Modeling the co-infection dynamics between tuberculosis and lung cancer: Insights from simulations

Abstract

The co-infection of Tuberculosis (TB) and Lung cancer poses a major global public health crisis, demanding a thorough understanding of their interactions. The interaction between diseases can be successfully modeled through a compartmental framework that incorporates TB vaccination class, manifesting critical awareness into disease propagation and treatment efficacy. The positivity, existence and invariant regions ensure biologically invariant and well-defined behaviors in the feasible region, making the model realistic. The next generation method is used to calculate the basic reproduction number $R_0$ which is pivotal in analyzing the potential for disease transmission. The sensitivity of fundamental reproduction numbers for both TB and Lung cancer was investigated using Partial Rank Correlation Coefficient analysis. Local stability at the disease-free equilibrium can be evaluated using Routh’s criteria, and global stability at the disease-free equilibrium is established through Lyapunov functions. It provides a robust framework for understanding the long-term behavior of the system. The least squares approach is used to estimate parameters, resulting in a best-fit curve that efficiently represents the underlying data. Numerical simulations, particularly using the Adams–Bashforth method, illustrate the model’s behavior under two distinct conditions: $R_0<1$ and $R_0>1$ and effect on increasing vaccine effectiveness. Furthermore, graphical representations are presented for analyzing how modifying the transmission rate affects disease progression. While modeling and analysis give helpful insights, the complexities of TB and lung cancer interactions demand more study to enhance therapies and improve health standards across populations. Understanding the complexities of this relationship is critical for controlling diseases and developing effective public health interventions.