A mathematical model of smoking behaviour in Indonesia with density-dependent death rate

Abstract

This work presents a mathematical model that investigates the impact of smokers on the transmission dynamics of smoking behavior in the Indonesian population. The population is classified into three classes: potential smokers, smokers, and ex-smokers. This model is described by non-linear differential equations using fractional quantities instead of actual populations by scaling the population of each class by the total population. There is also the density-dependent and density-independent death rate in the model to accommodate the difference between the death rate of potential smokers, smokers, and ex-smokers. In this model, two equilibrium points are found. One of them is the smoking-free equilibrium and the other relates to the presence of smoking. Then, the local stability of both equilibrium points is examined. Lastly, numerical simulations are carried out to illustrate the sensitivity of the smoker class to the parameters: the rate of non-smokers become smokers, the rate of smokers become smokers, also the rate of ex-smokers re-adapt smoking habit. The result of this paper can be considered to make a policy to reduce the number of smokers in Indonesia.

Numerical Approximation of Riccati Fractional Differential Equation in the Sense of Caputo-Type Fractional Derivative

“…In this section, we present some basic results and definitions. For details about fractional calculus, we refer [43][44][45][46][47][48][49], and for details about modeling, we refer [50,51] and references therein.…”

Numerical Solution of Fractional-Order Fredholm Integrodifferential Equation in the Sense of Atangana–Baleanu Derivative

“…Many real-world phenomena [26][27][28][29] are analyzed via the solutions of fractional-order equations, which are derived from or based on Caputo-Liouville's operators [15,19,[30][31][32]. Meanwhile, the study of fractional-order integrodifferential equations (FIDEs) is also much important as these equations occur in many phenomena of applied nature such as electromagnetic [33] and heat conduction [34].…”