Stochastic dynamics of dengue epidemics

TL;DR

This paper models dengue epidemic spread using a stochastic Markovian framework that couples human SIR and mosquito SIS dynamics, deriving thresholds and reproductive ratios through analytical and numerical methods.

Contribution

It introduces a coupled stochastic model for dengue transmission and develops a truncation scheme to analyze epidemic thresholds and reproductive ratios.

Findings

Disease spreading is impossible at certain infection rates regardless of mosquito death rate.

The model accurately predicts epidemic thresholds and reproductive ratios.

Numerical simulations validate the analytical results.

Abstract

We use a stochastic Markovian dynamics approach to describe the spreading of vector-transmitted diseases, like dengue, and the threshold of the disease. The coexistence space is composed by two structures representing the human and mosquito populations. The human population follows a susceptible-infected-recovered (SIR) type dynamics and the mosquito population follows a susceptible-infected-susceptible (SIS) type dynamics. The human infection is caused by infected mosquitoes and vice-versa so that the SIS and SIR dynamics are interconnected. We develop a truncation scheme to solve the evolution equations from which we get the threshold of the disease and the reproductive ratio. The threshold of the disease is also obtained by performing numerical simulations. We found that for certain values of the infection rates the spreading of the disease is impossible whatever is the death rate of infected mosquito.