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Global dynamics of autonomous and nonautonomous SI epidemic models with nonlinear incidence rate and feedback controls

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Abstract

This paper discusses autonomous and nonautonomous epidemic models with nonlinear incidence rate of saturated mass action and feedback controls. The global asymptotic stability of disease-free equilibrium and the endemic equilibrium of the autonomous system is established using suitable Lyapunov functional. It is shown that by choosing suitable values of feedback control variables, one can make the disease endemic or extinct as time evolves. Moreover, the effect of coefficient of inhibition on the persistence of disease is also discussed. We discuss the permanence, existence, uniqueness and asymptotic stability of an almost periodic solution of the model. The analytical results obtained in this paper are illustrated with the help of numerical examples.

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Acknowledgments

We are very thankful to the anonymous reviewers and the handling editor for their constructive comments and suggestions which helped us to improve the quality of the paper. This work is fully supported by Central University of Rajasthan, India

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Authors and Affiliations

  1. Department of Mathematics, Central University of Rajasthan, NH-8, Bandarsindri, Kishangarh, Ajmer, Rajasthan, 305801, India

    Jai Prakash Tripathi

  2. School of Basic Sciences, Indian Institute of Technology Mandi, Mandi, Himachal Pradesh, 175001, India

    Syed Abbas

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Tripathi, J.P., Abbas, S. Global dynamics of autonomous and nonautonomous SI epidemic models with nonlinear incidence rate and feedback controls. Nonlinear Dyn 86, 337–351 (2016). https://doi.org/10.1007/s11071-016-2892-0

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