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When the body gets infected by a pathogen the immune system developspathogen-specific immunity. Induced immunity decays in time and years afterrecovery the host might become susceptible again. Exposure to the pathogen inthe environment boosts the immune system thus prolonging the time in which arecovered individual is immune. Such an interplay of within host processes andpopulation dynamics poses significant challenges in rigorous mathematicalmodeling of immuno-epidemiology. We propose a new framework to model SIRSdynamics, monitoring the immune status of individuals and including both waningimmunity and immune system boosting. Our model is formulated as a system of twoODEs coupled with a PDE. After showing existence and uniqueness of a classicalsolution, we investigate the local and the global asymptotic stability of theunique disease-free stationary solution. Under particular assumptions on thegeneral model, we can recover known examples such as large systems of ODEs forSIRWS dynamics, as well as SIRS with constant delay. Moreover, a new class ofSIS models with delay can be obtained in this framework.

Immuno-epidemiology of a population structured by immune status: a mathematical study of waning immunity and immune system boosting