Mathematical Modelling of Tuberculosis with Vaccination and Saturated Incidence Rate in Indonesia
DOI:
https://doi.org/10.31571/ijcmasted.v1i1.1035Keywords:
Tuberculosis, Mathematical modeling, Vaccine efficacy, Vaccine rate , Latent infectionAbstract
This study was motivated by the high incidence of tuberculosis (TB) in Indonesia over the years. Various preventive intervention strategies have been developed to reduce the spread of TB among vulnerable populations. However, tuberculosis continues to contribute significantly to mortality in Indonesia. In this study, a deterministic mathematical model is proposed to describe population dynamics by combining vaccine efficacy and vaccination rates. This model includes individuals in both infectious and latent states. Individuals in the latent stage are not infectious and do not show clinical symptoms, but they carry Mycobacterium tuberculosis bacteria in their bodies. This latent state can progress to active TB when the immune system weakens. Therefore, the latent population acts as a reservoir of infection that can contribute to the emergence of new TB cases in the future. Based on TB data from Indonesia, sensitivity analyses and numerical simulations were conducted to examine the effect of variations in vaccine efficacy and vaccination rates on transmission dynamics involving the latent and infectious populations. The results showed that increasing vaccine efficacy significantly reduced the size of the latent population, which in turn decreased the transmission rate among infected individuals. Furthermore, higher vaccine efficacy reduces the controlled reproduction number affected by latent and infected groups, thereby limiting the spread of TB in susceptible populations. Furthermore, increased vaccination rates reduce the controlled reproduction number associated with latent individuals, contributing to the suppression of disease transmission. These findings highlight the importance of developing vaccines with higher efficacy and expanding vaccination coverage as key strategies for controlling and ultimately eliminating tuberculosis in the community
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