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}) 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.
Highlights
The study of the infectious diseases dynamics is one of the most important and essential tasks to be done in order to have a good understanding of the emergence of diseases in a population
Efforts are made each year and funds are used to reduce the burden of TB, for its control through the TB stop strategy from 2015 for its elimination in 2035 in line with the Sustainable Development Goals (SDG) of the United Nations (UN) which focus on the global tuberculosis epidemic elimination
The results obtained demonstrate that control lost to follow-up and transferred individuals, monitoring contact, detection of latent individuals and their treatment are actions to be taken to reduce the incidence of the disease and effectively control it in the Democratic Republic of the Congo (DRC) population
Summary
The study of the infectious diseases dynamics is one of the most important and essential tasks to be done in order to have a good understanding of the emergence of diseases in a population. One of the main objectives of these mathematical models is to try to understand how a given disease spreads in the population, in order to try to eradicate it in the future [17]. We model, analyze and simulate a mathematical model of the dynamics of pulmonary tuberculosis with eight compartments that include groups of individuals lost to follow-up and transferred. The concluding remarks finalize this research paper In this model, infected and infectious individuals, who are in the I, Le and Lf compartments can heal spontaneously and move in the compartment R2 according, respectively, to the rates σ , g2 and k2. 3.2 Existence and uniqueness of the solution The system (1) is described by a system of autonomous non-linear first order ordinary differential equations It can be rewritten in the following matrix form:. Disease-free equilibrium (DFE) and the endemic equilibrium (EE) are found
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