Dynamical Models of Tuberculosis and Their Applications - Carlos Castillo-Chavez; Baojun Song (Mathematical Biosciences and Engineering)
The reemergence of tuberculosis (TB) from the 1980s to the early1990s instigated extensive researches on the mechanisms behind thetransmission dynamics of TB epidemics. This article provides adetailed review of the work on the dynamics and control of TB. Theearliest mathematical models describing the TB dynamics appeared inthe 1960s and focused on the prediction and control strategies usingsimulation approaches. Most recently developed models not only payattention to simulations but also take care of dynamical analysisusing modern knowledge of dynamical systems. Questions addressed bythese models mainly concentrate on TB control strategies, optimalvaccination policies, approaches toward the elimination of TB in theU.S.A., TB co-infection with HIV/AIDS, drug-resistant TB, responsesof the immune system, impacts of demography, the role of publictransportation systems, and the impact of contact patterns. Modelformulations involve a variety of mathematical areas, such as ODEs(Ordinary Differential Equations) (both autonomous andnon-autonomous systems), PDEs (Partial Differential Equations),system of difference equations, system of integro-differentialequations, Markov chain model, and simulation models.