Analysis and simulation of a mathematical model of tuberculosis transmission in Democratic Republic of the Congo

• Published in: Advances in difference equations Vol. 2020; no. 1; pp. 1 - 19
• Main Authors: Kasereka Kabunga, Selain, Doungmo Goufo, Emile F., Ho Tuong, Vinh
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 16.11.2020; Springer Nature B.V; Hindawi Publishin Corporation / SpringerOpen; SpringerOpen
• Subjects: Analysis; Cases (containers); Difference and Functional Equations; Differential equations; Disease; Disease control; DRC; Equation-based model; Evolution; Functional Analysis; Mathematical model; Mathematical models; Mathematical Models of Infectious Diseases; Mathematics; Mathematics and Statistics; Modeling-simulation; Ordinary Differential Equations; Partial Differential Equations; Population; Simulation; Tuberculosis; Congo-Democratic Republic of Congo; Modeling-simulation; Tuberculosis; Equation-based model; DRC; Mathematical model; Differential equations; Tuberculosis Mathematical model Modeling-simulation DRC Equation-based model Differential equations
• ISSN: 1687-1847; 1687-1839; 1687-1847
• DOI: 10.1186/s13662-020-03091-0

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 ( 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.