Contributed talks

Effect of a novel generalized incidence rate function in SIR model: stability switches and bifurcations

Tanuja Das

true  Wednesday, 11:00 ! Ongoingin  Room 204for  30min

In the event of a disease outbreak in a population, the incidence rate function initially increases with an increase in the number of infectives, but then decreases due to inhibitory effects before reaching saturation. To address this, a new generalized incidence rate function is proposed, and an SIR compartmental model is studied with a Holling type II saturated treatment rate function. The non-monotonic nature of this incidence rate function has an impact on the stability of endemic equilibria. Backward bifurcation, forward (transcritical) bifurcation, saddle-node bifurcation, and Hopf bifurcation are observed, leading to the possibility of multiple endemic equilibria and multi-stability. When the model system accounts for the delay in incubation, multiple Hopf bifurcations with the same frequency and two frequency Hopf-Hopf bifurcations exist, resulting in two different oscillatory solutions. The exhibition of these two-frequency oscillations are novel and have not been explored much in epidemiological models.

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