Related papers: Lyapunov stability of an SIRS epidemic model with …
This paper demonstrates input-to-state stability (ISS) of the SIR model of infectious diseases with respect to the disease-free equilibrium and the endemic equilibrium. Lyapunov functions are constructed to verify that both equilibria are…
We study a class of SIRS epidemic dynamical models with a general non-linear incidence rate and transfer from infectious to susceptible. The incidence rate includes a wide range of monotonic, con- cave incidence rates and some non-monotonic…
We study the global dynamics of a reaction-diffusion SEIR infection model with distributed delay and nonlinear incidence rate. The well-posedness of the proposed model is proved. By means of Lyapunov functionals, we show that the disease…
This paper studies the dynamics of a network-based SIRS epidemic model with vaccination and a nonmonotone incidence rate. This type of nonlinear incidence can be used to describe the psychological or inhibitory effect from the behavioral…
We consider SIR and SIRS models with differential mortality. Global stability of equilibria is established by using Lyapunov's method
In this chapter, we consider a reaction-diffusion SVIR infection model with dis-tributed delay and nonlinear incidence rate. The wellposedness of the proposed model is proved. By means of Lyapunov functionals, we show that the disease-free…
We consider an epidemiological SIR model with an infection rate depending on the recovered population. We establish sufficient conditions for existence, uniqueness, and stability (local and global) of endemic equilibria and consider also…
In this paper we consider the stability of a class of deterministic and stochastic SEIRS epidemic models with delay. Indeed, we assume that the transmission rate could be stochastic and the presence of a latency period of $r$ consecutive…
We investigate the global behaviour of a SIRI epidemic model with distributed delay and relapse. From the theory of functional differential equations with delay, we prove that the solution of the system is unique, bounded, and positive, for…
We propose and investigate an SEI infection's age model with a general class of nonlinear incidence rates. We give a necessary and sufficient condition for global asymptotic stability of the free-equilibrium related to the basic…
The aim of this paper is to study the dynamics of a reaction--diffusion SIS (susceptible-infectious-susceptible) epidemic model with a nonlinear incidence rate describing the transmission of a communicable disease between individuals. We…
We study an SAIRS-type epidemic model with vaccination, where the role of asymptomatic and symptomatic infectious individuals are explicitly considered in the transmission patterns of the disease. We provide a global stability analysis for…
In recent years, classical epidemic models, which assume stationary behavior of individuals, have been extended to include an adaptive heterogeneous response of the population to the current state of the epidemic. However, it is widely…
In this paper, we discussed an infinitely distributed delayed viral infection model with nonlinear immune response and general incidence rate. We proved the existence and uniqueness of the equilibria. By using the Lyapunov functional and…
This paper proposes and analyzes a malaria transmission model structured by the chronological age of the human host population. The model couples an age-structured SIRS system for humans, incorporating waning immunity, with an SI system for…
Transmission dynamics of infectious diseases are often studied using compartmental mathematical models, which are commonly represented as systems of autonomous ordinary differential equations. A key step in the analysis of such models is to…
We study a multi-group SAIRS-type epidemic model with vaccination. The role of asymptomatic and symptomatic infectious individuals is explicitly considered in the transmission pattern of the disease among the groups in which the population…
An epidemic Susceptible-Vaccinated-Infected-Removed-Susceptible (SVIRS) model is presented on a weighted-undirected network with graph Laplacian diffusion. Disease-free equilibrium always exists while the existence and uniqueness of endemic…
We investigate global stability properties of a HIV/AIDS population model with constant recruitment rate, mass action incidence, and variable population size. Existence and uniqueness results for disease-free and endemic equilibrium points…
We study a competitive infection-age structured SI model between two diseases. The well-posedness of the system is handled by using integrated semigroups theory, while the existence and the stability of disease-free or endemic equilibria…