Lyapunov function and global asymptotic stability for a new multiscale viral dynamics model incorporating the immune system response: Implemented upon HCV

Analysis of HBV and COVID-19 Coinfection Model with Intervention Strategies

Coinfection of hepatitis B virus (HBV) and COVID-19 is a common public health problem throughout some nations in the world. In this study, a mathematical model for hepatitis B virus (HBV) and COVID-19 coinfection is constructed to investigate the effect of protection and treatment mechanisms on its spread in the community. Necessary conditions of the proposed model nonnegativity and boundedness of solutions are analyzed. We calculated the model reproduction numbers and carried out the local stabilities of disease-free equilibrium points whenever the associated reproduction number is less than unity. Using the well-known Castillo-Chavez criteria, the disease-free equilibrium points are shown to be globally asymptotically stable whenever the associated reproduction number is less than unity. Sensitivity analysis proved that the most influential parameters are transmission rates. Moreover, we carried out numerical simulation and shown results: some parameters have high spreading effect on the disease transmission, single infections have great impact on the coinfection transmission, and using protections and treatments simultaneously is the most effective strategy to minimize and also to eradicate the HBV and COVID-19 coinfection spreading in the community. It is concluded that to control the transmission of both diseases in a population, efforts must be geared towards preventing incident infection with either or both diseases.

Modelling disease spread with spatio-temporal fractional derivative equations and saturated incidence rate

The global analysis of a spatio-temporal fractional order SIR infection model with saturated incidence function is suggested and studied in this paper. The dynamics of the infection is described by three partial differential equations including a time-fractional derivative order for each one of them. The equations of our model describe the evolution of the susceptible, the infected and the recovered individuals with taking into account the spatial diffusion for each compartment. We will choose a saturated incidence rate in order to describe the nonlinear force of the infection. First, we will prove the well-posedness of our suggested model in terms of existence and uniqueness of the solution. Also in this context, the boundedness and the positivity of solutions are established. Afterward, we will give the forms of the disease-free equilibrium and the endemic one. It was demonstrated that the global stability of the each equilibrium depends mainly on the basic reproduction number. Finally, numerical simulations are performed to validate the theoretical results and to show the effect of vaccination in reducing the infection severity. It was shown that the fractional derivative order has no effect on the equilibria stability but only on the convergence speed towards the steady states. It was also observed that vaccination is amongst the good strategies in controlling the disease spread.

Stability Analysis of Equilibrium Point and Limit Cycle of Two-Dimensional Nonlinear Dynamical Systems—A Tutorial

The equilibrium state of a dynamical system can be divided into the equilibrium point and limit cycle. In this paper, the stability analysis of the equilibrium point and limit cycle of dynamical systems are presented through different and all possible approaches, and those approaches are compared as well. In particular, the author presented the stability analysis of the equilibrium point through phase plane approach, Lyapunov–LaSalle energy-based approach, and linearization approach, respectively, for two-dimensional nonlinear system, while the stability analysis of the limit cycle is analyzed by using the LaSalle local invariant set theorem and Poincaré–Bendixson theorem, which is only valid in two-dimensional systems. Different case studies are used to demonstrate the stability analysis of equilibrium point and limit cycle.