Abstract
We study the qualitative behavior of a smoking model in which the population is divided into five classes, that is, non-smokers, smokers, people who temporarily quit smoking, people who permanently quit smoking, and people who are associated with illness due to smoking. The global asymptotic stability of the unique positive equilibrium point is presented. More precisely, a graph-theoretic method is used to prove the global stability of the unique positive equilibrium point.
Highlights
Smoking is one of the main causes of health problems and continues to be one of the world’s most significant health challenges
We first established the local stability of the endemic equilibrium by using a Hurwitz criterion and used a graph-theoretic approach to prove the global stability
It has been observed that the endemic level of smokers and temporarily quit smokers is decreased by increasing the factor η
Summary
Smoking is one of the main causes of health problems and continues to be one of the world’s most significant health challenges. Zaman [ ] extended the work of Castillo-Garsow et al [ ] and developed a model taking into account the occasional smokers compartment in the given smoking model and presented its qualitative behavior. The existence of endemic equilibrium and its local stability is presented in Section . In Section , we use a graph-theoretic method to show the global stability of the endemic equilibrium.
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