Junyuan Yang

Global threshold dynamics of an SIVS model with waning vaccine-induced immunity and nonlinear incidence

Vaccination is the most effective method of preventing the spread of infectious diseases. For many diseases, vaccine-induced immunity is not life long and the duration of immunity is not always fixed. In this paper, we propose an SIVS model taking the waning of vaccine-induced immunity and general nonlinear incidence into consideration. Our analysis shows that the model exhibits global threshold dynamics in the sense that if the basic reproduction number is less than 1, then the disease-free equilibrium is globally asymptotically stable implying the disease dies out; while if the basic reproduction number is larger than 1, then the endemic equilibrium is globally asymptotically stable indicating that the disease persists. This global threshold result indicates that if the vaccination coverage rate is below a critical value, then the disease always persists and only if the vaccination coverage rate is above the critical value, the disease can be eradicated.

Existence of a Nonautonomous SIR Epidemic Model with Age Structure

A nonautonomous SIR epidemic model with age structure is studied. Using integro-differential equation and a fixed point theorem, we prove the existence and uniqueness of a positive solution to this model. We conclude our results and discuss some problems to this model in the future. We simulate our analyzed results.

Imitation dynamics of vaccine decision-making behaviours based on the game theory.

ABSTRACT Based on game theory, we propose an age-structured model to investigate the imitation dynamics of vaccine uptake. We first obtain the existence and local stability of equilibria. We show that Hopf bifurcation can occur. We also establish the global stability of the boundary equilibria and persistence of the disease. The theoretical results are supported by numerical simulations.

An HIV model: Theoretical analysis and experimental verification

An HIV-infection model is proposed, its global stability of the disease free equilibrium is studied, and existence of the endemic equilibria is analyzed. The observed data in a city in China is used to determine the parameters in the model using the least-squares approach. The theoretical prediction agrees well with the data available from a local government agency in the city.

A note on an age-of-infection SVIR model with nonlinear incidence

In this paper, nonlinear incidence rate is incorporated into an age-of-infection SVIR epidemiological model. By the method of Lyapunov functionals, it is shown that the basic reproduction number ℛ0...

Dynamics of a competing two-strain SIS epidemic model on complex networks with a saturating incidence rate

This paper studies a two-strain SIS epidemic model with a competing mechanism and a saturating incidence rate on complex networks. This type of incidence rate can be used to reflect the crowding effect of the infective individuals. We first obtain the associated reproduction numbers for each of the two strains which determine the existence of the boundary equilibria. The stability of the disease-free and boundary equilibria are further examined. Besides this, we also show that the two competing strains can coexist under certain conditions. Interestingly, the saturating incidence rate can have specific effects on not only the stability of the boundary equilibria, but also the existence of the coexistence equilibrium. Numerical simulations are presented to support the theoretical results.

A TUBERCULOSIS (TB) MODEL WITH UNDETECTED COMPARTMENT: AN APPLICATION TO CHINA

This article introduces a novel model that studies the major factors jeopardizing tuberculosis (TB) control programme in China. A previously developed two-strain TB model is augmented with a class of individuals not registered under the TB control programme. The paper investigates the basic reproduction number and proves the global stability of the disease-free equilibrium. The presence of three endemic equilibria is established in the model. With the help of numerical simulations, a comparative study has been performed to test the validity of the model presented here to the real data available from the Ministry of Health of the Peoples Republic of China. Sensitivity and elasticity analysis give the key parameters that would govern successful TB control in China.

Theoretical and numerical results for an age-structured SIVS model with a general nonlinear incidence rate

ABSTRACT In this paper, we propose an SIVS epidemic model with continuous age structures in both infected and vaccinated classes and with a general nonlinear incidence. Firstly, we provide some basic properties of the system including the existence, uniqueness and positivity of solutions. Furthermore, we show that the solution semiflow is asymptotic smooth. Secondly, we calculate the basic reproduction number by employing the classical renewal process, which determines whether the disease persists or not. In the main part, we investigate the global stability of the equilibria by the approach of Lyanpunov functionals. Some numerical simulations are conducted to illustrate the theoretical results and to show the effect of the transmission rate and immunity waning rate on the disease prevalence.

Asymptotical profiles of a viral infection model with multi-target cells and spatial diffusion

Abstract In this paper, we propose a viral infection model with multi-target cells on a heterogeneous environment. Then we use the semigroup theory and a variational characterization to compute the local reproduction number R ( x ) and the basic reproduction number R 0 . Furthermore, the model exhibits a threshold dynamics: the virus-free steady state E 0 is globally asymptotically stable if R 0 1 ; otherwise, the endemic steady state E ∗ is globally asymptotically stable. Finally, we perform some numerical examples to illustrate the theoretical results.