Abstract
Khat is a green leaf and greenish plant where its branches and leaves are chewed to discharge liquid having active chemicals that change the user’s mood. The purpose of this article is to develop and analyze a mathematical model that can be used to understand the dynamics of chewing Khat. The proposed model monitors the dynamics of five compartments, namely, a group of people who do not chew Khat, designated as N t ; a group of people who are surrounded by Khat chewers but do not chew at present and may chew Khat in the future, denoted this as Σ t ; a group of people who chew Khat, which is represented in C t ; a group of people contains individuals who consumed Khat quite temporarily for social, spiritual, and recreational purposes, and we describe this group in T t ; and a group of people those who constantly chew Khat, and they are denoted by H t . We determined the Khat chewing generation number R c 0 using the next-generation matrix method, and we have examined the biological meaningfulness, mathematical wellposedness, and stability of both Khat chewing-free and Khat chewing-present equilibrium points of the model analytically. Numerical simulations were presented by solving our dynamical system using Matlabode45 to check the analytical results by considering parameter estimations. The results of this study show that, for R c 0 = .00039 , the Khat chewing-free equilibrium point is stable, and it is unstable for R c 0 = 1.194 , and the Khat chewing-present equilibrium point is stable if R c 0 = 1.194 , and it is unstable if R c 0 = .00039 . The stability of both equilibrium points implies that, for a high rate of conversion from non-Khat chewer to exposed groups ρ , the inflow of an insignificant number of Khat chewers to the community produces a significant number of Khat chewers , and if the return back from Khat chewing to the exposed group because of socio-economic, environmental, and religious influences α 2 grows exponentially, the inflow of an insignificant number of Khat chewers to the community produces an insignificant number of Khat chewers. It is found that increasing the rate of conversion from non-Khat chewer to exposed groups ρ makes the disease eradication more challenging. We, therefore, strongly urge religious leaders, social committee leaders, elders, and health experts to teach their followers to reduce their Khat-chewing habits.
Highlights
Khat has different names in different countries
We stratified the total human population into five compartments, namely, a group of people who do not chew Khat, designated by N(t), a group of people who are surrounded by Khat chewers but do not chew at present; they may chew Khat in the future, and we denote this as Σ(t), a group of people who chew Khat, which we represent in C(t), a group of people containing individuals who consumed Khat quite temporarily for social, spiritual, and recreational purposes, and we describe this group in T(t), and a group of people those who constantly chew Khat, and they are denoted by H(t), and the general population is denoted by Z(t) and is expressed as Z(t) N(t) + Σ(t) + C(t) + T(t) + Η (t)
Theorem 3. e Khat chewing-free equilibrium point Ec∗ of (1) is stable if Rc0 < 1, and it is unstable if Rc0 > 1
Summary
Land for Khat production from 2001/2002 to 2014/2015 increased by 160%, and new areas of the country, which had not been used before, cultivated rapidly [11] It plays a significant role in the social life of many people in most parts of Ethiopia and is economically beneficial to producers. We proposed here a deterministic ordinary differential equation model that can represent the dynamics of Khatchewing communicable diseases, and its control mechanisms in public health and socio-economic crises of a country. E article is organized as follows; in the second section, we formulate a Khat-chewing model, by classifying a constant and heterogeneous entire population into five groups; in the third section, we analyzed our model, checked its biological completeness and mathematically correct significance, determined equilibrium points and the Khat-chewing generation number, and tested existence and stability of equilibrium points of the dynamical system. We conclude the manuscript with a conclusion and recommendation in the fifth section
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