From random walks to epidemic spreading: Compartment model with mortality for vector transmitted diseases

TL;DR

This paper introduces a new compartmental model for vector-borne diseases that incorporates mortality of infected individuals and analyzes how these factors influence disease spread over complex networks.

Contribution

The model explicitly accounts for mortality in infected individuals and derives new expressions for basic reproduction numbers, enhancing understanding of disease dynamics with death.

Findings

Mortality reduces the basic reproduction number from $R_0$ to $R_M$.

Healthy state becomes unstable when $R_M, R_0 > 1$.

Simulations confirm mean-field predictions on strongly connected graphs.

Abstract

We propose a compartmental model for vector-transmitted diseases, such as Malaria and Dengue, spreading over complex networks. Individuals are represented by independent random walkers and vectors by infected nodes. Both walkers and nodes can be susceptible (S) or infected (I). Infected walkers may die (entering the dead compartment D), while infected nodes remain alive. Susceptible walkers can be infected by visiting infected nodes, and susceptible nodes by visits from infected walkers. We derive explicit expressions for the basic reproduction numbers $R_0$ (without mortality) and $R_M$ (with mortality), proving that $R_M < R_0$. When $R_M , R_0 > 1$, the healthy state is unstable, and for zero mortality, an endemic equilibrium emerges. We also study the effects of confinement measures. Simulations align well with mean-field predictions on strongly connected graphs but deviate for weakly connected networks. Our model has various interdisciplinary applications which include the modeling of chemical reaction kinetics, contaminant spread, and wildfire propagation.