Modelling the potential impact of TB-funded prevention programs on the transmission dynamics of TB

Tuberculosis (TB) continues to be a major global health challenge, with millions of new cases and deaths each year despite the massive efforts and funding put in the fight against the disease. In this paper, we develop a mathematical model to evaluate the impact of TB-funded prevention programs on the transmission dynamics of TB. The model incorporates stages of TB infection (latent and active), and accounts for the effects of treatment, funding and TB-funded prevention programs. Our analysis shows that increased funding and enhanced prevention programs reduce the number of active TB cases, thereby decreasing the reproduction number and TB endemicity. Specifically, higher funding rates lead to improved prevention and treatment outcomes, resulting in the lowering of the effective reproduction number <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>(</mml:mo> <mml:mrow> <mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow> <mml:mrow><mml:mn>0</mml:mn></mml:mrow> </mml:msub> </mml:mrow> <mml:mo>)</mml:mo></mml:mrow> </mml:math> and reduced transmission. The model's steady states are determined and it is shown that the model has a disease-free equilibrium that is locally asymptotically stable whenever <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow> <mml:mrow><mml:mn>0</mml:mn></mml:mrow> </mml:msub> <mml:mo><</mml:mo> <mml:mn>1</mml:mn></mml:math> and multiple endemic equilibria for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup><mml:mrow><mml:mi>R</mml:mi></mml:mrow> <mml:mrow><mml:mn>0</mml:mn></mml:mrow> <mml:mrow><mml:mi>c</mml:mi></mml:mrow> </mml:msubsup> <mml:mo><</mml:mo> <mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow> <mml:mrow><mml:mn>0</mml:mn></mml:mrow> </mml:msub> <mml:mo><</mml:mo> <mml:mn>1</mml:mn></mml:math> and a unique endemic equilibrium for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow> <mml:mrow><mml:mn>0</mml:mn></mml:mrow> </mml:msub> <mml:mo>></mml:mo> <mml:mn>1</mml:mn></mml:math> . The model is shown to exhibit a backward bifurcation that vanishes as the funding for TB is increased. The paper also highlights that treatment alone, while beneficial, is less effective than a combined strategy involving funding and prevention. Numerical simulations are carried out and the influences of various parameters on the effective reproduction number are investigated. The implications of TB-funded prevention programs on TB dynamics and control of TB are discussed and valuable insights for policymakers in designing effective TB control programs are highlighted.