In this study, we investigate the COVID-19 propagation dynamics using a stochastic SIQR model with Gaussian white noise and semi-Markovian switching, focusing on the impacts of Gaussian white noise and semi-Markovian switching on the propagation dynamics of COVID-19. It is suggested that the fate of COVID-19 is entirely determined by the basic reproduction number , under mild extra conditions. By making sensitivity analysis on , we found that the effect of quarantine rate on was more significant compared to transmission rate. Our results demonstrate that: (i) The presence of Gaussian white noise, while reducing the basic reproduction number of COVID-19, also poses more challenges for the prediction and control of COVID-19 propagation. (ii) The conditional holding time distribution has a significant effect on the kinetics of COVID-19. (iii) The semi-Markov switching and Gaussian white noise can support irregular recurrence of COVID-19 outbreaks.

In this paper a delayed stochastic SLVIQR epidemic model, which can be applied for modeling the new coronavirus COVID-19 after a calibration, is derived. Model is constructed by assuming that transmission rate satisfies the mean-reverting Ornstain-Uhlenbeck process and, besides a standard Brownian motion, another two driving processes are considered: a stationary Poisson point process and a continuous finite-state Markov chain. For the constructed model, the existence and uniqueness of positive global solution is proven. Also, sufficient conditions under which the disease would lead to extinction or be persistent in the mean are established and it is shown that constructed model has a richer dynamic analysis compared to existing models. In addition, numerical simulations are given to illustrate the theoretical results.

The COVID-19 epidemic has infected millions of people and cast a shadow over the global economic recovery. To explore the epidemic's transmission law and provide theoretical guidance for epidemic prevention and control. In this paper, we investigate a novel SEIR-A reaction-diffusion COVID-19 system with direct and aerosol transmission. First, the solution's positivity and boundedness for the system are discussed. Then, the system's the basic reproduction number is defined. Further, the uniform persistence of disease when is explored. In addition, the system equilibrium's global stability based on is demonstrated. Next, the system's NSFD scheme is investigated and the discrete system's positivity, boundedness, and global properties are studied. Meantime, global sensitivity analysis on threshold is investigated. Interestingly, the effects of three strategies, including vaccination, receiving treatment, and wearing a mask, are evaluated numerically. The results suggest that the above three strategies can effectively control the peak and final scale of infection and shorten the duration of the epidemic. Finally, theoretical simulations and instance predictions are used to give several key indicators of the epidemic, including threshold , peak, time to peak, time to clear cases, and final size. The instance prediction results are as follows: (1) The basic reproduction numbers of Yangzhou and Putian in China are and , respectively. (2) This epidemic round in Yangzhou will peak at 56 new daily confirmed cases on the 9th day (August 5), and Putian will peat at 37 new daily confirmed cases on the 6th day (September 15). (3) The final scale of infections in Yangzhou and Putian reached 570 and 205 cases, respectively. (4) The Yangzhou epidemic is expected to be completely cleared on the 25th day (August 21). In addition, the Putian epidemic will continue for 15 days and be cleared on September 24. The analysis results mean that we should improve our immunity by actively vaccinating, reducing the possibility of aerosol transmission by wearing masks. In particular, people should maintain proper social distance, and the government should strengthen medical investment and COVID-19 project research.

This paper proposes a new distributed model predictive control (DMPC) for positive Markov jump systems subject to uncertainties and constraints. The uncertainties refer to interval and polytopic types, and the constraints are described in the form of 1-norm inequalities. A linear DMPC framework containing a linear performance index, linear robust stability conditions, a stochastic linear co-positive Lyapunov function, a cone invariant set, and a linear programming based DMPC algorithm is introduced. A global positive Markov jump system is decomposed into several subsystems. These subsystems can exchange information with each other and each subsystem has its own controller. Using a matrix decomposition technique, the DMPC controller gain matrix is divided into nonnegative and non-positive components and thus the corresponding stochastic stability conditions are transformed into linear programming. By virtue of a stochastic linear co-positive Lyapunov function, the positivity and stochastic stability of the systems are achieved under the DMPC controller. A lower computation burden DMPC algorithm is presented for solving the min-max optimization problem of performance index. The proposed DMPC design approach is extended for general systems. Finally, an example is given to verify the effectiveness of the DMPC design.

A new mathematical model is formulated to investigate the transmission dynamics of cholera under vaccination, with a focus on the impact of vaccination age. The basic reproduction number is derived and proved to be a sharp control threshold determining whether or not the infection is persistent. We conduct a rigorous analysis on the local and global stability properties of the equilibria in system. Meanwhile, we compare the results to those of the simplified model based on ordinary differential equations where the effects of vaccination age are not incorporated. Numerical simulation results verify our analytical findings.

In this paper, we propose and discuss a stochastic SIRS epidemic model with non-monotone incidence rate under regime-switching. First of all, we show that there is a unique positive solution, which is a prerequisite for analyzing the long-term behavior of the stochastic model. Then, a threshold dynamic determined by the basic reproduction number is established: the disease can be eradicated almost surely if and under mild extra conditions, whereas if the densities of the distributions of the solution can converge in to an invariant density by using the Markov semigroups theory. Finally, based on realistic parameters obtained from previous literatures, numerical simulations have been performed to verify our analytical results.