| Abstract: |
| The stochastic version of the SIRV (susceptible-infected-recovered- vaccinated) model in the population of non-constant size and finite period of immunity is considered. Among many parameters, the most important is the contact rate, i.e. the average number of adequate contacts of an infective person. It is expected that this parameter exhibits time-space clusters which reflects in interchanging periods of low and steady transmission and periods of high and volatile transmission of the disease. The stochastics in the SIRV model considered here 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. From a modeling perspective, incorporating time-charged noise is an effective method for capturing temporal dependencies in noise, such as clustering and stretching periods.. The existence and uniqueness of positive global solution of the stochastic SIRV process is proven by classical techniques. Furthermore, persistence and extinction of infection in population in long-run scenario are analyzed. |
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