Abstract
Based on the mechanism of prevention and control of infectious disease, we propose, in this paper, an SIRS epidemic model with varying total population size and state-dependent control, where the fraction of susceptible individuals in population is as the detection threshold value. By the Poincaré map, theory of differential inequalities and differential equation geometry, the existence and orbital stability of the disease-free periodic solution are discussed. Theoretical results show that by state-dependent pulse vaccination we can make the proportion of infected individuals tend to zero, and control the transmission of disease in population.
Highlights
It is generally known that the spread of infectious diseases has been a threat to healthy of human beings and other species
Based on the mechanism of prevention and control of infectious disease, we propose, in this paper, an SIRS epidemic model with varying total population size and statedependent control, where the fraction of susceptible individuals in population is as the detection threshold value
In order to explore the effects of the state-dependent pulse control strategies on the transmission of the infectious diseases in a population of varying size, an SIRS epidemic model with varying total population and state-dependent pulse control strategy is proposed and analyzed in this paper
Summary
It is generally known that the spread of infectious diseases has been a threat to healthy of human beings and other species. It fails to hold for diseases that are endemic in communities with changing populations, and for diseases which raise the mortality rate substantially In such situation, we can hardly expect a population remaining constant, and more complicated epidemic models with varying population size should be considered. Results are obtained in terms of three threshold which respectively determines whether or not the disease dies out and dynamics of epidemic model when births of population are throughout a year At same time, they discussed the existence of disease-free periodic solution when births of population are birth pulse. As far as we know, epidemic model with varying total population and state-dependent feedback control strategies had never been done in the literatures. In this paper, the dynamical behavior of an SIRS epidemic model with varying total population and state-dependent pulse control strategy is studied. Some concluding remarks are presented in the last section
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