Global Stability Indices of the Transmission and Bilinear Control Functions for Tobacco Smoking Epidemic
DOI:
https://doi.org/10.47363/JMCA/2023(2)191Keywords:
Bassey Echeng Bassey, Igwe O Ewona, Adagba Odey Henry, Delphine Rexson BasseyAbstract
Background: The seeming insurmountable effect of tobacco-smoking, coupled with intense laxity by society towards the avalanche consequential effects of tobacco-smoking consumption and the yet-to-be-available mathematical model for comprehensive treatment of multiple effects of tobacco-smoking, necessitated this present investigation. The present research arguably presented an insight into the global stability indices of not just the impact of smoking transmission but explicitly demonstrated the methodological application of designated bilinear control functions in the presence of screening techniques for the eradication of consequential effects of smoking and tobacco consumption.
Methods: The model explored deterministic 6-subpopulations, formulated using first-order differential equations. System interactions was investigated using bilinear control functions with system well-posedness established. Furthermore, system smoking generation number for both off- and onsettreatment scenarios was determined. Analytic predictions for both local and global indices explored second additive compound matrix in conjunction with Lozinski measure . Numerical simulations evolved Runge-Kutta of order of precision 4 in a Mathcad surface.
Results: Accompanying simulations indicated protracted initial asymptomatic saddle period of smoking infection for t f < 140 days under the off-treatment scenario. Inducement of bilinear control functions under screening method yielded drastic reduction to near zero within the first t f < 80 days as vindicated by the exponential rejuvenation of potential smokers.
Conclusion: Investigation concludes that eradication of consequential effects of tobacco-smoking is achievable provided both smokers, tobacco companies and the governments implement concurrently, the application of designated bilinear control functions the world over. Immensely, the study exhibits mutual benefits to the society and scientists in the field of Bio-mathematics and epidemiologists.