Mathemathical Modeling And Optimal Control Analysis Of Covid-19 Pandemic

Abstract

Coronaviruses (Cov) Are A Large Family Of Viruses That Cause Illness Ranging From The Commoncold To More Severe Diseases. This Study Aims To Develop And Analyze A Mathematical Model Ofcovid-19 Transmission Dynamics With Optimal Control. For This, We Formulated And Analyzeda Deterministic Mathematical Model Of Five Compartments For The Transmission Dynamicsof Covid-19 Infection Using A System Of Non-Linear Ordinary Differential Equations. These Compartments Are Namely Susceptible, Exposed, Asymptomatic, Infected And Recovered. We Investigated The Dynamical Behavior Of This Model And Performed The Qualitative Analysis Ofthe Model. The System Has Two Equilibrium Points, Namely The Disease Free Equilibrium Pointand The Endemic Equilibrium Point. The Basic Reproduction Number R0 Was Calculated Usingthe Next-Generation Matrix And The Stability Of The Equilibrium Points Were Analyzed. From The Qualitative Analysis, The Disease Free Equilibrium Point Is Both Locally And Globally Stable Ifr0 < 1, And The Endemic Equilibrium Point Is Also Both Locally And Globally Stable If R0 > 1under Some Conditions On The System Parameters. Furthermore, Sensitivity Analysis Of The Model Equation Was Performed On The Key Parameters To Find Out Their Relative Significance And Potential Impact On The Transmission Dynamics Of Covid-19. Then The Optimal Control Strategyis Found By Minimizing The Number Of Exposed And Infected Population Taking Into Account Thecost Of Prevention And Treatment. The Existence Of Optimal Controls And Characterization Isestablished With The Help Of Pontryagin?��?S Minimum Principle. Finally, Numerical Simulations Of The Model Equations Were Carried Out Using Matlab R2018b. The Findings Of This Study Shows That Comprehensive Impacts Of Personal Protective And Treatment Strategies Outperformin Reducing The Covid-19 Infection.