<![CDATA[Tuberculosis (TB) is a global health concern, with a significant proportion of the population at severe risk of infection. Mathematical models can provide valuable insights into the transmission dynamics of TB, especially with the use of vaccination and the mixed proportional incidence rate. In this study, we developed a compartmental model to analyze the impact of mixing proportional incidence rates with vaccination on TB transmission. We conducted a qualitative study on the mathematical model, which included showing that it is unique, positively invariant, and bounded, showing that it is epidemiologically sound to study the physical transmission of TB. We used the homotopy perturbation method to obtain numerical solutions to the model. Using python software, we simulated the obtained results, and our results show that increasing vaccination coverage is an effective measure for reducing TB incidence. Furthermore, our analysis suggests that the mixing proportional incidence rate can be used to predict the spatial spread of TB in a population. It was concluded that vaccination and proportional incidence rate mixing are critical factors to be considered when developing effective TB control strategies.]]>
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