Abstract
According to the World Health Organization (WHO), Chronic Heart Disease (CHD) is one of the greatest defies currently confronting humankind which is sweeping the whole globe, with an expanding trend in developing countries. In this paper, a mathematical model (MM) was proposed to study the connection between fish consumption and CHD mortality in Egypt, by considering a system of ordinary differential equations (ODEs) involving time-fractional derivative (FD). We considered here the study on Egypt for the ease of obtaining real data, but the method and approach adopted here is not limited to Egypt only and can be applied to any country in the world with the information of the real data related to the subject of the study. Additionally, the control function which represents the metabolic and the behavioural risk factors of CHD that help to reduce the number of mortality due to CHD is incorporated in the proposed MM. A fractional optimal control problem (FOCP) with a proposed control is formulated and studied theoretically using the Pontryagin maximum principle, to minimize the susceptible population and also to decrease the mortality rate of CHD. Moreover, firstly we discussed the positivity and boundedness of solutions; then, the model equilibria are determined and their local stability analysis was investigated; furthermore, we use the improved forward-backward sweep method (FBSM) based on the predictor-corrector method (PCM) in order to obtain the solution of proposed FOCP. In addition, some numerical simulations were performed to show the effect of the proposed optimal control (OC) besides the impact of fish consumption on the mortality of CHD.
Highlights
Chronic Heart Disease (CHD) is defined as lack of oxygen supply to the heart due to narrowing of the coronary arteries
E main aim of this paper is to find the best strategy to significantly reduce CHD mortality by using the fractional optimal control (OC) technique with consumption of an appropriate amount of fish. is is carried out by formulating a fractional mathematical model (FMM) involving a control function, which depends on the relationship between fish consumption from the fish population living along the Egyptian coasts and the dynamics of a population at risk of CHD
We discussed that a mathematical model contains the time fractional derivative (FD), which describes the relationship between fish consumption and CHD mortality in Egypt
Summary
CHD is defined as lack of oxygen supply to the heart due to narrowing of the coronary arteries (so it is called coronary artery disease). E main aim of this paper is to find the best strategy to significantly reduce CHD mortality by using the fractional OC technique with consumption of an appropriate amount of fish. Is is carried out by formulating a fractional mathematical model (FMM) involving a control function, which depends on the relationship between fish consumption from the fish population living along the Egyptian coasts and the dynamics of a population at risk of CHD. We have two trends to reduce the rate of individuals at risk of CHD: increasing fish consumption (depend on total production, imports, and exports of fishery products) and controlling metabolic and behavioural risk factors. 2. Model Formulation e first available MM was proposed by Lamlili et al [47] to study the impact of fish consumption on CHD mortality in Morocco.
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