Mathematical analysis of giving up smoking model via harmonic mean type incidence rate

摘要

This article deals with qualitative analysis of a smoking model and provides parametric conditions for controlling diseases under the influence of smoking. The model is obtained by taking into account a novel uptake function, which relates the incidence of potential smoker with occasional smoker, of harmonic mean type for the potential and occasional smokers. Introducing a new type of incidence rate, the local as well as global stabilities for the proposed model are discussed at its steady–states. Minimizing the number of individuals involved in a substance abuse in any community is very difficult task, therefore we have introduced four control variables in the controlled system. Pontrygin’s maximum principal is used to derive optimality system. Finally, the obtained results are illustrated numerically and graphically.