Qualitative Analysis of the Transmission Dynamics and Optimal Control of Covid-19

Globally, the COVID-19 presents a serious concern to the wellbeing of people. COVID-19 was first detected in Wuhan, China. The disease became a source of concern for Nigerians after the country registered its first case in February 2020. Currently, the country has recorded 255,103 confirmed cases, 249,246 recovered cases, and 3,142 deaths as of March 21, 2022. We proposed a SEQIHRV model to investigate the spread of coronavirus disease in Nigeria. This model defines the infection dynamics' transmission routes as well as effect of contaminated surfaces on the human population. Unfortunately, the virus's propagation and mortality from COVID-19 is increasing daily. Therefore, it is required to manage and control the flow of the infection. The impact of control measures as time-dependent interventions was investigated in this study utilizing optimization technique to determine their effects on the spread of Corona virus. The basic reproduction was calculated and used to calcite the sensitive parameters affecting the system, which revealed the key parameters leading to COVID-19 propagation. The control optimization of the sytem was performed using Pontryagin's maximum principle to determine the best approach for controlling the spread. The discoveries from the simulation showed that the combination of all four control approaches will help to reduce infection to zero in the population.