Open AccessDynamics of a Multi-Stage Epidemic Model with and without Treatment
Author(s) -
Smriti Agrawal,
Akanksha Dubey,
Nimisha Mishra*,
Joydip Dhar
Publication year - 2020
Publication title -
international journal of recent technology and engineering
Language(s) - English
Resource type - Journals
ISSN - 2277-3878
DOI - 10.35940/ijrte.c5707.018520
Subject(s) - basic reproduction number , epidemic model , equilibrium point , stability theory , mathematics , set (abstract data type) , sensitivity (control systems) , mathematical economics , computer science , mathematical analysis , physics , nonlinear system , differential equation , population , demography , engineering , quantum mechanics , electronic engineering , sociology , programming language
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.