Search

In this paper, a SEIR epidemic model related to media coverage and exogenous reinfections is established to explore the transmission dynamics of COVID-19. The basic reproduction number is calculated using the next generation matrix method. First, the existence of equilibrium points is investigated, and different kinds of equilibrium points indicate that the disease may disappear, or exist that result in different quantity of susceptible individuals, pre-symptomatic infected individuals and symptomatic infected individuals. The stability of the equilibria is discussed by a geometric approach, and it is found that controlling reproduction number to be lower than 1 is not sufficient for eradication of COVID-19. Second, transcritical bifurcation is explored, and it is found that improving the ratio of exogenous reinfection may lead to backward bifurcation under poor medical conditions, which indicates that two endemic equilibrium points appear. Third, to investigate the influence of parameters on the basic reproduction, sensitivity analysis is done to choose relatively sensitive parameters, and the parameters for treatment and media coverage are selected. An optimal control model is established to balance the treatment and media awareness. By exploring the existence and the uniqueness of the optimal control solution, the optimal control strategies are given. Finally, we run numerical simulations to verify the theoretical analysis on actual data of China, and the data from the four different states of India is used for forecasting the situation of infected individuals in a short period. It is found by the simulation that the co-function of treatment and media coverage results in the reduced number of infectious individuals. [ABSTRACT FROM AUTHOR]

The parameters of biological system may change under the influence of different states or state processes. The change of parameters can also affect the dynamic behaviors of epidemic disease. This paper presents a mean field stochastic susceptible-infected-vaccinated (SIV) epidemic model which parameters depend on the state process. The sufficient and necessary conditions of optimal control of the novel epidemic model are obtained by maximum principle. Finally, we perform representative numerical simulations to illustrate the theoretical results and further discuss the feasibility based on the hand, foot and mouth disease (HFMD) data in China. [ABSTRACT FROM AUTHOR]

This paper formulates a diffusive tuberculosis (TB) model with early and late latent infections, vaccination and treatment that may more properly describe the slow and fast dynamics of TB transmission. We develop a new concise approach to determine the combination coefficients in the Lyapunov function candidate for the model and its time derivative in the case that both are the linear combinations of several Volterra-type functions, which highly simplifies the computations in global dynamical analysis for the nonlinear high-dimensional model. Based on the TB case data reported in China, the parameter values of the model are estimated. We further predict the TB prevalence trend in China. Sensitivity analysis for the control reproduction number and endemic equilibrium is conducted to seek some effective interventions that can significantly reduce initial TB transmission and lower TB prevalence levels in China. In the end, numerical simulations show that the bigger diffusive rates pick up the speeds of convergence to the equilibria of the model. [ABSTRACT FROM AUTHOR]