A tuberculosis model with seasonality

Global analysis of an age-structured tuberculosis model with an application to Jiangsu, China

Diagnostic delay for TB infected individuals and the lack of TB vaccines for adults are the main challenges to achieve the goals of WHO by 2050. In order to evaluate the impacts of diagnostic delay and vaccination for adults on prevalence of TB, we propose an age-structured model with latent age and infection age, and we incorporate Mycobacterium TB in the environment and vaccination into the model. Diagnostic delay is indicated by the age of infection before receiving treatment. The threshold dynamics are established in terms of the basic reproduction number R 0 . WhenR 0 < 1 , the disease-free equilibrium is globally asymptotically stable, which means that TB epidemic will die out; WhenR 0 = 1 , the disease-free equilibrium is globally attractive; there exists a unique endemic equilibrium and the endemic equilibrium is globally attractive whenR 0 > 1 . We estimate that the basic reproduction numberR 0 = 0.5320 (95% CI (0.3060, 0.7556)) in Jiangsu Province, which means that TB epidemic will die out. However, we find that the annual number of new TB cases by 2050 is 1,151 (95%CI: (138, 8,014)), which means that it is challenging to achieve the goal of WHO by 2050. To this end, we evaluate the possibility of achieving the goals of WHO if we start vaccinating adults and reduce diagnostic delay in 2025. Our results demonstrate that when the diagnostic delay is reduced from longer than four months to four months, or 20% adults are vaccinated, the goal of WHO in 2050 can be achieved, and 73,137 (95%CI: (23,906, 234,086)) and 54,828 (95%CI: (15,811, 206,468)) individuals will be prevented from being infected from 2025 to 2050, respectively. The modeling approaches and simulation results used in this work can help policymakers design control measures to reduce the prevalence of TB.

Analysis of the current status of TB transmission in China based on an age heterogeneity model

Tuberculosis (TB) is an infectious disease transmitted through the respiratory system. China is one of the countries with a high burden of TB. Since 2004, an average of more than 800,000 cases of active TB has been reported each year in China. Analyzing the case data from 2004 to 2018, we found significant differences in TB incidence by age group. A model of TB is put forward to explore the effect of age heterogeneity on TB transmission. The nonlinear least squares method is used to obtain the key parameters in the model, and the basic reproduction number Rv = 0.8017 is calculated and the sensitivity analysis of Rv to the parameters is given. The simulation results show that reducing the number of new infections in the elderly population and increasing the recovery rate of elderly patients with the disease could significantly reduce the transmission of TB. Furthermore, the feasibility of achieving the goals of the World Health Organization (WHO) End TB Strategy in China is assessed, and we obtained that with existing TB control measures it will take another 30 years for China to reach the WHO goal to reduce 90% of the number of new cases by the year 2049. However, in theory it is feasible to reach the WHO strategic goal of ending TB by 2035 if the group contact rate in the elderly population can be reduced, though it is difficult to reduce the contact rate.

Integer time series models for tuberculosis in Africa

Tuberculosis, an airborne disease, is the deadliest human infectious disease caused by one single agent. The African region is among the most affected and most burdensome area in terms of tuberculosis cases. In this paper, we modeled the number of new cases of tuberculosis for 2000-2021 by integer time series. For each African country, we fitted twenty different models and selected the model that best fitted the data. The twenty models were mostly based on the number of new cases following either the Poisson or negative binomial distribution with the rate parameter allowed to vary linearly or quadratically with respect to year. The best fitted models were used to give predictions for 2022-2031.

The influence of ambient air pollution on the transmission of tuberculosis in Jiangsu, China

In this paper, based on the statistical data, we investigate the effects of long-term exposure to ambient particulate air pollution on the transmission dynamics of tuberculosis (TB) in Jiangsu, China by studying the threshold dynamics of the TB epidemic model via the statistical data analytically and numerically. The basic reproduction number R 0 > 1 reveals that TB in Jiangsu, China is an endemic disease and will persist for a long time. And the numerical results show that, in order to control the TB in Jiangsu effectively, we must decrease the depuration coefficient of PM₁₀ in the body, the proportion of TB symptomatic infectious by direct transmission, the reactivation rate of the pre-symptomatic infectious and the effect coefficient of PM₁₀ and MTB inhaled of TB transmission, and increase the uptake coefficient, the recovery rate of the symptomatic/pre-symptomatic infectious and the influence coefficient of PM₁₀ on the body of mortality. Our study shows that PM₁₀ is closely related to the incidence of TB, and the effective control efforts are suggested to focus on increasing close-contact distance and wearing protective mask to decrease the influence of PM₁₀ on the TB transmission, which may shed a new light on understanding the environmental drivers to TB.

[Analysis of the seasonality of tuberculosis in Brazilian capitals and the Federal District from 2001 to 2019]

The literature has few studies on the seasonality of tuberculosis (TB) in the southern hemisphere, entailing the fill of this knowledge gap. This study aims to analyze whether TB incidence in Brazilian capitals and the Federal District is seasonal. This is an ecological study of a time series (2001-2019) of TB cases, conducted with 26 capitals and the Federal District. The Ministry of Health database, with 516,524 TB cases, was used. Capitals and the Federal District were divided into five groups based on social indicators, disease burden, and the Koppen climate classification. The seasonal variation of TB notifications and group amplitude were evaluated. We found TB seasonality in Brazil with a 1% significance in all capital groups (Stability assumption and Krusall-Wallis tests, p < 0.01). In the combined seasonality test, capital groups A, D, and E showed seasonality, whereas groups B and C, its probability. Our findings showed that health service supply and/or demand - rather than climate - may be the most relevant underlying factor in TB seasonality. It is challenging to raise the other seasonal factors underlying TB seasonality in tropical regions in the Southern Hemisphere.

Inferring the effective reproductive number from deterministic and semi-deterministic compartmental models using incidence and mobility data

The effective reproduction number (ℜt) is a theoretical indicator of the course of an infectious disease that allows policymakers to evaluate whether current or previous control efforts have been successful or whether additional interventions are necessary. This metric, however, cannot be directly observed and must be inferred from available data. One approach to obtaining such estimates is fitting compartmental models to incidence data. We can envision these dynamic models as the ensemble of structures that describe the disease’s natural history and individuals’ behavioural patterns. In the context of the response to the COVID-19 pandemic, the assumption of a constant transmission rate is rendered unrealistic, and it is critical to identify a mathematical formulation that accounts for changes in contact patterns. In this work, we leverage existing approaches to propose three complementary formulations that yield similar estimates for ℜt based on data from Ireland’s first COVID-19 wave. We describe these Data Generating Processes (DGP) in terms of State-Space models. Two (DGP1 and DGP2) correspond to stochastic process models whose transmission rate is modelled as Brownian motion processes (Geometric and Cox-Ingersoll-Ross). These DGPs share a measurement model that accounts for incidence and transmission rates, where mobility data is assumed as a proxy of the transmission rate. We perform inference on these structures using Iterated Filtering and the Particle Filter. The final DGP (DGP3) is built from a pool of deterministic models that describe the transmission rate as information delays. We calibrate this pool of models to incidence reports using Hamiltonian Monte Carlo. By following this complementary approach, we assess the tradeoffs associated with each formulation and reflect on the benefits/risks of incorporating proxy data into the inference process. We anticipate this work will help evaluate the implications of choosing a particular formulation for the dynamics and observation of the time-varying transmission rate.

Evaluating Strategies For Tuberculosis to Achieve the Goals of WHO in China: A Seasonal Age-Structured Model Study

Although great progress has been made in the prevention and mitigation of TB in the past 20 years, China is still the third largest contributor to the global burden of new TB cases, accounting for 833,000 new cases in 2019. Improved mitigation strategies, such as vaccines, diagnostics, and treatment, are needed to meet goals of WHO. Given the huge variability in the prevalence of TB across age-groups in China, the vaccination, diagnostic techniques, and treatment for different age-groups may have different effects. Moreover, the statistics data of TB cases show significant seasonal fluctuations in China. In view of the above facts, we propose a non-autonomous differential equation model with age structure and seasonal transmission rate. We derive the basic reproduction number, [Formula: see text], and prove that the unique disease-free periodic solution, [Formula: see text] is globally asymptotically stable when [Formula: see text], while the disease is uniformly persistent and at least one positive periodic solution exists when [Formula: see text]. We estimate that the basic reproduction number [Formula: see text] ([Formula: see text]), which means that TB is uniformly persistent. Our results demonstrate that vaccinating susceptible individuals whose ages are over 65 and between 20 and 24 is much more effective in reducing the prevalence of TB, and each of the improved vaccination strategy, diagnostic strategy, and treatment strategy leads to substantial reductions in the prevalence of TB per 100,000 individuals compared with current approaches, and the combination of the three strategies is more effective. Scenario A (i.e., coverage rate [Formula: see text], diagnosis rate [Formula: see text], relapse rate [Formula: see text]) is the best and can reduce the prevalence of TB per 100,000 individuals by [Formula: see text] and [Formula: see text] in 2035 and 2050, respectively. Although the improved strategies will significantly reduce the incidence rate of TB, it is challenging to achieve the goal of WHO in 2050. Our findings can provide guidance for public health authorities in projecting effective mitigation strategies of TB.

Mathematical analysis of a two-strain tuberculosis model in Bangladesh

Tuberculosis (TB) is an airborne infectious disease that causes millions of deaths worldwide each year (1.2 million people died in 2019). Alarmingly, several strains of the causative agent, Mycobacterium tuberculosis (MTB)—including drug-susceptible (DS) and drug-resistant (DR) variants—already circulate throughout most developing and developed countries, particularly in Bangladesh, with totally drug-resistant strains starting to emerge. In this study we develop a two-strain DS and DR TB transmission model and perform an analysis of the system properties and solutions. Both analytical and numerical results show that the prevalence of drug-resistant infection increases with an increasing drug use through amplification. Both analytic results and numerical simulations suggest that if the basic reproduction numbers of both DS (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{{0{\text{s}}}}$$\end{document}R0s) and DR (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{{0{\text{r}}}}$$\end{document}R0r) TB are less than one, i.e. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\max \left[ {{\text{R}}_{{0{\text{s}}}} ,{\text{ R}}_{{0{\text{r}}}} } \right] < 1,$$\end{document}maxR0s,R0r<1, the disease-free equilibrium is asymptotically stable, meaning that the disease naturally dies out. Furthermore, if \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{{0{\text{r}}}} > {\text{max}}\left[ {{\text{R}}_{{0{\text{s}}}} ,1} \right]$$\end{document}R0r>maxR0s,1, then DS TB dies out but DR TB persists in the population, and if \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{R}}_{{0{\text{s}}}} > {\text{max}}\left[ {{\text{R}}_{{0{\text{r}}}} ,1} \right]$$\end{document}R0s>maxR0r,1 both DS TB and DR TB persist in the population. Further, sensitivity analysis of the model parameters found that the transmission rate of both strains had the greatest influence on DS and DR TB prevalence. We also investigated the effect of treatment rates and amplification on both DS and DR TB prevalence; results indicate that inadequate or inappropriate treatment makes co-existence more likely and increases the relative abundance of DR TB infections.

Analysis of COVID-19 using a modified SLIR model with nonlinear incidence

Infectious diseases kill millions of people each year, and they are the major public health problem in the world. This paper presents a modified Susceptible-Latent-Infected-Removed (SLIR) compartmental model of disease transmission with nonlinear incidence. We have obtained a threshold value of basic reproduction number ( R 0 ) and shown that only a disease-free equilibrium exists whenR 0 < 1 and endemic equilibrium whenR 0 > 1 . With the help of the Lyapunov-LaSalle Invariance Principle, we have shown that disease-free equilibrium and endemic equilibrium are both globally asymptotically stable. The study has also provided the model calibration to estimate parameters with month wise coronavirus (COVID-19) data, i.e. reported cases by worldometer from March 2020 to May 2021 and provides prediction until December 2021 in China. The Partial Rank Correlation Coefficient (PRCC) method was used to investigate how the model parameters' variation impact the model outcomes. We observed that the most important parameter is transmission rate which had the most significant impact on COVID-19 cases. We also discuss the epidemiology of COVID-19 cases and several control policies and make recommendations for controlling this disease in China.

Seasonality in extra-pulmonary tuberculosis notifications in Germany 2004-2014- a time series analysis

BACKGROUND

Seasonality in tuberculosis (TB) has been found in different parts of the world, showing a peak in spring/summer and a trough in autumn/winter. The evidence is less clear which factors drive seasonality. It was our aim to identify and evaluate seasonality in the notifications of TB in Germany, additionally investigating the possible variance of seasonality by disease site, sex and age group.

METHODS

We conducted an integer-valued time series analysis using national surveillance data. We analysed the reported monthly numbers of started treatments between 2004 and 2014 for all notified TB cases and stratified by disease site, sex and age group.

RESULTS

We detected seasonality in the extra-pulmonary TB cases (N = 11,219), with peaks in late spring/summer and troughs in fall/winter. For all TB notifications together (N = 51,090) and for pulmonary TB only (N = 39,714) we did not find a distinct seasonality. Additional stratified analyses did not reveal any clear differences between age groups, the sexes, or between active and passive case finding.

CONCLUSION

We found seasonality in extra-pulmonary TB only, indicating that seasonality of disease onset might be specific to the disease site. This could point towards differences in disease progression between the different clinical disease manifestations. Sex appears not to be an important driver of seasonality, whereas the role of age remains unclear as this could not be sufficiently investigated.

Threshold Dynamics in a Model for Zika Virus Disease with Seasonality

We present a compartmental population model for the spread of Zika virus disease including sexual and vectorial transmission as well as asymptomatic carriers. We apply a non-autonomous model with time-dependent mosquito birth, death and biting rates to integrate the impact of the periodicity of weather on the spread of Zika. We define the basic reproduction number [Formula: see text] as the spectral radius of a linear integral operator and show that the global dynamics is determined by this threshold parameter: If [Formula: see text] then the disease-free periodic solution is globally asymptotically stable, while if [Formula: see text] then the disease persists. We show numerical examples to study what kind of parameter changes might lead to a periodic recurrence of Zika.

Modelling the effects of the contaminated environments on tuberculosis in Jiangsu, China

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A tuberculosis model incorporating contaminated environments is developed.

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A threshold theorem of the model is established.

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The annual average of the basic reproduction number is obtained.

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TB in Jiangsu is an endemic disease and will persist for a long time.

Tuberculosis (TB) is still an important public health issue in Jiangsu province, China. In this study, based on the TB transmission routes and the statistical data of TB cases, we formulate a novel TB epidemic model accounting for the effects of the contaminated environments on TB transmission dynamics. The value of this study lies in two aspects. Mathematically, we define the basic reproduction number, R0, and prove that R0 can be used to govern the threshold dynamics of the model. Epidemiologically, we find that the annual average R0 is 1.13,>1 and TB in Jiangsu is an endemic disease. Therefore, in order to control the TB in Jiangsu efficiently, we must decrease the virus shedding rate or increase the recovery rates, and increase the environmental clearance rate.

Effects of periodic intake of drugs of abuse (morphine) on HIV dynamics: Mathematical model and analysis

Drugs of abuse, such as opiates, have been widely associated with diminishing host-immune responses, including suppression of HIV-specific antibody responses. In particular, periodic intake of the drugs of abuse can result in time-varying periodic antibody level within HIV-infected individuals, consequently altering the HIV dynamics. In this study, we develop a mathematical model to analyze the effects of periodic intake of morphine, a widely used opiate. We consider two routes of morphine intake, namely, intravenous morphine (IVM) and slow-release oral morphine (SROM), and integrate several morphine pharmacodynamic parameters into HIV dynamics model. Using our non-autonomous model system we formulate the infection threshold, R_i, for global stability of infection-free equilibrium, which provides a condition for avoiding viral infection in a host. We demonstrate that the infection threshold highly depends on the morphine pharmacodynamic parameters. Such information can be useful in the design of antibody-based vaccines. In addition, we also thoroughly evaluate how alteration of the antibody level due to periodic intake of morphine can affect the viral load and the CD4 count in HIV infected drug abusers.

Modeling and dynamic analysis of tuberculosis in mainland China from 1998 to 2017: the effect of DOTS strategy and further control

Background

Tuberculosis (TB) is one of the most important health topics in the world. Directly observed treatment and short course chemotherapy (DOTS) strategy combines medicine care and modern health system firmly, and it has been carried out by World Health Organization (WHO) since 1997. In the struggle with TB, China has promoted the process of controlling the disease actively, and the full coverage of DOTS strategy has been reached around 2004. Mathematical modeling is a very useful tool to study the transmission of diseases. Understanding the impact of DOTS strategy on the control of TB is important for designing further prevention strategy.

Methods

We investigate the impact of control strategy on the transmission of TB in China by dynamic model. Then we discuss further control for TB aiming at developing new vaccine and improving treatment. The optimal control problem, minimizing the total number of infectious individuals with the lowest cost, is proposed and analyzed by Pontryagin’s maximum principle. Numerical simulations are provided to illustrate the theoretical results.

Results

Theoretical analysis for the epidemic model is given. Based on the data reported by National Bureau of Statistics of China (NBSC), the basic reproduction number of each stage is estimated and compared, and they are \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {R}_{0}^{1}=1.7885$\end{document}R01=1.7885 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {R}_{0}^{2}=1.0741$\end{document}R02=1.0741, respectively. Optimal control strategy for further control is designed and proved well. An intuitionistic comparison between the optimal control strategy and the current control strategy is given.

Conclusions

The diagnosis and treatment of TB in China have been promoted a lot and the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {R}_{0}$\end{document}R0 is reduced by the full coverage of DOTS strategy. However, the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {R}_{0}$\end{document}R0 in China is still greater than 1 now. The relationship between \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {R}_{0}$\end{document}R0 and vaccination strategy is shown. Optimal strategy aiming at exposed and infected population is suggested for further control.

Climate-dependent malaria disease transmission model and its analysis

Malaria infection continues to be a major problem in many parts of the world including Africa. Environmental variables are known to significantly affect the population dynamics and abundance of insects, major catalysts of vector-borne diseases, but the exact extent and consequences of this sensitivity are not yet well established. To assess the impact of the variability in temperature and rainfall on the transmission dynamics of malaria in a population, we propose a model consisting of a system of non-autonomous deterministic equations that incorporate the effect of both temperature and rainfall to the dispersion and mortality rate of adult mosquitoes. The model has been validated using epidemiological data collected from the western region of Ethiopia by considering the trends for the cases of malaria and the climate variation in the region. Further, a mathematical analysis is performed to assess the impact of temperature and rainfall change on the transmission dynamics of the model. The periodic variation of seasonal variables as well as the non-periodic variation due to the long-term climate variation have been incorporated and analyzed. In both periodic and non-periodic cases, it has been shown that the disease-free solution of the model is globally asymptotically stable when the basic reproduction ratio is less than unity in the periodic system and when the threshold function is less than unity in the non-periodic system. The disease is uniformly persistent when the basic reproduction ratio is greater than unity in the periodic system and when the threshold function is greater than unity in the non-periodic system.

Delay effect and burden of weather-related tuberculosis cases in Rajshahi province, Bangladesh, 2007-2012

Tuberculosis (TB) is a potentially fatal infectious disease that continues to be a public health problem in Bangladesh. Each year in Bangladesh an estimated 70,000 people die of TB and 300,000 new cases are projected. It is important to understand the association between TB incidence and weather factors in Bangladesh in order to develop proper intervention programs. In this study, we examine the delayed effect of weather variables on TB occurrence and estimate the burden of the disease that can be attributed to weather factors. We used generalized linear Poisson regression models to investigate the association between weather factors and TB cases reported to the Bangladesh National TB control program between 2007 and 2012 in three known endemic districts of North-East Bangladesh. The associated risk of TB in the three districts increases with prolonged exposure to temperature and rainfall, and persisted at lag periods beyond 6 quarters. The association between humidity and TB is strong and immediate at low humidity, but the risk decreases with increasing lag. Using the optimum weather values corresponding to the lowest risk of infection, the risk of TB is highest at low temperature, low humidity and low rainfall. Measures of the risk attributable to weather variables revealed that weather-TB cases attributed to humidity is higher than that of temperature and rainfall in each of the three districts. Our results highlight the high linearity of temporal lagged effects and magnitudes of the burden attributable to temperature, humidity, and rainfall on TB endemics. The results can hopefully advise the Bangladesh National TB control program and act as a practical reference for the early warning of TB cases.

Modeling transmission dynamics of lyme disease: Multiple vectors, seasonality, and vector mobility

Lyme disease is the most prevalent tick-borne disease in the United States, which humans acquire from an infected tick of the genus Ixodes (primarily Ixodes scapularis). While previous studies have provided useful insights into various aspects of Lyme disease, the tick's host preference in the presence of multiple hosts has not been considered in the existing models. In this study, we develop a transmission dynamics model that includes the interactions between the primary vectors involved: blacklegged ticks (I. scapularis), white-footed mice (Peromyscus leucopus), and white-tailed deer (Odocoileus virginianus). Our model shows that the presence of multiple vectors may have a significant impact on the dynamics and spread of Lyme disease. Based on our model, we also calculate the basic reproduction number, R 0 , a threshold value that predicts whether a disease exists or dies out. Subsequent extensions of the model consider seasonality of the tick's feeding period and mobility of deer between counties. Our results suggest that a longer tick peak feeding period results in a higher infection prevalence. Moreover, while the deer mobility may not be a primary factor for short-term emergence of Lyme disease epidemics, in the long-run it can significantly contribute to local infectiousness in neighboring counties, which eventually reach the endemic steady state.

Epidemiological characteristics of pulmonary tuberculosis in mainland China from 2004 to 2015: a model-based analysis

BACKGROUND

We used data released by the government to analyze the epidemiological distribution of pulmonary tuberculosis in mainland China from 2004 to 2015, in order to provide a deeper understanding of trends in the epidemiology of pulmonary tuberculosis in China and a theoretical basis to assess the effectiveness of government interventions and develop more targeted prevention and control strategies.

METHODS

A discrete dynamic model was designed based on the epidemiological characteristics of pulmonary tuberculosis and fitted to data published by the government to estimate changes in indicators such as adequate contact rate, prevalence of non-treated pulmonary tuberculosis (abbreviated as prevalence), and infection rate. Finally, we performed sensitivity analyses of the effects of parameters on the population infection rate.

RESULTS

The epidemiological features of pulmonary tuberculosis in China include a pattern of seasonal fluctuations, with the highest rates of infection in autumn and winter. The adequate contact rate has increased slightly from an average of 0.12/month in 2010 to an average of 0.21/month in 2015. The prevalence in the population has continued to decrease from 3.4% in early 2004 to 1.7% in late 2015. The Mycobacterium tuberculosis (M. tuberculosis) infection rate in the population decreased gradually from 42.3% at the beginning of 2004 to 36.7% at the end of 2015. The actual number of new infections gradually decreased from 1,300,000/year in 2010 to 1,100,000/year in 2015. The actual number of new patients each year has been relatively stable since 2010 and remains at approximately 2,600,000/year.

CONCLUSIONS

The population prevalence and the M. tuberculosis infection rate have decreased year by year since 2004, indicating that the tuberculosis epidemic in China has been effectively controlled. However, pulmonary tuberculosis has become increasingly contagious since 2010. China should focus on the prevention and control of pulmonary tuberculosis during autumn and winter.

A periodic SEIRS epidemic model with a time-dependent latent period

Many infectious diseases have seasonal trends and exhibit variable periods of peak seasonality. Understanding the population dynamics due to seasonal changes becomes very important for predicting and controlling disease transmission risks. In order to investigate the impact of time-dependent delays on disease control, we propose an SEIRS epidemic model with a periodic latent period. We introduce the basic reproduction ratio [Formula: see text] for this model and establish a threshold type result on its global dynamics in terms of [Formula: see text]. More precisely, we show that the disease-free periodic solution is globally attractive if [Formula: see text]; while the system admits a positive periodic solution and the disease is uniformly persistent if [Formula: see text]. Numerical simulations are also carried out to illustrate the analytic results. In addition, we find that the use of the temporal average of the periodic delay may underestimate or overestimate the real value of [Formula: see text].

Estimating the incidence of tuberculosis cases reported at a tertiary hospital in Ghana: a time series model approach

Background

The incidence of Tuberculosis (TB) differs among countries and contributes to morbidity and mortality especially in the developing countries. Trends and seasonal changes in the number of patients presenting with TB have been studied worldwide including sub-Saharan Africa. However, these changes are unknown at the Korle-Bu Teaching Hospital (KBTH). The aim of this study was to obtain a time series model to estimate the incidence of TB cases at the chest clinic of the Korle-Bu Teaching hospital.

Methods

A time series analysis using a Box-Jenkins approach propounded as an autoregressive moving average (ARIMA) was conducted on the monthly TB cases reported at the KBTH from 2008 to 2017. Various models were stated and compared and the best was found to be based on the Akaike Information Criterion and Bayesian Information Criterion.

Results

There was no evidence of obvious increasing or decreasing trend in the TB data. The log-transformed of the data achieved stationarity with fairly stable variations around the mean of the series. ARIMA (1, 0, 1) or ARMA (1,1) was obtained as the best model. The monthly forecasted values of the best model ranged from 53 to 55 for the year 2018; however, the best model does not always produce the best results with respect to the mean absolute and mean square errors.

Conclusions

Irregular fluctuations were observed in the 10 -year data studied. The model equation to estimate the expected monthly TB cases at KBTH produced an AR coefficient of 0.971 plus an MA coefficient of − 0.826 with a constant value of 4.127. The result is important for developing a hypothesis to explain the dynamics of TB occurrence so as to outline prevention programmes, optimal use of resources and effective service delivery.

Electronic supplementary material

The online version of this article (10.1186/s12889-018-6221-z) contains supplementary material, which is available to authorized users.

On the dynamics of brucellosis infection in bison population with vertical transmission and culling

We introduce a new mathematical modeling framework that seek to improve our quantitative understanding of the influence of chronic brucellosis and culling control on brucellosis dynamics in periodic and non-periodic environments. We conduct both epidemic and endemic analysis, with a focus on the threshold dynamics characterized by the basic reproduction numbers. In addition, we also perform an optimal control study to explore optimal culling strategy in periodic and non-periodic environment.

Quantifying TB transmission: a systematic review of reproduction number and serial interval estimates for tuberculosis

Tuberculosis (TB) is the leading global infectious cause of death. Understanding TB transmission is critical to creating policies and monitoring the disease with the end goal of TB elimination. To our knowledge, there has been no systematic review of key transmission parameters for TB. We carried out a systematic review of the published literature to identify studies estimating either of the two key TB transmission parameters: the serial interval (SI) and the reproductive number. We identified five publications that estimated the SI and 56 publications that estimated the reproductive number. The SI estimates from four studies were: 0.57, 1.42, 1.44 and 1.65 years; the fifth paper presented age-specific estimates ranging from 20 to 30 years (for infants <1 year old) to <5 years (for adults). The reproductive number estimates ranged from 0.24 in the Netherlands (during 1933-2007) to 4.3 in China in 2012. We found a limited number of publications and many high TB burden settings were not represented. Certain features of TB dynamics, such as slow transmission, complicated parameter estimation, require novel methods. Additional efforts to estimate these parameters for TB are needed so that we can monitor and evaluate interventions designed to achieve TB elimination.

Mixing in regional-structure model about the influence of floating population and optimal control about TB in Guangdong province of China

In the last 60 years, great progress has been made in controlling and preventing tuberculosis in China. However, the number of tuberculosis cases has increased dramatically in the last 25 years, mainly due to the lack of effective control measures of immigrating populations with tuberculosis. In order to explore the effective control and prevention measures we propose a deterministic model to study the transmission dynamics of tuberculosis in Guangdong province of China in this paper. The model consists of susceptible, exposed and infectious recovered subpopulations of immigrating populations from other provinces and the local population of Guangdong. We obtain the effective reproduction number. Based on the analysis, we also establish an optimal immune programming model, and get the optimal proportion of vaccine coverage with control of the effective reproduction number. Simulation is used to determine the validation and reliability. Our study demonstrates that the immigrating population from different provinces needs to be vaccinated according to the incidence rate of TB in their original provinces, and it is an effective way to prevent the outbreak of tuberculosis in Guangdong.

Analysis of Transmission and Control of Tuberculosis in Mainland China, 2005-2016, Based on the Age-Structure Mathematical Model

Tuberculosis (TB), an air-borne infectious disease, is a major public-health problem in China. The reported number of the active tuberculosis cases is about one million each year. The morbidity data for 2005–2012 reflect that the difference in morbidity based on age group is significant, thus the role of age-structure on the transmission of TB needs to be further developed. In this work, based on the reported data and the observed morbidity characteristics, we propose a susceptible-exposed-infectious-recovered (SEIR) epidemic model with age groupings, involving three categories: children, the middle-aged, and senior to investigate the role of age on the transmission of tuberculosis in Mainland China from 2005 to 2016. Then, we evaluated the parameters by the Least Square method and simulated the model and it had good alignment with the reported infected TB data in Mainland China. Furthermore, we estimated the basic reproduction number R0 of 1.7858, with an obtained 95% confidence interval for R0 of (1.7752,1.7963) by Latin hypercube sampling, and we completed a sensitivity analysis of R0 in terms of some parameters. Our study demonstrates that diverse age groups have different effects on TB. Two effective measures were found that would help reach the goals of the World Health Organization (WHO) End TB Strategy: an increase in the recovery rate and the reduction in the infectious rate of the senior age group.

Optimal timing of drug sensitivity testing for patients on first-line tuberculosis treatment

Effective treatment for tuberculosis (TB) patients on first-line treatment involves triaging those with drug-resistant (DR) TB to appropriate treatment alternatives. Patients likely to have DR TB are identified using results from repeated inexpensive sputum-smear (SS) tests and expensive but definitive drug sensitivity tests (DST). Early DST may lead to high costs and unnecessary testing; late DST may lead to poor health outcomes and disease transmission. We use a partially observable Markov decision process (POMDP) framework to determine optimal DST timing. We develop policy-relevant structural properties of the POMDP model. We apply our model to TB in India to identify the patterns of SS test results that should prompt DST if transmission costs remain at status-quo levels. Unlike previous analyses of personalized treatment policies, we take a societal perspective and consider the effects of disease transmission. The inclusion of such effects can significantly alter the optimal policy. We find that an optimal DST policy could save India approximately $1.9 billion annually.

Mixed vaccination strategy for the control of tuberculosis: A case study in China

This study first presents a mathematical model of TB transmission considering BCG vaccination compartment to investigate the transmission dynamics nowadays. Based on data reported by the National Bureau of Statistics of China, the basic reproduction number is estimated approximately as R0=1.1892. To reach the new End TB goal raised by WHO in 2015, considering the health system in China, we design a mixed vaccination strategy. Theoretical analysis indicates that the infectious population asymptotically tends to zero with the new vaccination strategy which is the combination of constant vaccination and pulse vaccination. We obtain that the control of TB is quicker to achieve with the mixed vaccination. The new strategy can make the best of current constant vaccination, and the periodic routine health examination provides an operable environment for implementing pulse vaccination in China. Numerical simulations are provided to illustrate the theoretical results and help to design the final mixed vaccination strategy once the new vaccine comes out.

MONTHLY PERIODIC OUTBREAK OF HEMORRHAGIC FEVER WITH RENAL SYNDROME IN CHINA

Hemorrhagic fever with renal syndrome (HFRS) spreading from rodent to human beings is a major public health problem in China, which causes high mortality rate. Data obtained from the China Ministry of Health shows that cases of HFRS in China exhibited monthly periodic outbreak. To well reveal the mechanisms about the outbreak of HFRS, we established a dynamical model to explain the periodic behaviors of HFRS in China. We obtained the basic reproduction number [Formula: see text], analyzed the dynamical behavior of the model, and used the model to fit the monthly data of HFRS cases. Our results demonstrated that periodic transmission rates and rodent periodic birth rate of HFRS in China can give rise to the periodic outbreak of HFRS, hence providing insights into taking measures to control HFRS in China.

Parameter and state estimation in a Neisseria meningitidis model: A study case of Niger

Neisseria meningitidis (Nm) is a major cause of bacterial meningitidis outbreaks in Africa and the Middle East. The availability of yearly reported meningitis cases in the African meningitis belt offers the opportunity to analyze the transmission dynamics and the impact of control strategies. In this paper, we propose a method for the estimation of state variables that are not accessible to measurements and an unknown parameter in a Nm model. We suppose that the yearly number of Nm induced mortality and the total population are known inputs, which can be obtained from data, and the yearly number of new Nm cases is the model output. We also suppose that the Nm transmission rate is an unknown parameter. We first show how the recruitment rate into the population can be estimated using real data of the total population and Nm induced mortality. Then, we use an auxiliary system called observer whose solutions converge exponentially to those of the original model. This observer does not use the unknown infection transmission rate but only uses the known inputs and the model output. This allows us to estimate unmeasured state variables such as the number of carriers that play an important role in the transmission of the infection and the total number of infected individuals within a human community. Finally, we also provide a simple method to estimate the unknown Nm transmission rate. In order to validate the estimation results, numerical simulations are conducted using real data of Niger.

Modelling Seasonal Brucellosis Epidemics in Bayingolin Mongol Autonomous Prefecture of Xinjiang, China, 2010-2014

Brucellosis is one of the severe public health problems; the cumulative number of new human brucellosis cases reached 211515 from 2010 to 2014 in China. Bayingolin Mongol Autonomous Prefecture is situated in the southeast of Xinjiang, where brucellosis infection occurs every year. Based on the reported data of newly acute human brucellosis cases for each season in Bayingolin Mongol Autonomous Prefecture, we proposed a susceptible, exposed, infected, and vaccinated (SEIV) model with periodic transmission rates to investigate the seasonal brucellosis transmission dynamics among sheep/cattle and from sheep/cattle to humans. Compared with the criteria of MAPE and RMSPE, the model simulations agree to the data on newly acute human brucellosis. We predict that the number of newly acute human brucellosis is increasing and will peak 15325 [95% CI: 11920-18242] around the summer of 2023. We also estimate the basic reproduction number R₀ = 2.5524 [95% CI: 2.5129-2.6225] and perform some sensitivity analysis of the newly acute human brucellosis cases and the basic reproduction number R₀ in terms of model parameters. Our study demonstrates that reducing the birth number of sheep/cattle, raising the slaughter rate of infected sheep/cattle, increasing the vaccination rate of susceptible sheep/cattle, and decreasing the loss rate of vaccination are effective strategies to control brucellosis epidemic.

A Dynamic Model of Human and Livestock Tuberculosis Spread and Control in Urumqi, Xinjiang, China

We establish a dynamical model for tuberculosis of humans and cows. For the model, we firstly give the basic reproduction number R₀. Furthermore, we discuss the dynamical behaviors of the model. By epidemiological investigation of tuberculosis among humans and livestock from 2007 to 2014 in Urumqi, Xinjiang, China, we estimate the parameters of the model and study the transmission trend of the disease in Urumqi, Xinjiang, China. The reproduction number in Urumqi for the model is estimated to be 0.1811 (95% confidence interval: 0.123–0.281). Finally, we perform some sensitivity analysis of several model parameters and give some useful comments on controlling the transmission of tuberculosis.

Seasonality Impact on the Transmission Dynamics of Tuberculosis

The statistical data of monthly pulmonary tuberculosis (TB) incidence cases from January 2004 to December 2012 show the seasonality fluctuations in Shaanxi of China. A seasonality TB epidemic model with periodic varying contact rate, reactivation rate, and disease-induced death rate is proposed to explore the impact of seasonality on the transmission dynamics of TB. Simulations show that the basic reproduction number of time-averaged autonomous systems may underestimate or overestimate infection risks in some cases, which may be up to the value of period. The basic reproduction number of the seasonality model is appropriately given, which determines the extinction and uniform persistence of TB disease. If it is less than one, then the disease-free equilibrium is globally asymptotically stable; if it is greater than one, the system at least has a positive periodic solution and the disease will persist. Moreover, numerical simulations demonstrate these theorem results.

Bayesian Melding Approach to Estimate the Reproduction Number for Tuberculosis Transmission in Indian States and Union Territories

Tuberculosis (TB) is one of the most common infectious diseases and a leading cause of death in the world. Despite the full implementation of Revised National Tuberculosis Control Programme, the disease continues to be a leading cause of morality and economic burden in India. The basic reproduction is a fundamental key parameter that quantifies the spread of a disease. In this article, we present a Bayesian melding approach to estimate the basic reproduction number using a deterministic model of TB. We present a point estimate of the basic reproduction number of 35 states and union territories of India during 2006 to 2011. The basic reproduction number of TB for India is computed to be 0.92, which indicates the slow elimination of TB in India during 2006 to 2011.

Analyzing seasonality of tuberculosis across Indian states and union territories

A significant seasonal variation in tuberculosis (TB) is observed in north India during 2006-2011, particularly in states like Himachal Pradesh, Haryana and Rajasthan. To quantify the seasonal variation, we measure average amplitude (peak to trough distance) across seasons in smear positive cases of TB and observe that it is maximum for Himachal Pradesh (40.01%) and minimum for Maharashtra (3.87%). In north India, smear positive cases peak in second quarter (April-June) and reach a trough in fourth quarter (October-December), however low seasonal variation is observed in southern region of the country. The significant correlations as 0.64 (p-value<0.001), 0.54 (p-value<0.01) and 0.42 (p-value<0.05) are observed between minimum temperature and seasonality of TB at lag-1 in north, central and northeast India respectively. However, in south India, this correlation is not significant.

A PERIODIC ROSS-MACDONALD MODEL IN A PATCHY ENVIRONMENT

Based on the classical Ross-Macdonald model, in this paper we propose a periodic malaria model to incorporate the effects of temporal and spatial heterogeneity on disease transmission. The temporal heterogeneity is described by assuming that some model coefficients are time-periodic, while the spatial heterogeneity is modeled by using a multi-patch structure and assuming that individuals travel among patches. We calculate the basic reproduction number [Formula: see text] and show that either the disease-free periodic solution is globally asymptotically stable if [Formula: see text] or the positive periodic solution is globally asymptotically stable if [Formula: see text]. Numerical simulations are conducted to confirm the analytical results and explore the effect of travel control on the disease prevalence.

Mathematical modeling of tuberculosis data of China

This paper concentrates on the tuberculosis data of China from January 2005 to December 2012. We set up a mathematical model to fit those data with the goodness of fit and obtain the optimal parameter values of the model. By the Chi-square test of the statistical inference, the optimal parameter values of the model are reasonable. We get the effective reproductive number of the disease for each year, and also investigate the preventive measures to control the tuberculosis.

Positive periodic solutions of an epidemic model with seasonality

An SEI autonomous model with logistic growth rate and its corresponding nonautonomous model are investigated. For the autonomous case, we give the attractive regions of equilibria and perform some numerical simulations. Basic demographic reproduction number R_d is obtained. Moreover, only the basic reproduction number R₀ cannot ensure the existence of the positive equilibrium, which needs additional condition R_d > R₁. For the nonautonomous case, by introducing the basic reproduction number defined by the spectral radius, we study the uniform persistence and extinction of the disease. The results show that for the periodic system the basic reproduction number is more accurate than the average reproduction number.

Modeling seasonal behavior changes and disease transmission with application to chronic wasting disease

Behavior and habitat of wildlife animals change seasonally according to environmental conditions. Mathematical models need to represent this seasonality to be able to make realistic predictions about the future of a population and the effectiveness of human interventions. Managing and modeling disease in wild animal populations requires particular care in that disease transmission dynamics is a critical consideration in the etiology of both human and animal diseases, with different transmission paradigms requiring different disease risk management strategies. Since transmission of infectious diseases among wildlife depends strongly on social behavior, mechanisms of disease transmission could also change seasonally. A specific consideration in this regard confronted by modellers is whether the contact rate between individuals is density-dependent or frequency-dependent. We argue that seasonal behavior changes could lead to a seasonal shift between density and frequency dependence. This hypothesis is explored in the case of chronic wasting disease (CWD), a fatal disease that affects deer, elk and moose in many areas of North America. Specifically, we introduce a strategic CWD risk model based on direct disease transmission that accounts for the seasonal change in the transmission dynamics and habitats occupied, guided by information derived from cervid ecology. The model is composed of summer and winter susceptible-infected (SI) equations, with frequency-dependent and density-dependent transmission dynamics, respectively. The model includes impulsive birth events with density-dependent birth rate. We determine the basic reproduction number as a weighted average of two seasonal reproduction numbers. We parameterize the model from data derived from the scientific literature on CWD and deer ecology, and conduct global and local sensitivity analyses of the basic reproduction number. We explore the effectiveness of different culling strategies for the management of CWD: although summer culling seems to be an effective disease eradication strategy, the total culling rate is limited by the requirement to preserve the herd.

Seasonal variations in notification of active tuberculosis cases in China, 2005-2012

Background

Although seasonal variation in tuberculosis (TB) incidence has been described in many countries, it remains unknown in China.

Methods

A time series decomposition analysis (X-12-ARIMA) was performed to examine the seasonal variation in active TB cases nationwide from 2005 through 2012 in China. Seasonal amplitude was calculated for the evaluation of TB seasonal variation.

Results

A total of 7.78 million active TB cases were reported over a period of 8 years. A spring peak (April) was observed with seasonal amplitude of 46.3%, compared with the winter trough (February). Most cases in provinces with subtropical and tropical monsoon climate showed lower amplitudes than those in temperate continental, plateau and mountain climate regions. The magnitude of seasonality varied inversely with annual average temperature, r (95% CI) = -0.71 (-0.79, -0.61). The seasonal amplitudes were 56.7, 60.5, 40.6, 46.4 and 50.9% for patients aged ≤14, 15–24, 25–44, 45–64, and ≥65 years, respectively. Students demonstrated greater seasonal amplitude than peasants, migrant workers and workers (115.3% vs. 43.5, 41.6 and 48.1%). Patients with pulmonary TB had lower amplitude compared to patients with pleural and other extra-pulmonary TB (EPTB) (45.9% vs. 52.0 and 56.3%). Relapse cases with sputum smear positive TB (SS+ TB) had significantly higher seasonal amplitude compared to new cases with sputum smear positive TB (52.2% vs. 41.6%).

Conclusions

TB is a seasonal disease in China. The peak and trough of TB transmission actually are in winter and in autumn respectively after factors of delay are removed. Higher amplitudes of TB seasonality are more likely to happen in temperate continental, plateau and mountain climate regions and regions with lower annual average temperature, and young person, students, patients with EPTB and relapse cases with SS+ TB are more likely to be affected by TB seasonality.

Seasonal dynamics of tuberculosis epidemics and implications for multidrug-resistant infection risk assessment

Understanding how seasonality shapes the dynamics of tuberculosis (TB) is essential in determining risks of transmission and drug resistance in (sub)tropical regions. We developed a relative fitness-based multidrug-resistant (MDR) TB model incorporated with seasonality and a probabilistic assessment model to assess infection risk in Taiwan regions. The model accurately captures the seasonal transmission and population dynamics of TB incidence during 2006-2008 and MDR TB in high TB burden areas during 2006-2010 in Taiwan. There is ~3% probability of having exceeded 50% of the population infected attributed to MDR TB. Our model not only provides insight into the understanding of the interactions between seasonal dynamics of TB and environmental factors but is also capable of predicting the seasonal patterns of TB incidence associated with MDR TB infection risk. A better understanding of the mechanisms of TB seasonality will be critical in predicting the impact of public control programmes.

Sliding mode control of outbreaks of emerging infectious diseases

This paper proposes and analyzes a mathematical model of an infectious disease system with a piecewise control function concerning threshold policy for disease management strategy. The proposed models extend the classic models by including a piecewise incidence rate to represent control or precautionary measures being triggered once the number of infected individuals exceeds a threshold level. The long-term behaviour of the proposed non-smooth system under this strategy consists of the so-called sliding motion-a very rapid switching between application and interruption of the control action. Model solutions ultimately approach either one of two endemic states for two structures or the sliding equilibrium on the switching surface, depending on the threshold level. Our findings suggest that proper combinations of threshold densities and control intensities based on threshold policy can either preclude outbreaks or lead the number of infected to a previously chosen level.

Modeling seasonal rabies epidemics in China

Human rabies, an infection of the nervous system, is a major public-health problem in China. In the last 60 years (1950–2010) there had been 124,255 reported human rabies cases, an average of 2,037 cases per year. However, the factors and mechanisms behind the persistence and prevalence of human rabies have not become well understood. The monthly data of human rabies cases reported by the Chinese Ministry of Health exhibits a periodic pattern on an annual base. The cases in the summer and autumn are significantly higher than in the spring and winter. Based on this observation, we propose a susceptible, exposed, infectious, and recovered (SEIRS) model with periodic transmission rates to investigate the seasonal rabies epidemics. We evaluate the basic reproduction number R₀, analyze the dynamical behavior of the model, and use the model to simulate the monthly data of human rabies cases reported by the Chinese Ministry of Health. We also carry out some sensitivity analysis of the basic reproduction number R₀ in terms of various model parameters. Moreover, we demonstrate that it is more reasonable to regard R₀ rather than the average basic reproduction number \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\bar{R}_{0}$\end{document} or the basic reproduction number \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\hat{R}_{0}$\end{document} of the corresponding autonomous system as a threshold for the disease. Finally, our studies show that human rabies in China can be controlled by reducing the birth rate of dogs, increasing the immunization rate of dogs, enhancing public education and awareness about rabies, and strengthening supervision of pupils and children in the summer and autumn.

Assessing trends and predictors of tuberculosis in Taiwan

BACKGROUND

Variety of environmental and individual factors can cause tuberculosis (TB) incidence change. The purpose of this study was to assess the characteristics of TB trends in the period 2004 - 2008 in Taiwan by month, year, gender, age, temperature, seasonality, and aborigines.

METHODS

The generalized regression models were used to examine the potential predictors for the monthly TB incidence in regional and national scales.

RESULTS

We found that (i) in Taiwan the average TB incidence was 68 per 100,000 population with mortality rate of 0.036 person-1 yr-1, (ii) the highest TB incidence rate was found in eastern Taiwan (116 per 100,000 population) with the largest proportion of TB relapse cases (8.17%), (iii) seasonality, aborigines, gender, and age had a consistent and dominant role in constructing TB incidence patterns in Taiwan, and (iv) gender, time trend, and 2-month lag maximum temperature showed strong association with TB trends in aboriginal subpopulations.

CONCLUSIONS

The proposed Poisson regression model is capable of forecasting patterns of TB incidence at regional and national scales. This study suggested that assessment of TB trends in eastern Taiwan presents an important opportunity for understanding the time-series dynamics and control of TB infections, given that this is the typical host demography in regions where these infections remain major public health problems.