Probabilistic analysis of a disturbed SIQP-SI model of mosquito-borne diseases with human quarantine strategy and independent Poisson jumps

In this paper, we propose a new mathematical model describing the dynamics of mosquito-borne epidemics. The main novelties of the proposed model in comparison to the previous literature are twofold. On the one hand, the inclusion of the quarantine control measure applied to the human population and, on the other hand, the incorporation of the impact of environmental variations. The resulting model is governed by two blocks of Ito–Lévy coupled stochastic differential equations driven by Gaussian noise and six independent compensated Poisson processes. Based on the Lyapunov approach and the stopping time method, we first address the well-posedness of the proposed model. Then, by means of stochastic computational techniques, we establish certain asymptotic properties pertaining to the extinction and persistence in the mean of the infected component of the solution. Finally, we provide the outcome of some numerical experiments, to corroborate our theoretical results and highlight the influence of the quarantine measure and the discontinuous environmental noise on the infectious-disease dynamics.