Estimating Drift Parameters in a Sub-Fractional Vasicek-Type Process.

This study deals with drift parameters estimation problems in the sub-fractional Vasicek process given by dxt=θ(µ−xt)dt+dStH, with θ>0, µ∈R being unknown and t≥0; here, SH represents a sub-fractional Brownian motion (sfBm). We introduce new estimators θ^ for θ and µ^ for µ based on discrete time observations and use techniques from Nordin−Peccati analysis. For the proposed estimators θ^ and µ^, strong consistency and the asymptotic normality were established by employing the properties of SH. Moreover, we provide numerical simulations for sfBm and related Vasicek-type process with different values of the Hurst index H.

Dynamics of a stochastic COVID-19 epidemic model with jump-diffusion.

For a stochastic COVID-19 model with jump-diffusion, we prove the existence and uniqueness of the global positive solution. We also investigate some conditions for the extinction and persistence of the disease. We calculate the threshold of the stochastic epidemic system which determines the extinction or permanence of the disease at different intensities of the stochastic noises. This threshold is denoted by ξ which depends on white and jump noises. The effects of these noises on the dynamics of the model are studied. The numerical experiments show that the random perturbation introduced in the stochastic model suppresses disease outbreak as compared to its deterministic counterpart. In other words, the impact of the noises on the extinction and persistence is high. When the noise is large or small, our numerical findings show that COVID-19 vanishes from the population if ξ < 1 ; whereas the epidemic cannot go out of control if ξ > 1 . From this, we observe that white noise and jump noise have a significant effect on the spread of COVID-19 infection, i.e., we can conclude that the stochastic model is more realistic than the deterministic one. Finally, to illustrate this phenomenon, we put some numerical simulations.