Dynamics of a Multi-Stage Epidemic Model with and without Treatment
Smriti Agrawal1, Akanksha Dubey2, Nimisha Mishra3, Joydip Dhar4
1Smriti Agrawal, Amity School Of Applied Sciences, Amity University, Lucknow, Uttar Pradesh, India.
2Akanksha Dubey, Amity School Of Applied Sciences, Amity University, Lucknow, Uttar Pradesh, India.
3Nimisha Mishra*, Amity School Of Applied Sciences, Amity University, Lucknow, Uttar Pradesh, India.
4Joydip Dhar, ABV – Indian Institute of Information Technology and Management, Gwalior, Madhya Pradesh, India.

Manuscript received on January 05, 2020. | Revised Manuscript received on January 25, 2020. | Manuscript published on January 30, 2020. | PP: 5293-5300 | Volume-8 Issue-5, January 2020. | Retrieval Number: C5707098319/2020©BEIESP | DOI: 10.35940/ijrte.C5707.018520

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Abstract: In this paper, a non-linear mathematical model is proposed with the thought of treatment to depict the spread of infectious illness and assessed with three contamination stages. We talk about the dynamical behaviour and analytical study of the framework for the mathematical model which shows that it has two non-negative equilibrium points i.e., disease-free equilibrium (DFE) and interior(endemic) equilibrium. The outcomes show that the dynamical behaviour of the model is totally determined by the basic reproduction number. For the basic reproduction number , the disease-free equilibrium is locally as well as globally asymptotically stable under a particular parameter set. In case , the model at the interior equilibrium is locally as well as globally asymptotically stable. Finally, numerical solutions of the model corroborate the analytical results and facilitate a sensitivity analysis of the model parameters.
Keywords: Epidemic Model, Three Stages of Treatment, Basic Reproduction Number, Global Stability, Local Stability, Sensitivity Analysis.
Scope of the Article: Foundations Dynamics.