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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]

China is one of the countries in the world carrying a heavy burden of tuberculosis. Due to the unbalanced economic development, the number of people working in other parts of country is huge, and the mobility of personnel has exacerbated the increase in tuberculosis cases. Most patients affected by this are in their middle and young ages. It is having a great impact among the family and society. Therefore, research on how to control this disease is absolutely necessary. The population is divided into two categories such as local population and the immigrant population. A pulmonary tuberculosis dynamic model with population heterogeneity is established. We calculate the basic reproductive number and the controlled reproductive number, and discuss the two types of population under the constraints given by the amount of vaccine and the optimal immunization ratio obtained is (0. 1 1 8 , 0. 1 0 7) , which can reduce the effective reproduction number from 5.85 to 0.227. It is understood that immunizing the local population will control the spread of the epidemic to a large extent, and we simulate the final scale of infection after immunization under the optimal immunization ratio. It can take a minimum of at least 10 years to reduce the spread of this disease, but to eliminate it forever, it needs at least a minimum of 100 years. [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]

Coronavirus disease 2019 (COVID-19) is a new respiratory disease caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). It started in China and spread quickly to all continents. This virus has changed the life style and the education system in many countries. As for other viruses, mathematical models have been rated as a useful tool to support the research on COVID-19. In this work, we develop a reaction–diffusion model to describe the within-host dynamics of SARS-CoV-2 in cancer patients. This model studies the interactions between nutrient, healthy epithelial cells, cancer cells, SARS-CoV-2 particles, and immune cells. The model incorporates the spatial mobility of the cells and viruses. The model includes parameters for measuring the effect of lymphopenia on SARS-CoV-2/cancer patients. We verify the basic features of the model's solutions including the uniqueness, nonnegativity and boundedness. We list all equilibrium points of the proposed model. We show the global stability and the local instability of the most meaningful equilibria. We display some numerical simulations to enhance our theoretical results. The results indicate that diffusion can have a clear effect at the beginning of SARS-CoV-2 infection. Lymphopenia in SARS-CoV-2/cancer patients impairs the immune responses against cancer and SARS-CoV-2, and worsens the health state of patients. [ABSTRACT FROM AUTHOR]

Hemorrhagic fever with renal syndrome (HFRS) is a rodent-borne disease caused by several serotypes of hantavirus and 90% of all reported HFRS cases occur in China. However, the dynamics of such outbreak, particularly the characteristics of two distinct annual peaks in China, are not well understood. Here, we investigate several of the biologically plausible causes for the peaks in monthly HFRS cases, and find that the key factor is the interplay between periodic transmission rates and rodent periodic birth rate. Analysis of dynamical model reveals that vaccination plays a significant role in the control of HFRS in China. Sensitive analysis of different interventions demonstrates that integrating rodent culling and environmental management with the current vaccination program is effective for HFRS control. Our results suggest that for diseases from animals to human beings, the features of both animals and humans beings should be taken into account in the control and prevention strategies. [ABSTRACT FROM AUTHOR]