In this paper we will derive an SIR model describing vaccination as well as waning immunity
and propose a finite difference scheme for its solution together with some qualitative results …

We study fast–slow versions of the SIR, SIRS, and SIRWS epidemiological models. The
multiple time scale behaviour is introduced to account for large differences between some of …

In this survey, we propose an overview on Lyapunov functions for a variety of compartmental
models in epidemiology. We exhibit the most widely employed functions, and provide a …

Immunity following natural infection or immunization may wane, increasing susceptibility to
infection with time since infection or vaccination. Symptoms, and concomitantly …

The COVID-19 pandemic is still ongoing, even if the emergency is over, and we now have
enough data to analyze the outbreak over a long timeline. There is evidence that the …

We study a fast–slow version of an SIRS epidemiological model on homogeneous graphs,
obtained through the application of the moment closure method. We use GSPT to study the …

When the body gets infected by a pathogen the immune system develops pathogen-specific
immunity. Induced immunity decays in time and years after recovery the host might become …

SIRS models capture transmission dynamics of infectious diseases for which immunity is not
lifelong. Extending these models by a W compartment for individuals with waning immunity …

Pertussis remains a challenging public health problem with many aspects of infection,
disease and immunity poorly understood. Initially controlled by mass vaccination, pertussis …

We propose a compartmental model for a disease with temporary immunity and secondary
infections. From our assumptions on the parameters involved in the model, the system …