Mathematical model of COVID-19 spread in Turkey and South Africa: Theory, methods and applications

Abstract

A comprehensive study about the spread of COVID-19 cases in Turkey and South Africa has been presented in this paper . An exhaustive statistical analysis encompassing arithmetic, geometric, harmonic means, standard deviation, skewness, variance, Pearson and Spearman correlation was derived from the data collected from Turkey and South Africa within the period of 11 . It was observed that in the case of Turkey, a negative Spearman correlation for the number of infected class and a positive Spearman correlation for both the number of deaths and recoveries were obtained. This implied that the daily infections could decrease, while the daily deaths and number of recovered people could increase under current conditions. In the case of South Africa, a negative Spearman correlation for both daily deaths and daily infected people was obtained, indicating that these numbers may decrease if the current conditions are maintained. The utilization of a statistical technique predicted the daily number of infected, recovered and dead people for each country; and three results were obtained for Turkey, namely an upper boundary, a prediction from current situation and lower boundary. The prediction shows that Turkey may register in the near future approximately more than 6000 new infections in a day as worst case scenario; and less than 300 cases in the perfect scenario. However, the country could register in the near future a daily number of 27000 people recovered from COVID-19 in the perfect scenario; and less than 5000 people in a worst scenario. Moreover, Turkey in a worst-case scenario could record a high number of approximately 200 deaths per day; and less than 150 deaths in a perfect scenario. Similarly, in the case of South Africa, the prediction results show that in the near future the country could register about 500 new infected cases daily and more than 25 deaths in the worst scenario; while in a perfect scenario less than 50 new infected and zero death cases could be recorded. The histograms of the daily number of newly infected, recovered and death showed a sign of lognormal and normal distribution, which is presented using the Bell curving method parameters estimation. A new mathematical model COVID-19 comprised of nine classes was suggested; of which a formula of the reproductive number, well-poseness of the solutions and the stability analysis were presented in details. The suggested model was further extended to the scope of nonlocal operators for each case; whereby the Atangana-Seda numerical method was used to provide numerical solutions, and simulations were performed for di¤erent non-integer numbers. Additionally, sections devoted to control optimal and others dedicated to compare cases between Turkey and South Africa with the aim to comprehend why there are less numbers of deaths and infected people in South Africa than Turkey were presented in details.

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

“…It is very necessary to ensure that, the proposed optimal solution exists. For this reason, we employ Filippove-Cesari theorem as used in [37] . In this case, we show that, the existence of the optimal control solution is guaranteed if the following conditions are satisfied; The admissible control set is compact and bounded.…”

“… A linear function in the state and control variables bound the state systems of differential equations. The convexity of the integrand of cost functional with respect to u on the set A [37] . …”

“…We now have the Hessian matrix of the given cost functional as; Since the computed Hessian matrix above is everywhere positive definite, it follows that, the objective functional, Q ( u 1 , u 2 , u 3 , u 4 , u 5 ) is strictly convex [37] . We also have that, given that the integrand of the objective functional, holds under the condition Applying Pontryagin’s maximum principle where we have the state variables as and gives the Hamiltonian function; We now take into accounts the existence of the adjoint function λ i , such that they satisfy the equations; with the transversality condition given that ∀ u i where we have The optimal control strategies with respect to the befitting variation argument is given as; We progress with the numerical simulations on the optimal control by using the estimated parameters in Table 2 .…”

On forecasting the spread of the COVID-19 in Iran: The second wave

“…The work of [8] has characterized the epidemic of COVID-19 in Heilongjiang province. For more works, interested readers are referred to [9] , [10] , [11] , [12] , [13] , [14] , [15] .…”

Modeling COVID-19 Cases in Nigeria Using Some Selected Count Data Regression Models

“…Some parameters were used to calibrate the parameters of the SIRD model on the reported COVID-19 cases in Hubei region, China, the selected model was used to forecast the evolution of the outbreak at the epicenter for three weeks ahead [16]. A comprehensive comparison was carried out on COVID-19 cases using some mathematical model between Turkey and South Africa [17]. It is against this background that this study attempts to model the daily cumulative active, critical and confirmed COVID-19 cases as it influences the number of reported deaths in Nigeria between 28 th of February to 6 th of July 2020, using count regression models like; Poisson Regression (PR), Negative Binomial Regression (NBR) and Generalized Poisson Regression (GPR) models.…”