Mathematical modelling and optimal cost-effective control of COVID-19 transmission dynamics
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Mathematical modelling and optimal cost-effective control of COVID-19 transmission dynamics S. Olaniyi1,a
, O. S. Obabiyi2 , K. O. Okosun3 , A. T. Oladipo1, S. O. Adewale1
1 Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, Ogbomoso,
Nigeria
2 Department of Mathematics, University of Ibadan, Ibadan, Nigeria 3 Department of Mathematics, University of Kansas, Lawrence, USA
Received: 3 September 2020 / Accepted: 18 November 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The novel coronavirus disease (COVID-19) caused by a new strain of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) remains the current global health challenge. In this paper, an epidemic model based on system of ordinary differential equations is formulated by taking into account the transmission routes from symptomatic, asymptomatic and hospitalized individuals. The model is fitted to the corresponding cumulative number of hospitalized individuals (active cases) reported by the Nigeria Centre for Disease Control (NCDC), and parameterized using the least squares method. The basic reproduction number which measures the potential spread of COVID-19 in the population is computed using the next generation operator method. Further, Lyapunov function is constructed to investigate the stability of the model around a disease-free equilibrium point. It is shown that the model has a globally asymptotically stable disease-free equilibrium if the basic reproduction number of the novel coronavirus transmission is less than one. Sensitivities of the model to changes in parameters are explored, and safe regions at certain threshold values of the parameters are derived. It is revealed further that the basic reproduction number can be brought to a value less than one in Nigeria, if the current effective transmission rate of the disease can be reduced by 50%. Otherwise, the number of active cases may get up to 2.5% of the total estimated population. In addition, two time-dependent control variables, namely preventive and management measures, are considered to mitigate the damaging effects of the disease using Pontryagin’s maximum principle. The most cost-effective control measure is determined through cost-effectiveness analysis. Numerical simulations of the overall system are implemented in MatLab for demonstration of the theoretical results.
1 Introduction It is no longer news that the current global threat to human existence is the novel coronavirus disease (COVID-19), which is caused by a new strain of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). The disease was first reported to the World Health Organization (WHO) in late December, 2019 in Wuhan, Hubei Province, China [1,2]. COVID-19 has been declared as a pandemic (global epidemic) affecting over 200 countries and territories
a e-mail: [email protected] (corresponding author)
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around the world.
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