Abstract
This paper considers the current global issue of containing the coronavirus pandemic as an optimal control problem. The goal is to determine the most advantageous levels of effectiveness of the various control and preventive measures that should be attained in order to cost effectively drive the epidemic towards eradication within a relatively short time. Thus, the problem objective functional is constructed such that it minimizes the prevalence as well as the cost of implementing the various control measures subject to a model for the disease transmission dynamics which incorporates the existing controls. The optimality system of the model is derived based on Pontryagin's maximum principle while the resulting system is solved numerically using the Runge-Kutta fourth order scheme with forward-backward sweep approach. Findings from our results show that the new cases and the prevalence of the disease can be remarkably reduced in a cost effective way, if the specified optimal levels of effectiveness of the various preventive and control measures are upheld continuously for at least a month. Moreover, the results also show that the disease can be eventually eradicated if these effectiveness levels are sustained over a reasonable length of time.
Highlights
The coronavirus disease (COVID-19), which originated from China towards the end of the year 2019, has the severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) as its causative agent
Just like similar infections caused by coronaviruses, namely the severe acute respiratory syndrome (SARS) and the middle east respiratory syndrome (MERS), the tendency of rapid said to have the most common genes of the ribonucleic acid viruses, though with possibility of genetic mutations
The foregoing is critical to the imple- the infection; the hospitalized compartment comprises of indimentation of any proposed control strategy, since it guarantees viduals who have been confirmed to be infected with disease measurable achievement on fund invested. This based on standard tests and are placed under isolation in desigpaper tries to fill this research gap as much as possible. In this nated isolation centres; the recovered compartments contains work, we investigate optimal control strategies for containing individuals who have recovered from the infection and the COVID-19 pandemic with a focus on Nigeria
Summary
We wish to determine the optimal combination of different levels of effectiveness of the controls u1, u2, u3 and u4 that will be adequate to minimize the cost of implementing the preventive measures, the cost of contact tracing of the exposed individuals, the cost of medical testing of infected individuals, and the cost associated with hospitalizing cum treating hospitalized individuals as well as reducing the prevalence of the disease within a set time frame
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