A novel tuberculosis model incorporating a Caputo fractional derivative and treatment effect via the homotopy perturbation method

Abstract

Background Tuberculosis (TB), caused by Mycobacterium tuberculosis, is a contagious infectious disease that primarily targets the lungs but can also impact other critical systems such as the bones, joints, and neurological system. Despite significant efforts to combat TB, it remains a major global health concern. To address this challenge, this study aims to explore and evaluate various tuberculosis control approaches using a mathematical modeling framework. Results The study utilized a novel SEITR mathematical model to investigate the impact of treatment on physical limitations in tuberculosis. The model underwent qualitative analysis to validate key aspects, including positivity, existence, uniqueness, and boundedness. Disease-free and endemic equilibria were identified, and both local and global stability of the model was thoroughly examined using the derived reproduction number. To estimate the impact of each parameter on each compartment, sensitivity analysis was conducted, and numerical simulations were performed using Maple 18 software with the homotopy perturbation method. The obtained results are promising and highlight the potential of the proposed interventions to significantly reduce tuberculosis virus prevalence. The findings emphasize the significance of fractional-order analysis in understanding the effectiveness of treatment strategies for mitigating tuberculosis prevalence. The study suggests that the time fractional dynamics of TB treatment correspond to the treatment’s efficacy, as the conceptual results showed that non-local interactions between the disease and the treatment may lead to more accurate ways of eradicating tuberculosis in real-world scenarios. These insights contribute to a better understanding of effective treatment strategies and their potential impact on tuberculosis control and public health. Conclusions In conclusion, scientists, researchers, and healthcare personnel are urged to take action and utilize the discoveries from this research to facilitate the eradication of the hazardous tuberculosis bacteria.

Caputo-Fabrizio Fractional Order Epidemiological Model of Tuberculosis Transmission along with Imperfect Vaccination, Exogenous Reinfection and Endogenous Reactivation

“…The time fractional dynamics of TB treatment correspond to the treatment's efficacy [43]. The study suggests that non-local interactions between the disease and the treatment may lead to more accurate ways of eradicating tuberculosis in real-world scenarios [43].…”

“…This is particularly important in the case of tuberculosis as the progression of the disease inside the body of a susceptible individual starts with infection and can remain latent for some time [42]. The time fractional dynamics of TB treatment correspond to the treatment's efficacy [43]. The study suggests that non-local interactions between the disease and the treatment may lead to more accurate ways of eradicating tuberculosis in real-world scenarios [43].…”

Deterministic and Stochastic Nonlinear Model for Transmission Dynamics of COVID-19 with Vaccinations Following Bayesian-Type Procedure

“…Compartmental models have been essentials tools for understanding the transmission dynamics of various infectious diseases. Researchers in this regard have formulated various mathematical models; we refer to [12]. In the same way, the author of [8] developed a SIRDtype model to investigate the transmission of COVID-19 in different countries.…”