A passive verses active exposure of mathematical smoking model: A role for optimal and dynamical control

Abstract 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 R 0 < 1 {R}_{0}\lt 1 . The ability to observe theoretically and through graphs is invoked to study the general behavior of single smoke present point. To make effective, vigorous, authentic, and stable strategies to control the disease, we have performed the sensitivity examination of threshold parameter and disease, present apartments.