arXiv subjects

Samuel Okyere

Publications and source records attributed to Samuel Okyere.

4 recordsLinked to original sources

arXiv2022

A mathematical model of COVID-19 with an underlying health condition using fraction order derivative

Studies have shown that some people with underlying conditions such as cancer, heart failure, diabetes and hypertension are more likely to get COVID-19 and have worse outcomes. In this paper, a fractional-order derivative is proposed to study the transmission dynamics of COVID-19 taking into consideration population having an underlying condition. The fractional derivative is defined in the Atangana Beleanu and Caputo (ABC) sense. For the proposed model, we find the basic reproductive number, the equilibrium points and determine the stability of these equilibrium points. The existence and the uniqueness of the solution are established along with Hyers Ulam Stability. The numerical scheme for the operator was carried out to obtain a numerical simulation to support the analytical results. COVID-19 cases from March to June 2020 of Ghana were used to validate the model. The numerical simulation revealed a decline in infections as the fractional operator was increased from 0.6 within the 120 days. Time-dependent optimal control was incorporated into the model. The numerical simulation of the optimal control revealed, vaccination reduces the number of individuals susceptible to the COVID-19, exposed to the COVID-19 and Covid-19 patients with and without an underlying health condition.

q-bio.PE↗

arXiv2022

An Optimal Control Model of transmission dynamics of COVID-19 in Ghana

Almost every country in the world is battling to limit the spread of COVID-19. As the world strives to get an effective medication to control the disease, appropriate intervention measures, for now, remains one of the effective methods to reduce the spread of the disease. Optimal control strategies have proven to be an effective method in curtailing the spread of infectious diseases. In this paper, a model has been formulated to study transmission dynamics of the disease. Basic properties of the model such as the basic reproduction number, equilibrium points and stability of the equilibrium points have been determined. Sensitivity analysis was carried on to determine the impact of the model parameters on the basic reproduction number. We also introduced a compartment for the deceased and examined the behaviour of COVID-19 related deaths. The numerical simulation prediction is consistent with real data from Ghana for the period March 2020 to March 2021. The simulation revealed the disease had less impact on the population during the first seven months of the outbreak. To help contain the spread of the disease, time dependent optimal controls were incorporated into the model and Pontryagin maximum principle was used to characterize vital conditions of the optimal control model. Numerical simulations of the optimal control model showed that, combination of optimal preventive strategies such as nose mask and vaccination are effective to significantly decrease the number of COVID-19 cases in different compartments of the model. Vaccination decreases the susceptibility to the disease whereas mask usage preserved the susceptible population from extinction.

q-bio.PE↗

arXiv2022

Fractional Optimal Control Model of SARS-CoV-2 (COVID-19) Disease in Ghana

Research focus on optimal control problems brought on by fractional differential equations has been extensively applied in practice. However, because they are still open-ended and challenging, a number of problems with fractional mathematical modeling and problems with optimal control require additional study. Using fractional-order derivatives defined in the Atangana Baleanu Caputo sense, we alter the integer-order model that has been proposed in the literature. We prove the solution's existence, uniqueness, equilibrium points, fundamental reproduction number, and local stability of the equilibrium points. The operator's numerical approach was put into practice to obtain a numerical simulation to back up the analytical conclusions. Fractional optimum controls were incorporated into the model to identify the most efficient intervention strategies for controlling the disease. Utilizing actual data from Ghana for the months of March 2020 to March 2021, the model is validated. The simulation's results show that the fractional operator significantly affected each compartment and that the incidence rate of the population rose when v>0.6. The examination of the most effective control technique discovered that social exclusion and vaccination were both very effective methods for halting the development of the illness.

q-bio.PE↗

arXiv2022

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

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 reproduction number 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 COVID-19 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 COVID-19 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.

q-bio.PE↗