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| Mathematical Analysis of SIR Epidemic Model with Piecewise Infection Rate and Control Strategies |
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| KeyWord:Epidemic model, prevention and control strategy, piecewise infection rate, Hopf bifurcation |
| Author Name | Affiliation | | Yu Yang | School of Mathematics and Physics, China University of Geosciences, Wuhan, Hubei 430074, China | | Tariq Q. S. Abdullah | School of Mathematics and Physics, China University of Geosciences, Wuhan, Hubei 430074, China | | Gang Huang | School of Mathematics and Physics, China University of Geosciences, Wuhan, Hubei 430074, China | | Yueping Dong | School of Mathematics and Statistics, Central China Normal University, Wuhan, Hubei 430079, China |
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| Abstract: |
| The limitation of contact between susceptible and infected individuals plays an important role in decreasing the transmission of infectious diseases. Prevention and control strategies contribute to minimizing the transmission rate. In this paper, we propose SIR epidemic model with delayed control strategies, in which delay describes the response and effect time. We study the dynamic properties of the epidemic model from three aspects: steady states, stability and bifurcation. By eliminating the existence of limit cycles, we establish the global stability of the endemic equilibrium, when the delay is ignored. Further, we find that the delayed effect on the infection rate does not affect the stability of the disease-free equilibrium, but it can destabilize the endemic equilibrium and bring Hopf bifurcation. Theoretical results show that the prevention and control strategies can effectively reduce the final number of infected individuals in the population. Numerical results corroborate the theoretical ones. |
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