A Mathematical Model of Transmission Dynamics of SARS-CoV-2 (COVID-19) with an Underlying Condition of Diabetes

Abstract

It is well established that people with diabetes are more likely to have serious complications from COVID-19. Nearly 1 in 5 COVID-19 deaths in the African region are linked to diabetes. World Health Organization (WHO) finds that 18.3% of COVID-19 deaths in Africa are among people with diabetes. In this paper, we have formulated and analysed a mathematical comorbidity model of diabetes-COVID-19 of the deterministic type. The basic properties of the model were explored. The basic reproductive number, equilibrium points, and stability of the equilibrium points were examined. Sensitivity analysis of the model was carried on to determine the impact of the model parameters on the basic reproductive number R 0 of the model. The model had a unique endemic equilibrium point, which was stable for R 0 > 1 . Time-dependent optimal controls were incorporated into the model with the sole aim of determining the best strategy for curtailing the spread of the disease. COVID-19 cases from March to September 2020 in Ghana were used to validate the model. Results of the numerical simulation suggest a greater number of individuals deceased when the infected individual had an underlying condition of diabetes. More so, the disease is endemic in Ghana with the basic reproduction number found to be R 0 = 1.4722 . The numerical simulation of the optimal control model reveals the lockdown control minimized the rate of decay of the susceptible individuals whereas the vaccination led to a number of susceptible individuals becoming immune to COVID-19 infections. In all, the two preventive control measures were both effective in curbing the spread of the disease as the number of COVID-19 infections was greatly reduced. We conclude that more attention should be paid to COVID-19 patients with an underlying condition of diabetes as the probability of death in this population was significantly higher.

Modeling and analysis of monkeypox disease using fractional derivatives

“…The model has a unique endemic equilibrium point if the following Routh-Hurwitz conditions are satisfied: g 1 > 0, g 3 > 0 and g 1 g 2 > g 3 [ 32 ]…”

“…On May 24, 2022, when the first five cases of monkeypox are confirmed by Ghanaian authorities [ 14 ], we start our simulation. The population of Ghana is 30.8 million, according to the 2021 Population and Housing Census [ 12 ]. The total population under study, N = 30.8 million, is taken into account in our model, which is in agreement.…”

Optimal control model of human-to-human transmission of monkeypox virus

“…Theorem 1 There is a domain 0 ≤ Φ < ∞ that contains and bounds the solution set (H S , H E , H I , H Q , H R , D) of the system (1). 8 Proof Considering the solution set…”

“…Mathematical models has been used to study the dynamics of diseases in the past. [4][5][6][7][8] The transmission of the Cholera-COVID-19 co-infection in Yemen was studied using an ordinary differential equation model, according to Hezam et al 4 To reduce the number of cases in the community, they built the model with the best control strategies, including social isolation, lockdown, the number of tests, and the quantity of chlorine water tablets. To analyze the transmission of cholera, Tessema et al 5 devised a mathematical model that included drug resistance and immunization of newborns.…”

Stability and Sensitivity Analysis of the COVID-19 Spread with Comorbid Diseases

“…In [29,30], the COVID-19 spread is examined where the individuals with comorbid diseases having interventions of natural remedies and vaccination. Okyere and Ackora-Prah [31] analyzed the COVID-19 transmission dynamics by taking into account of diabetes.…”