An sveir model for assessing potential impact of an imperfect anti-SARS vaccine

Abstract

Abstract. The control of severe acute respiratory syndrome (SARS), a fatal contagious viral disease that spread to over 32 countries in 2003, was based on quarantine of latently infected individuals and isolation of individuals with clinical symptoms of SARS. Owing to the recent ongoing clinical trials of some candidate anti-SARS vaccines, this study aims to assess, via mathematical modelling, the potential impact of a SARS vaccine, assumed to be imperfect, in curtailing future outbreaks. A relatively simple deterministic model is designed for this purpose. It is shown, using Lyapunov function theory and the theory of compound matrices, that the dynamics of the model are determined by a certain threshold quantity known as the control reproduction number (Rv ). If Rv ≤ 1, the disease will be eliminated from the community; whereas an epidemic occurs if Rv > 1. This study further shows that an imperfect SARS vaccine with infection-blocking efficacy is always beneficial in reducing disease spread within the community, although its overall impact increases with increasing efficacy and coverage. In particular, it is shown that the fraction of individuals vaccinated at steady-state and vaccine efficacy play equal roles in reducing disease burden, and the vaccine must have efficacy of at least 75% to lead to effective control of SARS (assuming R 0 = 4). Numerical simulations are used to explore the severity of outbreaks when Rv > 1.

A Dynamical Map to Describe COVID-19 Epidemics

“…Pulse vaccination is one kind of strategy characterized to be periodic in time [23, 24]. On the other hand, continuous vaccination strategy is the alternative that is descbribed by Gumel et al [25] that showed the potential impact of SARS vaccine over the pandemic that spread to over 32 countries in 2003. Alexander et al [26] built a model to study the transmission of influenza virus, computing the threshold vaccination rate necessary for community wide control.…”

Mathematical model of tuberculosis spread within two groups of infected population

“…Modifications are done by considering the assumption that exposed individual can move naturally into recovered population and it is assumed that individual who has been recovered can not be re-infected by tuberculosis. Modifications of the model are also done by adding V compartment [4], namely vaccinated population, so that this model is called SVEIR model. The organization of this paper is as follows.…”

Global Stability of a SVEIR Epidemic Model: Application to Poliomyelitis Transmission Dynamics

“…However, the global dynamics when the basic reproduction number is greater than one have not been resolved before. By allowing different death rates for each of the compartments, the model studied in this paper is slight generalization of the model studied in [20]. Using Lyapunov-LaSalle methods, we fully resolve the global dynamics of the model for the full parameter space.…”

“…This requires, in most cases, the use of several different techniques, such as the theory of compound matrix [25] [26], the comparison theorem [27], or the use of Lyapunov functions associated with the Lassalle invariance principle [28], to name a few techniques commonly used by authors. For example, in [20], the authors used compound matrix techniques to show the global stability of the endemic equilibrium under some constraints on the parameters of the system. Huiming Wei et al [29] proposed an SVEIR model with time delay, and analyzed the dynamic behavior under pulse vaccination.…”

“…Some SVEIR models are used to assess the potential impact of an imperfect SARS vaccine like SARS vaccine [20], Hepatitis B vaccine [21], Tuberculosis vaccine [22], HIV vaccine [23] [24], to mention only these four diseases. From a mathematical point of view, to show the global asymptotic stability of equilibrium points in general, and especially, the global asymptotic stability of the endemic equilibrium, is not an easy task.…”