Author(s)

Fuwei Zhang, Linfei Nie^*

College of Mathematics and Systems Science, Xinjiang University, Urumqi, China.

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.

SIRS Epidemic Model, Varying Total Population, State-Dependent Pulse Control, Periodic Solution, Orbital Stability

Zhang, F. and Nie, L. (2016) The Effect of State-Dependent Control for an SIRS Epidemic Model with Varying Total Population. Journal of Applied Mathematics and Physics, 4, 1889-1898. doi: 10.4236/jamp.2016.410191.