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Dynamics of an SEIR epidemic model with nonlinear incidence and treatment rates

Publication Type : Journal Article

Publisher : Nonlinear Dynamics

Source : Nonlinear Dynamics 96, 2351–2368

Campus : Coimbatore

School : School of Engineering

Center : Amrita Innovation & Research

Department : Mathematics

Verified : Yes

Year : 2019

Abstract : The control of highly contagious diseases is very important today. In this paper, we proposed an SEIR model with Crowley–Martin-type incidence rate and Holling type II and III treatment rates. Dynamics of the spread of infection and its control are performed for both the cases of treatment functions. We have performed the stability and bifurcation analyses of the model system. The sensitivity analysis of all the parameters with respect to the basic reproduction number has been performed. Furthermore, we discussed the optimal control strategy using Pontryagin’s maximum principle and determined the effect of control parameter u on the model dynamics. Moreover, we validate the theoretical results using numerical simulations. Between both the treatment functions, we observe that the implementation of Holling type II treatment is most effective to prevent the spread of diseases.

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