial heterogeneity factor is not considered. In fact, distances between people and mosquitoes greatly influence the spread of dengue. This paper discusses a microscopic model of the spread of dengue based on spatial heterogeneity. In this microscopic model, every human and mosquito is regarded as a particle and the corresponding human and mosquito populations with their health status are considered as a system of particles. Three important dynamical factors and processes are constructed for each particle, i.e., position and health status of each particle, natural birth and death, infection and transition processes. An estimate of the corresponding basic reproductive ratio is introduced to accommodate the variation of health status and spatial spread of particles