Abstract
Cardiovascular diseases (CVDs) have remained the leading causes of global death in the last 16 years which is the cause of mortality of 17.7 million people every year. Nowadays, people live in a time where sitting takes up the majority of their daily affairs. The sedentary behavior for prolonged periods of time can leads to a problem of deadly disease such as heart disease, obesity, and diabetes. In this paper a deterministic model for the effects of prolonged sitting is designed. The model, which consists of three ordinary differentials equations is developed and analyzed to study the optimal control analysis on sedentary behavior, physical activity in relation to cardiovascular disease (CVD) in a community. The solutions of the model uniquely exist, nonnegative for all t ≥ 0 with nonnegative initial conditions in R3+, and bounded in a region ΩN. The basic reproduction number which measures the relationship threshold is presented. The model was extended and optimal control theory was applied to examine optimal strategies for controlling or eradicating the new cases of CVD that may be borne due to a life of inactivity. The control measures comprises of education or sensitization u1, living a healthy lifestyle (good nutrition, weight management) u2, and getting plenty of physical activity u3. The impact of using possible combinations of the three intervention strategies was investigated and analyzed. The results of the optimal control model using Pontryagin maximum principle (PMP) revealed that combination of education or sensitization with any other control strategy yields better result to reduce or eradicate the risk of new cases of CVD from sedentary lifestyle.
Highlights
Over the last hundred years, there has been a large transformation from manual labor jobs for instance, farming, manufacturing, building to office jobs which is due to many contributing factors including globalization, outsourcing of jobs and technological advances internet and computers
The main objective of this paper is to develop a basic model of sedentary behavior and physical activity in relation to cardiovascular disease using compartmental model and apply Pontryagin maximum principle to study the model optimal control analysis to understand the deep dynamical nature of the relationship
Compartment reduces until an equilibrium position is obtained due to the fact that to meet up with the daily obligation from work, they neglect engaging in profitable physical activities that can lower the risk of Cardiovascular diseases (CVDs)
Summary
Over the last hundred years, there has been a large transformation from manual labor jobs for instance, farming, manufacturing, building to office jobs which is due to many contributing factors including globalization, outsourcing of jobs and technological advances internet and computers. Modern lifestyle in nowadays requires working machines, which do much of the people’s work, eliminating the need for manual labor. Working in the office by using those machines force people to sit there for eight or more hours a day. Epidemiological evidence suggests that sedentary behavior (loosely defined as sitting, television viewing, and couch time) is associated with increased risk for at least 35 chronic diseases/clinical conditions and increased mortality rates. Epidemiological reports suggest that regular defined bouts of exercise may not protect against early mortality in certain populations if excessive sedentary behavior occurs
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