Using advanced analysis together with fractional order derivative to investigate a smoking tobacco cancer model

This research manuscript is devoted to investigate a smoking tobacco cancer model by applying some advanced techniques based on second derivative. The snuffing class is included in the construction of our model. The stability of the spread of the cancer disease due to tobacco is examined using the reproductive number concept. It is also advisable to look into the many scenarios in which the infectious classes might decline or vanish. Researchers calculated the reproductive number to create projections for the future. It hardly guarantees a thorough investigation, though. In light of this, the concept of strength number and the study of second derivatives for mathematical models are recommended using Laypunove functions to get more detailed information for future predictions. As a result, we investigate the proposed model using the second derivative technique to compute strengthen number. By calculating the aforesaid number, future proposals can be predicted. Finally, we make an effort to examine the proposed model under fractional order derivative to present some graphical simulations using different fractional order. In this regard, some numerical tools are utilized to approximate the proposed model for graphical investigations.