DYNAMICAL MODELS OF TUBERCULOSIS AND THEIR APPLICATIONS

DYNAMICAL MODELS OF TUBERCULOSIS AND THEIR APPLICATIONS

September 2004 | CARLOS CASTILLO-CHAVEZ, BAOJUN SONG
The reemergence of tuberculosis (TB) in the 1980s and early 1990s prompted extensive research into the transmission dynamics of TB epidemics. This article provides a comprehensive review of the dynamics and control strategies of TB, covering models from the 1960s to the present. Early models focused on prediction and control strategies using simulation approaches, while more recent models incorporate dynamical analysis using modern dynamical systems theory. The models address various aspects of TB control, including optimal vaccination policies, elimination strategies in the U.S.A., co-infection with HIV/AIDS, drug-resistant TB, immune system responses, demographic impacts, public transportation systems, and contact patterns. The models use a variety of mathematical frameworks, including ordinary differential equations (ODEs), partial differential equations (PDEs), systems of difference equations, systems of integro-differential equations, Markov chain models, and simulation models. The article is structured into several sections, starting with an introduction to TB, its historical context, and the impact of effective antibiotics. It then reviews early dynamical models, exploring the impact of epidemiological factors and contact types on TB dynamics. The role of demography and cell-based models at the immune system level is discussed, followed by a Markov chain model on TB projections. The article also covers models dealing with TB control strategies, the impact of public mass transportation, and a list of challenges associated with modeling TB dynamics. The review highlights the evolution of TB models from simple compartmental models to more complex, realistic frameworks that incorporate various biological and social factors.The reemergence of tuberculosis (TB) in the 1980s and early 1990s prompted extensive research into the transmission dynamics of TB epidemics. This article provides a comprehensive review of the dynamics and control strategies of TB, covering models from the 1960s to the present. Early models focused on prediction and control strategies using simulation approaches, while more recent models incorporate dynamical analysis using modern dynamical systems theory. The models address various aspects of TB control, including optimal vaccination policies, elimination strategies in the U.S.A., co-infection with HIV/AIDS, drug-resistant TB, immune system responses, demographic impacts, public transportation systems, and contact patterns. The models use a variety of mathematical frameworks, including ordinary differential equations (ODEs), partial differential equations (PDEs), systems of difference equations, systems of integro-differential equations, Markov chain models, and simulation models. The article is structured into several sections, starting with an introduction to TB, its historical context, and the impact of effective antibiotics. It then reviews early dynamical models, exploring the impact of epidemiological factors and contact types on TB dynamics. The role of demography and cell-based models at the immune system level is discussed, followed by a Markov chain model on TB projections. The article also covers models dealing with TB control strategies, the impact of public mass transportation, and a list of challenges associated with modeling TB dynamics. The review highlights the evolution of TB models from simple compartmental models to more complex, realistic frameworks that incorporate various biological and social factors.
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Understanding Dynamical models of tuberculosis and their applications.