Estimation of epidemiological and population parameters from molecular sequence data has become central to the understanding of infectious disease dynamics. Various models have been proposed to infer details of the dynamics that describe epidemic progression. These include inference approaches derived from Kingman's coalescent theory. Here, we use recently described coalescent theory for epidem...

A stochastic SIR epidemic dynamic model with distributed-time-delay, for a two-scale dynamic population is derived. The distributed time delay is the varying naturally acquired immunity period of the removal class of individuals who have recovered from the infection, and have acquired natural immunity to the disease. We investigate the stochastic asymptotic stability of the disease free equilib...

An SIR epidemic model with pulse birth and standard incidence is presented. The dynamics of the epidemic model is analyzed. The basic reproductive number R∗ is defined. It is proved that the infection-free periodic solution is global asymptotically stable if R∗ < 1. The infection-free periodic solution is unstable and the disease is uniform persistent if R∗ > 1. Our theoretical results are conf...