Stability analysis of an age-structured SIR model with nonlocal diffusion and indirect contacts

This paper aims to study the age-structured SIR model with nonlocal diffusion in which direct (person-to-person) and indirect contact are considered. We assume that an individual at a particular instant of time can only get infected either from a direct contact or from an indirect contact. It is evident that indirect contact is a crucial factor in the spread of many infectious diseases. We assume that the rate of diffusion is independent of the individual's age and is the same for the individuals in all three compartments. We also kept all age-zero individuals in the susceptible compartment only. The existence of a solution is shown by using semigroup theory. Moreover, we show the stability of zero steady state by using the spectral properties of the infinitesimal generator of the semigroup.