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An SIRS epidemiological model with immunity caused by low level of infection. (English) Zbl 0832.92020

Summary: It has been seen in many epidemic diseases that low level exposure of a susceptible individual to infection of a disease for a certain interval of time can cause immunity in that individual whereas to transmit infection an exposure to a higher level of infection, viz., number of bites by the infected mosquitoes, number of bacteria, virus etc. during that interval is required. Here, these properties of transmission of a disease have been considered by constructing an SIRS epidemiological model with nonlinear incidence rate \(\beta_1 I^p S\) \((p > 1)\) for infection and bilinear incidence rate \(\beta_2 IS\) for causing immunity. The dynamics of the model have been investigated.

MSC:

92D30 Epidemiology
34D05 Asymptotic properties of solutions to ordinary differential equations
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