Abstract
An epidemic model with non-monotonic incidence rate under a limited resource for treatment is proposed to understandthe e ect of the capacity for treatment. We have assume that treatment rate is proportional to the number of infectivewhen it is below the capacity and is a constant when the number of infective is larger than the capacity. Existence andstability of the disease free and endemic equilibrium are investigated for both the cases. Some numerical simulations aregiven to illustrate the analytical results.
Highlights
The incidence in an epidemiological model is the rate at which susceptible become infectious
Ruan and Wang (2003) studied an epidemic model with a specific nonlinear incident rate λI2S /(1 + αI2) and presented a detailed qualitative and bifurcation analysis of the model. They derived sufficient conditions to ensure that the system has none, one, or two limit cycles and showed that the system undergoes a Bogdanov-Takens bifurcation at the degenerate equilibrium which include a saddle-node bifurcation, a Hopf bifurcation, and homoclinic bifurcation
In our proposed model we have considered an epidemic model with non monotonic incidence rate under the treatment
Summary
The incidence in an epidemiological model is the rate at which susceptible become infectious. Ruan and Wang (2003) studied an epidemic model with a specific nonlinear incident rate λI2S /(1 + αI2) and presented a detailed qualitative and bifurcation analysis of the model. They derived sufficient conditions to ensure that the system has none, one, or two limit cycles and showed that the system undergoes a Bogdanov-Takens bifurcation at the degenerate equilibrium which include a saddle-node bifurcation, a Hopf bifurcation, and homoclinic bifurcation. Every country or society should have a suitable capacity for treatment If it is too large, the country or society pays for unnecessary cost.
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