FU Jin-bo, CHEN Lan-sun. Stability of an SIR Epidemic Model With 2 Patches and Population Movement[J]. Applied Mathematics and Mechanics, 2017, 38(4): 486-494. doi: 10.21656/1000-0887.370087
Citation: FU Jin-bo, CHEN Lan-sun. Stability of an SIR Epidemic Model With 2 Patches and Population Movement[J]. Applied Mathematics and Mechanics, 2017, 38(4): 486-494. doi: 10.21656/1000-0887.370087

Stability of an SIR Epidemic Model With 2 Patches and Population Movement

doi: 10.21656/1000-0887.370087
Funds:  The National Natural Science Foundation of China(11371306)
  • Received Date: 2016-03-28
  • Rev Recd Date: 2016-09-18
  • Publish Date: 2017-04-15
  • Based on the epidemic dynamics, in view of the population movement between 2 patches and the nonlinear infection rate, a class of SIR epidemic model with 2 patches and population movement was established. With the qualitative method and the stability method for ordinary differential equations, the permanence of the model and the existence of nonnegative equilibrium points were analyzed. Through construction of proper Lyapunov functions and according to the limit system theory, the sufficient conditions for the global asymptotic stability of the diseasefree equilibrium points and the endemic equilibrium points were obtained. The results show that, the basic reproduction number makes a threshold to determine wether the disease spreads or not. When the basic reproduction number is less than or equal to 1, the infection will gradually disappear, the virus will tend to be extinct; when the dominant regeneration number of the virus is greater than 1 and satisfies the permanence conditions, the infection will persist, and the virus will continue to prevail and become an endemic disease.
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