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Dynamic behaviors of a modified SIR model in epidemic diseases using nonlinear incidence and recovery rates

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  • Gui-Hua Li
  • Yong-Xin Zhang

Abstract

The transmission of infectious diseases has been studied by mathematical methods since 1760s, among which SIR model shows its advantage in its epidemiological description of spread mechanisms. Here we established a modified SIR model with nonlinear incidence and recovery rates, to understand the influence by any government intervention and hospitalization condition variation in the spread of diseases. By analyzing the existence and stability of the equilibria, we found that the basic reproduction number R 0 is not a threshold parameter, and our model undergoes backward bifurcation when there is limited number of hospital beds. When the saturated coefficient a is set to zero, it is discovered that the model undergoes the Saddle-Node bifurcation, Hopf bifurcation, and Bogdanov-Takens bifurcation of codimension 2. The bifurcation diagram can further be drawn near the cusp type of the Bogdanov-Takens bifurcation of codimension 3 by numerical simulation. We also found a critical value of the hospital beds bc at R 0

Suggested Citation

  • Gui-Hua Li & Yong-Xin Zhang, 2017. "Dynamic behaviors of a modified SIR model in epidemic diseases using nonlinear incidence and recovery rates," PLOS ONE, Public Library of Science, vol. 12(4), pages 1-28, April.
    • Handle: RePEc:plo:pone00:0175789
    DOI: 10.1371/journal.pone.0175789
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