Effect of human mobility on the spatial spread of airborne diseases: an epidemic model with indirect transmission (Q2141306)

This paper studies the effect of human mobility on the spatial spread of airborne diseases. Based on the Lagrangian method, the paper presents a coupled partial differential equation and ordinary differential equation model with human mobility and then reduces the dimensionless coupled model to a nonlinear system of ordinary differential equations in the limit of fast diffusing pathogens using the matched asymptotic expansions approach. In the considered model, human populations with localized patches that have partially transmitting boundaries through which pathogens are shed into the atmosphere by infected populations. It is assumed that the spread of infection in each population patch depends on the density of pathogens around the patch and did not explicitly model pathogens within the patches. The population of the system is fixed. The basic reproduction number and final size relation of the epidemic are calculated for a reduced system. Some numerical studies have also been presented for a two-patch scenario to illustrate the usefulness of the theory.