A new approach of exogenous effects in SIR epidemic models

Abstract

In this work, we study the dynamical behavior of a modified SIR epidemiological model by introducing exogenous effects. Controlling the reproduction rate is considered by the addition of a slow feedback effect given by an exponent and the infertility by a fraction, both influencing pandemics. An analytic expression of the replacement ratios that depend on the effects is determined. The results obtained show that the local stability of the disease-free equilibrium is determined by the value of a certain threshold parameter, and the local stability of the free disease equilibrium depends on the replacement ratios. Qualitative analysis shows that the slowing feedback exponent promotes more changes in the propagation of the disease than other parameters. A Hopf bifurcation is also analytically verified in terms of some parameters. Finally, sensitivity analysis and simulations show the efficiency of feedback and partial infertility in the dynamics of an epidemic model.

References

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