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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]

Brucellosis, a zoonotic disease, has brought about enormous human suffering and tremendous economic burden to animal husbandry in China. However, Inner Mongolia is the hardest hit area of brucellosis in China. A total of 132,037 human cases have been reported from 2010 to 2020. Endogenous mechanisms of brucellosis spreading across Inner Mongolia till remains to be revealed. We propose a periodic epidemic model to investigate the effect of periodic parameter changes on brucellosis epidemics. Then we evaluate the basic reproduction number R 0 and analyze the global dynamics of the model. Furthermore, key parameters related to periodic transmission are estimated based on the monthly data of human brucellosis cases and the trend of newly infected human brucellosis cases are predicted in Inner Mongolia. Our modeling results illustrate that periodical birth and sheep shearing play a significant role in inducing periodical outbreak of brucellosis in Inner Mongolia. Moreover, it is exhibited that the annual peak number and the final scale of human brucellosis cases will be reduced dramatically with the delayed peak time of sheep birth. While the annual peak time will be lagged and the annual peak number will be decreased as the peak time of sheep shearing is postponed. In addition, we discover that it is difficult to stem brucellosis even if all sheep are vaccinated besides ewes. Nevertheless, the detection rate exceed a certain value 0.032 or the decaying rate of Brucella surpass a critical value 0.585, the human brucellosis can be regulated in Inner Mongolia according to the sensitivity analysis of R 0 . The insights shed herein may contribute to the careful implementation of brucellosis control strategies in other regions. [ABSTRACT FROM AUTHOR]