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On the Z-type control of backward bifurcations in epidemic models. (English) Zbl 1425.92187

Summary: We investigate how the Z-type dynamic approach can be applied to control backward bifurcation phenomena in epidemic models. Because of its rich phenomenology, that includes stationary or oscillatory subcritical persistence of the disease, we consider the SIR model introduced by L. Zhou and M. Fan [Nonlinear Anal., Real World Appl. 13, No. 1, 312–324 (2012; Zbl 1238.37041)] and apply the Z-control approach in the specific case of indirect control of the infective population. We derive the associated Z-controlled model both when the desired Z-controlled equilibrium is an endemic equilibrium with a very low number of infectives and when the Z-controlled equilibrium is a disease-free equilibrium. We investigate the properties of these Z-controlled models from the point of view of the dynamical system theory and elucidate the key role of the design parameter \(\lambda\). Numerical investigations on the model also highlight the impacts of the Z-control method on the backward scenario and on a variety of dynamical regimes emerging from it.

MSC:

92D30 Epidemiology
35B32 Bifurcations in context of PDEs
35Q92 PDEs in connection with biology, chemistry and other natural sciences

Citations:

Zbl 1238.37041
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References:

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