A Novel compartmental VSLIT model used to analyze the dynamics of tuberculosis in Algeria and Ukraine and the assessment of vaccination and treatment effects

Bouchra Chennaf; Mohammed Salah Abdelouahab; René Lozi

doi:10.3842/umzh.v75i12.7658

Bouchra Chennaf Laboratory of Mathematics and Their Interactions, Abdelhafid Boussouf University Center, Mila, Algeria
Mohammed Salah Abdelouahab Laboratory of Mathematics and Their Interactions, Abdelhafid Boussouf University Center, Mila, Algeria
René Lozi Laboratoire J. A. Dieudonné, CNRS, Université Côte d'Azur, Nice, France

DOI: https://doi.org/10.3842/umzh.v75i12.7658

Keywords: Tuberculosis, epidemic, vaccination, parameter estimation, reproduction number

Abstract

UDC 517.9

Despite having low rates of tuberculosis (TB) mortality in many countries, like China, Europe, and the United States, other countries, like India continue to struggle to contain the epidemic. This study intends to examine the effects of vaccinations and treatments on the dynamics of TB in two countries, Ukraine and Algeria, with contrasted demographic profiles. A mathematical model called the VSLIT model is considered for this purpose. The stability of both disease-free and endemic equilibrium is discussed qualitatively. For numerical simulations, the parameters are evaluated by the least squares approach according to the TB-reported data for Algeria and Ukraine from 1990 to 2020.

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