Mathematical modelling and optimal cost-effective control of COVID-19 transmission dynamics

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.

Dynamics of coronavirus pandemic: effects of community awareness and global information campaigns

“…Olaniyi et al [ 28 ] formulated an epidemic model by considering the transmission routes from symptomatic, asymptomatic and hospitalized individuals. The optimal preventive measure was suggested to be better than management control in reducing the burden of the disease, but the combined control has great effect in reducing the number of infectious individuals in the population, that is the most cost-effective when compared with the single implementation of each control measure.…”

Impact of control interventions on COVID-19 population dynamics in Malaysia: a mathematical study

“…Olaniyi et al [ 59 ] formulated a deterministic model governing an autonomous system of ODEs for the dynamics of COVID-19 population in Nigeria. The study reveals that value for the disease outbreak in the country can be reduced below one if the current disease effective transmission rate is lowered by 50%.…”

Modeling of COVID-19 with limited public health resources: a comparative study of three most affected countries

“…They used different functions like Gaussian, Lognormal, Planck law function and others to fit the ratio of new daily cases per swab. A similar approach along with Gauss error function is used in [ 28 ].The authors in [ 29 ] have presented an optimal control analysis by considering preventive and management measures as two control variables, and further determined the most cost-effective control measure. A single ordinary integro-differential equation is used in [ 30 ], and its similarities with classic epidemic models are laid out along with its plus over other models.…”