Analysis of a new SIR-M epidemic model with infection during transport

Abstract

In this paper, we propose a new epidemic SIR model with infection during transport, SIR-M. Under biologically motivated assumptions, we prove the positivity and boundedness of the solutions, calculate the basic reproduction number and the disease-free equilibrium. We prove that the disease-free equilibrium is globally asymptomatically stable if R₀ is less than one, and then propose a generalized SIR-M model with n interacting populations. Finally, we numerically compare the behavior of the disease in different scenarios such as the perfect exit screening scenario, the mobility of infectious individuals from a single population, the prohibition of mobility (confinement), etc. We find that the use of certain health and precautionary measures such as screening, border control methods and containment, could significantly reduce the spread of the disease in both populations. On the other hand, the lack of control of the mobility of individuals may lead to a chaotic dispersion of the disease in both populations.