An SIRS epidemic model with a rapidly decreasing probability for immunity

作者：Carr Thomas W^*

来源：IMA Journal of Applied Mathematics, 2016, 81(2): 281-307.

DOI：10.1093/imamat/hxv036

• integro-differential equations
• delay-differential equations
• Hopf bifurcation
• temporary immunity
• recurrent epidemics

We consider an SIRS model for disease dynamics that accounts for temporary immunity whereby recovered individuals return to the susceptible class. Temporary immunity occurs in diseases such as influenza, cholera, pertussis and malaria. We allow for a general probability function of remaining immune for a given time after recovery such that the model is a system of integro-differential equations. We first show that by considering a rapidly decreasing probability function, the original model can be approximated by a system of delay-differential equations. Perturbation methods are then applied to the delay equations to determine how the amplitude of oscillations, which correspond to repeated epidemics, depends on the system parameters and, in particular, the zeroth, first and second moments of the probability density.

• 出版日期2016-4