Optimal Control Analysis of a Mathematical Model for Covid-19 Transmission Dynamics in Nigeria

The outbreak of the novel coronavirus diseases caused by SARS-CoV-2 is causing great challenges to the global health. Nonpharmaceutical interventions are being deployed due to the unavailability of certified effective drugs or vaccine for the virus. In this study, a compartmental model is formulated to explore the transmission dynamics of COVID-19 in Nigeria. The model has six non- linear differential equations which describe the spread of corona virus disease. The disease free equilibrium point and existence of endemic point was determined. The basic reproduction number which is the threshold value for determining the pattern of coronavirus disease was calculated to be R0=0.9330. Pontryagin Maximum Principle was applied on the model in order to develop strategies to counteract corona virus disease pandemic. Four control methods were used which are combination of social distance, contact tracing, treatment and face masks usage. This study reveals that observation of social distancing and uses of face masks should be strictly comply with by susceptible, exposed and infectious detected individual in order to combat COVID-19. Finally, contact tracing should be force on both exposed and infectious undetected individual with disease. Treatment is only effective at early stage of infectious detected that is between 1-20 days of detection, anything above that treatment is no longer effective.