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.

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BackgroundThe increasing prevalence of colorectal cancer (CRC) in China and the paucity of information about relevant expenditure highlight the necessity of better understanding the financial burden and effect of CRC diagnosis and treatment. We performed a survey to quantify the direct medical and non-medical expenditure as well as the resulting financial burden of CRC patients in China.MethodsWe conducted a multicenter, cross-sectional survey in 37 tertiary hospitals in 13 provinces across China between 2012 and 2014. Each enrolled patient was interviewed using a structured questionnaire. All expenditure data were inflated to the 2014 Chinese Yuan (CNY; 1 CNY = 0.163 USD). We quantified the overall expenditure and financial burden and by subgroup (hospital type, age at diagnosis, sex, education, occupation, insurance type, household income, clinical stage, pathologic type, and therapeutic regimen). We then performed generalized linear modeling to determine the factors associated with overall expenditure.ResultsA total of 2356 patients with a mean age of 57.4 years were included, 57.1% of whom were men; 13.9% of patients had stage I cancer; and the average previous-year household income was 54,525 CNY. The overall average direct expenditure per patient was estimated to be 67,408 CNY, and the expenditures for stage I, II, III, and IV disease were 56,099 CNY, 59,952 CNY, 67,292 CNY, and 82,729 CNY, respectively. Non-medical expenditure accounted for 8.3% of the overall expenditure. The 1-year out-of-pocket expenditure of a newly diagnosed patient was 32,649 CNY, which accounted for 59.9% of their previous-year household income and caused 75.0% of families to suffer an unmanageable financial burden. Univariate analysis showed that financial burden and overall expenditure differed in almost all subgroups (P < 0.05), except for sex. Multivariate analysis showed that patients who were treated in specialized hospitals and those who were diagnosed with adenocarcinoma or diagnosed at a later stage were likely to spend more, whereas those with a lower household income and those who underwent surgery spent less (all P < 0.05).ConclusionsFor patients in China, direct expenditure for the diagnosis and treatment of CRC seemed catastrophic, and non-medical expenditure was non-ignorable. The financial burden varied among subgroups, especially among patients with different clinical stages of disease, which suggests that, in China, CRC screening might be cost-effective.