Search

Smoking has become one of the major causes of health problems around the globe. It harms almost every organ of the body. It causes lung cancer and damage of different muscles. It also produces vascular deterioration, pulmonary disease, and ulcer. There is no advantage to smoking except the monetary one to the tobacco producers, manufacturers, and advertisers. Due to these facts, a passive verse active exposure of mathematical smoking model has been analyzed subject to the dynamical aspects for giving up smoking. In this context, mathematical modelling and qualitative analysis have been traced out for smoking model having five classes. Mathematical forms of smoke absent and smoke present points of equilibrium have been calculated for knowing optimal and dynamical control. By making use of the Lyapunov function theory, we have shown the global asymptotic behavior of smoke-free equilibrium for threshold parameter R0

The square-root dynamics of smoking model with cravings to smoke, in which square root of potential smokers and smokers is the interaction term, has been studied. We categorized net population in four different chambers: non-smokers/potential smokers, smokers/infected people, non-permanent smokers/temporary quitters and the permanent quitters. By dynamical systems approach, we analyzed our model. Moreover, for proving the unique equilibrium point to be globally stable, we took help of graph theoretic approach. The sensitivity analysis of the model is performed through the diseased classes effectively to design reliable, robust and stable control strategies. The model is designed like optimal control trouble to find out importance of various control actions on our system that are insisted by the sensitivity analysis. We have applied two controls, which are the awareness campaign through the media transmission to control the potential smokers and temporary quit smokers to become smokers and the treatment of smokers. Analytical and numerical methods are utilized for ensuring presence of these two control actions.

This study aims to develop a mathematical model for analyzing Lassa fever transmission dynamics and proposing effective control measures. The stability of the Lassa fever-free equilibrium point is examined and the model's accuracy is assessed using real-world data. Additionally, the parameter values and the basic reproduction number are estimated. A sensitivity analysis is also conducted, which identifies the key drivers influencing transmission dynamics. Moreover, the impact of model parameters on basic reproduction numbers is investigated. Multiple control methodologies including use of Ribavirin, implementing mobile health technology and incorporating natural predators are devised and analyzed using optimal control theory to curtail virus transmission. [ABSTRACT FROM AUTHOR]