A Binary Stability and Monte Carlo Simulation Analysis of the Simultaneous Impact of Smoking on the Dynamics of Lung Cancer
Keywords:
Lung Cancer, Cigarette Smoking, Mathematical Model, sensitivity analysis, Binary Stability, Mente Carlos SimulationAbstract
In this study, the mathematical model of the dynamics of Lung cancer defined by system of non-linear ordinary differential equations was investigated. The study considered a binary stability and Mente Carlos simulation analysis approach in the determination of the impact of cigarette smoking on Lung Cancer prevalence. The analysis of a total population size in a region N(t) at any time t which is subdivided into five compartments such as, S( t) (susceptible population that is the vulnerable subpopulation who are not infected with lung cancer, but at a high risk of infection as a result of smoking), population who are active smoker ????????( t) , population who are victim of smoking Ep ( t), number of individual infected with lung cancer I( t) and number of population recovered from lung cancer R(t) was involved in the study. The positivity, uniqueness and boundedness of solutions were verified whereas the sensitivity and basic reproductive number was determined analytically. The study adopted numerical approach to achieve the objectives. On the binary stability states across parameter ranges, results obtained shows a critical value which marks the threshold for bifurcation, indicating a shift in system behaviour. The transitions are sharp in these simplified models, ideal for illustrative purposes. The sensitivity of five eigenvalues (λ1 through λ5) to changes in various parameters (r, m, g, d, h, e, f) was obtained. Generally, it is observed that on parameter dominance, the parameter m shows the highest sensitivity across all eigenvalues, with consistently positive and significant values. This suggests m is the most influential parameter in the system, Having a high positive sensitivity to parameter m (value 0.95 with negligible to no sensitivity to other parameters, except for a slight negative sensitivity to ???? (-0.05) and ℎ (-0.01). this implies the behavior of λ1 is predominantly influenced by m, while the other parameters play a minimal role. Also, the results of a Monte Carlo simulation for seven parameters highlighting their mean values and 95% confidence intervals (CIs) with a growth rate (r) mean around 0.048 and mortality rate (m) has a noticeably higher mean, around 0.097. the study has provided provides a conceptual framework to model how behaviours like smoking lead to drastic changes in health outcomes. And understanding the thresholds can inform public health policies, emphasizing the importance of early cessation before reaching critical levels of exposure.
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