Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1060.92041
Castillo-Chavez, Carlos; Song, Baojun
Dynamical models of tuberculosis and their applications. (English)
[J] Math. Biosci. Eng. 1, No. 2, 361-404 (2004). ISSN 1547-1063; ISSN 1551-0018/e

Summary: 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), systems of difference equations, systems of integrodifferential equations, Markov chain models, and simulation models.

MSC 2000:: *92C60 Medical epidemiology
37N25 Dynamical systems in biology
93C95 Appl. of control theory
92D30 Epidemiology

Keywords: prevention; global dynamics; bifurcation; disease emergence and reemergence; basic reproductive number

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]