Endemic threshold analysis for the Kermack-McKendrick reinfection model

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  • Modeling and Simulation in Applied Mathematics : Proceedings of Annual Workshop on Modeling and Simulation in Applied Mathematics, December 20, 2015 JOSAI UNIVERSITY

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In a seminal series of papers published during the 1930s, Kermack and McKendrick developed an infection-age structured endemic model, which takes into account the demography of the host population, and the waning immunity (variable susceptibility) and reinfection of recovered individuals. The host population is structured by a duration variable for each status, as the susceptibility of the recovered individuals depends on the duration since the last recovery. The idea of reinfection has become increasingly important in understanding emerging and reemerging infectious diseases, since it makes the control of infectious diseases difficult, and waning immunity is widely observed if there is no (natural or artificial) boosting. For the reinfection model, we can introduce the reinfection threshold of R0 at which a qualitative change in the epidemiological implication occurs for the prevalence and controllability. If any enhancement of epidemiological reproductivity by reinfection exists, we also expect that endemic steady states backwardly bifurcate when the basic reproduction number crosses unity, which implies that attaining a subcritical level of R0 is not necessarily a complete policy for disease prevention. The main aim of this survey is to demonstrate the possible usefulness of the Kermack-McKendrick reinfection model and its extensions to understand reinfection phenomena in the spread of infectious diseases.

Modeling and Simulation in Applied Mathematics : Proceedings of Annual Workshop on Modeling and Simulation in Applied Mathematics, held at Josai Unversity on December 20 in 2015 / edited by Masahiro FUJITA, Manabu INUMA, Takahiro TSUCHIYA, Hidenori YASUDA

identifier:JOS-13447777-0910

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