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In this paper, an SEAI epidemic model with asymptomatic infection is studied under the background of mass transmission of COVID-19. First, we use the next-generation matrix method to obtain the basic reproductive number R 0 and calculate the equilibrium point. Secondly, when R 0 < 1 , the local asymptotic stability of the disease-free equilibrium is proved by Hurwitz criterion, and the global asymptotic stability of the disease-free equilibrium is proved by constructing the Lyapunov function. When R 0 > 1 , the system has a unique endemic equilibrium point and is locally asymptotically stable, and it is also proved that the system is uniformly persistent. Then, the application of optimal control theory is carried out, and the expression of the optimal control solution is obtained. Finally, in order to verify the correctness of the theory, the stability of the equilibrium point is numerically simulated and the sensitivity of the parameters of R 0 is analyzed. We also simulated the comparison of the number of asymptomatic infected people and symptomatic infected people before and after adopting the optimal control strategy. This shows that the infection of asymptomatic people cannot be underestimated in the spread of COVID-19 virus, and an isolation strategy should be adopted to control the spread speed of the disease. [ABSTRACT FROM AUTHOR]

This paper investigates a two-species amensalism model that includes the fear effect on the first species and the Beddington–DeAngelis functional response. The existence and stability of possible equilibria are investigated. Under different parameters, there exist two stable equilibria which means that this model is not always globally asymptotically stable. Together with the existence of all possible equilibria and their stability, saddle connection and close orbits, we derive some conditions for transcritical bifurcation and saddle-node bifurcation. Furthermore, global dynamics analysis of the model is performed. It is observed that under certain parameter conditions, when the intensity of the fear effect is below a certain threshold value, as the fear effect increases it will only reduce the density of the first species population and will have no influence the extinction or existence of the first species population. However, when the fear effect exceeds this threshold, the increase of the fear effect will accelerate the extinction of the first species population. Finally, numerical simulations are performed to validate theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, a generalized fractional three-species food chain model with delay is investigated. First, the existence of a positive equilibrium is discussed, and the sufficient conditions for global asymptotic stability are given. Second, through selecting the delay as the bifurcation parameter, we obtain the sufficient condition for this non-control system to generate Hopf bifurcation. Then, a nonlinear delayed feedback controller is skillfully applied to govern the system's Hopf bifurcation. The results indicate that adjusting the control intensity or the control target's age can effectively govern the bifurcation dynamics behavior of this system. Last, through application examples and numerical simulations, we confirm the validity and feasibility of the theoretical results, and find that the control strategy is also applicable to eco-epidemiological systems. [ABSTRACT FROM AUTHOR]

Hepatitis B is a viral infection that can cause inflammation of the liver and lead to severe liver damage and even death. The study of hepatitis in Burkina Faso is crucial for several reasons. Indeed, understanding the epidemiology of hepatitis in Burkina Faso can help develop effective prevention and control strategies. Its study can also contribute to a better understanding of the global burden of the disease and the development of effective interventions in other parts of the world. To this aim, a new differential susceptibility and infectivity mathematical model of Hepatitis B transmission was developed in order to simulate the potential spread of the Hepatitis B virus in the population of Burkina Faso. Once the mathematical model is presented, the existence and uniqueness of non-negative solutions are proved. The model has a globally asymptotically stable disease-free equilibrium when the basic reproduction number R0 < 1 and a globally asymptotically stable endemic equilibrium when R0 > 1. The global asymptotic stability of the disease-free equilibrium has been studied using the Castillo Chavez method. The Lyapunov function and the LaSalle invariance principle are used to prove the global asymptotic stability of the endemic equilibrium. To simulate the proposed model, a Matlab numerical code has been developed. Numerical simulations are performed using data of Burkina Faso. The obtained numerical results confirm analytical results as well as the evolution of hepatitis B in Burkina Faso. [ABSTRACT FROM AUTHOR]