Dynamical models of tuberculosis and their applications.

By Carlos Castillo-Ch'avez, Baojun Song. Mathematical biosciences and engineering : MBE, 2004

2,036 citations recorded by the source corpus.

The reemergence of tuberculosis (TB) from the 1980s to the early 1990s instigated extensive researches on the mechanisms behind the transmission dynamics of TB epidemics. This article provides a detailed review of the work on the dynamics and control of TB. The earliest mathematical models describing the TB dynamics appeared in the 1960s and focused on the prediction and control strategies using simulation approaches. Most recently developed models not only pay attention to simulations but also take care of dynamical analysis using modern knowledge of dynamical systems. Questions addressed by these models mainly concentrate on TB control strategies, optimal vaccination policies, approaches toward the elimination of TB in the U.S.A., TB co-infection with HIV/AIDS, drug-resistant TB, responses of the immune system, impacts of demography, the role of public transportation systems, and the impact of contact patterns. Model formulations involve a variety of mathematical areas, such as ODEs (Ordinary Differential Equations) (both autonomous and non-autonomous systems), PDEs (Partial Differential Equations), system of difference equations, system of integro-differential equations, Markov chain model, and simulation models.

Subfields: Genetics, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/52682be297a95455e5ac277dd5a7de76b7ccf50a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Genetics

1. Bruno Buonomo
2. Deborah Lacitignola
3. P. van den Driessche
4. Xiao-Qiang Zhao

In Modeling and Simulation

1. Bruno Buonomo
2. Deborah Lacitignola
3. P. van den Driessche
4. Xiao-Qiang Zhao

In Public Health, Environmental and Occupational Health

1. Bruno Buonomo
2. Deborah Lacitignola
3. Xin-You Meng
4. P. van den Driessche
5. Xiao-Qiang Zhao

Citations in the corpus

• Reproduction numbers of infectious disease models (2017, background): “However, in some models that have more complicated structure (e.g., include vaccination that is not perfect (Arino, McCluskey, & van den Driessche, 2003; Brauer, 2004; Kribs-Zaleta & VelascoHernandez, 2000)) multigroup models (Hadeler & Castillo-Ch avez, 1995) endemic equilibria may exist near the D”
• Using Mathematical Models in Controlling the Spread of Malaria (2005, neutral): “Other examples of epidemiological models with subcritical (backward) bifurcations at R0 = 1 include those described by Castillo-Chavez and Song [11], Gómez-Acevedo and Yi [28] and van den Driessche and Watmough [67].”
• On the dynamics of an SEIR epidemic model with a convex incidence rate (2008, background): “Correspondently, a negative unstable equilibrium becomes positive and locally asymptotically stable. Proof (see [ 15 ]).”
• Modelling Alcoholism as a Contagious Disease: A Mathematical Model with Awareness Programs and Time Delay (2015, background): “It is well known that delay differential equations exhibit much more complicated dynamics than ordinary differential equations since the time delay may affect the stability of the system and even lead to instability, oscillation, or bifurcation phenomena [34, 36–39].”
• Bifurcation Analysis of a Mathematical Model for Malaria Transmission (2006, neutral): “Other examples of epidemiological models with subcritical bifurcations at R0 = 1 include those described by Castillo-Chavez and Song [6], Gómez-Acevedo and Yi [13], and van den Driessche and Watmough [26].”