SIRSISSEIR

SIRSISSEIR is a class of compartmental infectious disease models that combines features from SIR, SIS, and SEIR frameworks to study pathogens for which there is a latent incubation period and immunity that may decline over time. As a hybrid, it captures the key stages of susceptibility, exposure, infectiousness, and temporary immunity, while allowing loss of immunity to return individuals to susceptibility. The approach treats the population as moving through distinct states, typically including susceptible (S), exposed (E), infectious (I), and recovered (R), with transitions that reflect infection, progression to infectiousness after an incubation period, recovery, and waning immunity.

In standard implementations, individuals become infected at a rate that depends on the number of infectious individuals, pass from exposed to infectious at a rate that represents the incubation period, recover at a rate reflecting the duration of illness, and lose immunity at a rate that returns them to susceptibility. Some variants incorporate SIS-like features by allowing partial or complete loss of immune protection to return individuals directly to S or to intermediate susceptible-like states, thereby enabling recurrent circulation of the pathogen. The framework is commonly represented by a system of ordinary differential equations and can be extended to include births and deaths in the population.

SIRSISSEIR is used to analyze diseases characterized by both latent periods and non-permanent immunity, enabling exploration of how waning immunity, incubation dynamics, and contact patterns influence outbreak timing, peak prevalence, and the potential for recurrent waves. It supports scenario analysis for vaccination strategies, waning-immunity effects, and interventions targeting either the latent or infectious stages. Limitations include sensitivity to parameter values, identifiability challenges, and the need for reliable data on incubation, infectious duration, and immunity duration.