Optimal control analysis of a mathematical model on smoking
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ORIGINAL ARTICLE
Optimal control analysis of a mathematical model on smoking Vinay Verma1 Received: 5 March 2020 / Accepted: 8 June 2020 © Springer Nature Switzerland AG 2020
Abstract In this paper,the dynamics of smoking behavior under the influence of educational and media programs is modeled in the presence of two control strategies. Optimal control theory is applied to a non-linear mathematical model on smoking: impact of anti-smoking campaign which helps in obtaining time dependent case detection strategy while minimizing the cost of implementation of such strategy. We prove the existence of an optimal control set and analyze the necessary and sufficient conditions, optimality and transversality conditions. The optimality of the system is deduced analytically and solved numerically. Keywords Smoking · Education · Media campaigns · Stability · Optimal control
Introduction The tobacco epidemic disease is one of the most biggest public health threats the world has ever faced, victim more than eight million people a year around the world and is required to double by 2025 (WHO (2013)). More than seven million of those dying are the outcome of observable tobacco harness until around 1.2 million are the result of non-smokers being uncovered to second-hand fume. Around 80% of the 1.1 billion smokers worldwide stay in low- and middle-income countries, where the burden of tobaccorelated sickness and death is serious. Tobacco use allow to tight circumstances by diverting family pass away from basic requirement such as food and protection to tobacco. This pass away experience is difficult to monitoring because tobacco is so addictive. The financial costs of tobacco use are sufficient and include important well-being observation costs for treating the disease raise up by tobacco use as well the missing human capital that outcome through tobaccoattributable illness and death rate. In many countries, children from penniless family are employed in tobacco farming to raise family income. These children are considerably impregnable to green tobacco sickness, which is caused by * Vinay Verma [email protected] 1
Faculty of Mathematical and Statistical Sciences, Institute of Natural Sciences & Humanities, Shri Ramswaroop Memorial University, Barabanki 225003, India
the nicotine that is absorbed through the skin from the handling of wet tobacco leaves. The flow of work, procedure, cartilage and outcomes can easily be studied with the help of mathematical concepts and theories. Therefore, biologists are now much dependent on mathematics. Mathematical modeling of biological sciences has been conducted (Biazar 2006; Busenberg et al. 1990; El-Sayed et al. 2009). The relationship during easy mathematical modeling mix biological mode, integer order differential equations that show their dynamics and complex system which describes their changing of structure. The non-linearity and multi-scale quality in mathematical modeling develop the mutual relationship between parameters (Arafa et al. 2012). In last few dicker, many biol
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