article · Advances in Difference Equations
Tuberculosis remains one of the world's most deadly diseases. A mathematical model incorporating eight distinct population compartments was formulated and analysed to simulate tuberculosis transmission dynamics in the Democratic Republic of the Congo. The evaluation incorporates groups frequently neglected in standard incidence projections and calculates the basic reproduction number to assess disease management. Findings reveal that while individuals lost to follow-up or transferred pose transmission risks, active germ carriers present a greater hazard. Rapidly progressing latent cases trigger short- and medium-term rises in incidence, whereas slowly evolving latent cases sustain long-term infection and postpone disease elimination. Existing public health strategies in the Democratic Republic of the Congo have proven inadequate for eradicating the endemic condition. Simulations demonstrate that focusing interventions on rigorous contact monitoring, early identification of latent infections, and targeted treatment can dramatically decrease incidence and control transmission.
Tuberculosis remains a persistent public health emergency in endemic regions. By pinpointing how different transmission pathways and latent states affect infection rates over both short and long horizons, this research clarifies why conventional interventions fall short. It demonstrates that targeting latent cases and reinforcing contact monitoring are vital for health programmes seeking to achieve disease control and eventual elimination.
This work represents early-stage mathematical and simulation research that could inform public health policy, epidemiological planning software, and resource allocation tools. The primary prospective users are public health agencies, international health organisations, and healthcare planners operating in the Democratic Republic of the Congo. While not a direct commercial product, the findings could underpin decision-support software for designing and targeting contact tracing and diagnostic testing programmes.
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Abstract According to the World Health Organization reports, tuberculosis (TB) remains one of the top 10 deadly diseases of recent decades in the world. In this paper, we present the modeling, analysis and simulation of a mathematical model of TB transmission in a population incorporating several factors and study their impact on the disease dynamics. The spread of TB is modeled by eight compartments including different groups, which are too often not taken into account in the projections of tuberculosis incidence. The rigorous mathematical analysis of this model is provided, the basic reproduction number ( $\mathcal{R}_{0}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>R</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math> ) is obtained and used for TB dynamics control. The results obtained show that lost to follow-up and transferred individuals constitute a risk, but less than the cases carrying germs. Rapidly evolving latent/exposed cases are responsible for the incidence increasing in the short and medium term, while slower evolving latent/exposed cases will be responsible for the persistent long-term incidence and maintenance of TB and delay elimination in the population. The numerical simulations of the model show that, with certain parameters, TB will die out or sensibly reduce in the entire Democratic Republic of the Congo (DRC) population. The strategies on which the DRC’s health system is currently based to fight this disease show their weaknesses because the TB situation in the DRC remains endemic. But monitoring contact, detection of latent individuals and their treatment are actions to be taken to reduce the incidence of the disease and thus effectively control it in the population.
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DOI: 10.1186/s13662-020-03091-0
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