Markers of Disease Evolution: The Case of Tuberculosis

doi:10.1006/jtbi.2001.2489

Journal of Theoretical Biology

Volume 215, Issue 2, 21 March 2002, Pages 227-237

https://doi.org/10.1006/jtbi.2001.2489 Get rights and content

Abstract

Abrupt changes in environmental conditions—broadly understood to include demographic and social dynamics—can seriously impact the local or global disease dynamics of a population. These changes in the evolutionary landscape, which may occur over relatively short time-scales, are very likely to play a critical role in disease evolution. The potential impact of demographic, social and epidemiological shifts on the evolution of tuberculosis epidemics in the United States over the past century and a half is the main subject of this article. Evidence is provided to support the hypothesis that the observed substantial decreases in the incidence of active tuberculosis are the result of abrupt reductions in the rates of disease progression.

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Tuberculosis remains one of the most dangerous diseases globally and has affected many people in Sub-Saharan Africa. In this paper, a fractional stochastic model of tuberculosis disease was formulated and analyzed. The existence and uniqueness of solutions are presented in the new approach far from the deterministic fractional operators. We carry out numerical simulations of the model using three fractional operators. Our numerical results suggest that the Caputo–Fabrizio operator has a more random effect among the three different operators than the Atangana–Baleanu and the Caputo operators. Further, it is envisaged that the fractional-order derivatives significantly impact the dynamics of the disease.
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That is to say, some acute cases become infected where their symptoms are obvious. Others enter the latent state, they are temporarily not infectious individuals [2,4,14,32–34,59,70,74,75,87]; (4) Given incomplete treatment, many patients stop the treatment process before they recover, and considering that they are not infectious individuals, it is assumed that they return to the latent state [16,29,32,56,59,79,107,108];
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Regular ArticleMarkers of Disease Evolution: The Case of Tuberculosis

Abstract

Clin. Chest. Med.

Lancet

Long-term dynamics and re-emergence of tuberculosis

Population dynamics: a Poisson approximation and its relation to the Langevin process

Phys. Rev. Lett.

Risk factors for a positive tuberculin skin test among employees of an urban, midwestern teaching hospital

Ann. Intern. Med.

The Making of a Social Disease: Tuberculosis in the Nineteenth-Century France

The intrinsic transmission dynamics of tuberculosis epidemics

Nature Med.

Cross-immunity in the dynamics of homogeneous and heterogeneous populations

Epidemiological models with age-structure, proportionate mixing, and cross-immunity

J. Math. Biol.