Speaker
Description
The stochastic version of the SIRV (susceptible-infected-recovered-vaccinated) epidemic model in the population of non-constant size and finite period of immunity is considered. Among many parameters influencing the dynamics of this model, the most important parameter is the contact rate, i.e. the average number of adequate contacts of an infective person, where an adequate contact is one which is sufficient for the transmission of an infection if it is between a susceptible and an infected individual. It is expected that this parameter exhibits time-space clusters which reflect interchanging of periods of low and steady transmission and periods of high and volatile transmission of the disease. The stochastics in the considered SIRV model comes from the noise represented as the sum of the conditional Brownian motion and Poisson random field, closely related to the corresponding time-changed Brownian motion and the time-changed Poisson random measure. The existence and uniqueness of positive global solution of the corresponding system of stochastic differential equations is proven by classical techniques. Furthermore, persistence and extinction of infection in population in long-run scenario are analyzed. In particular, conditions depending on parameters of the model and the underlying measure, under which the persistence and the extinction of the disease appear, are derived. The theoretical results are illustrated via simulated examples. In particular, transmission coefficient is simulated as the mean-reverting diffusion with jumps with different propositions for the absolutely continuous time-change process.
