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

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.