Global stability and cost-effectiveness analysis of COVID-19 considering the impact of the environment: using data from Ghana

•COVID-19 spread dynamics with environmental compartment is proposed.•Global stability of the disease-free and endemic equilibria was obtain using Lyapunov’s function.•Global sensitivity analysis was studied.•A cost-effectiveness analysis presented. COVID-19 potentially threatens the lives and livelihood of people all over the world. The disease is presently a major health concern in Ghana and the rest of the world. Although, human to human transmission dynamics has been established, not much research is done on the dynamics of the virus in the environment and the role human play by releasing the virus into the environment. Therefore, investigating the human-environment-human by use of mathematical analysis and optimal control theory is relatively necessary. The dynamics of COVID-19 for this study is segregated into compartments as: Susceptible (S), Exposed (E), Asymptomatic (A), Symptomatic (I), Recovered (R) and the Virus in the environment/surfaces (V). The basic reproduction number R0 without controls is computed. The application of Lyapunov’s function is used to analyse the global stability of the proposed model. We fit the model to real data from Ghana in the time window 12th March 2020 to 7th May 2020, with the aid of python programming language using the least-squares method. The average basic reproduction number without controls, R0a, is approximately 2.68. An optimal control is formulated based on the sensitivity analysis. Numerical simulation of the model is also done to verify the analytic results. The admissible control set such as: effective testing and quarantine when boarders are opened, the usage of masks and face shields through media education, cleaning of surfaces with home-based detergents, practising proper cough etiquette and fumigating commercial areas; health centers is simulated in MATLAB. We used forward-backward sweep Runge-Kutta scheme which gave interesting results in the main text, for example, the cost-effectiveness analysis shows that, Strategy 4 (safety measures adopted by the asymptomatic and symptomatic individuals such as practicing proper coughing etiquette by maintaining a distance, covering coughs and sneezes with disposable tissues or clothing and washing of hands after coughing or sneezing) is the most cost-effective strategy among all the six control intervention strategies under consideration.