Background
China has the second highest burden of pulmonary tuberculosis worldwide [
1]. Since 2004, pulmonary tuberculosis has been consistently ranked as having the highest number of newly diagnosed patients among all respiratory infectious diseases listed in the statutory notification system of infectious diseases in China [
2]. According to the National Tuberculosis Control Program (2011–2015), with the widespread implementation of China’s modern control strategy including early detection of patients, increasing the treatment level, and increasing public awareness, prevention and control measures have achieved remarkable results, and the epidemic has been effectively controlled. From 1990 to 2010, the prevalence of smear-positive tuberculosis decreased from 170 cases to 59 cases per 100,000 of the population [
3]. However, the burden, especially of drug-resistant pulmonary tuberculosis, remained high [
4‐
6]. Thus, pulmonary tuberculosis remains a severe, highly infectious respiratory disease with a high population susceptibility and is difficult to treat [
7,
8].
In 1979, 1985, 1990, 2000, and 2010, China conducted five national epidemiological surveys of tuberculosis to assess the epidemiological features, such as infection, morbidity, and mortality [
4]. However, the data obtained from the surveys are from cross-sectional surveys with limited time points. Moreover, only the population infection rate, population prevalence, and epidemiological distribution characteristics such as patient gender, age, and region were assessed. There was no assessment of trends or changes over time, and the surveys were unable to estimate the adequate contact rate (the number of persons infected by one contagious individual per month in an entirely susceptible population), the number of newly infected persons and new cases per month, as well as other important indicators of the severity of the epidemic. The lack of these indicators makes it difficult to formulate an adequate and accurate judgment of the epidemic.
Assessing these factors requires the use of mathematical models. Many scholars have used mathematical models to analyze the prevalence of pulmonary tuberculosis in China. For example, Li XX et al. established a time series model to analyze the seasonal variation in the number of patients with active tuberculosis in China from 2005 to 2012 [
9]; Mehra M et al. established a dynamic model to predict the number of people infected with multidrug-resistant tuberculosis (MDR-TB, which is resistant to at least isoniazid and rifampicin) [
10]; and Hu XL et al. and Liu LJ et al. used dynamic models incorporating the effect of seasonal fluctuations to predict national tuberculosis epidemic trends [
11,
12]. These models are essential tools for the quantitative analysis of the distribution of pulmonary tuberculosis in China. However, previous studies analyzed only some groups of the population or individual indicators, such as newly diagnosed patients, MDR-TB infections, the stability of solutions to systems of equations, and the basic reproduction number. To date, there is no mathematical model that comprehensively considers the epidemiologic characteristics of pulmonary tuberculosis among the whole population in China over the past decade or longer.
In this study, we developed a discrete dynamic model. The parameters were estimated from literature searches and data released by the government. We assessed trends in indicators that analyze the time and population distribution trends of pulmonary tuberculosis in China from 2004 to 2015. Additionally, we evaluated the implementation status of the national pulmonary tuberculosis prevention and control plan. Our study is of great significance because it provides a deeper understanding of the epidemiological characteristics and can help in developing more effective prevention and control policies.
Discussion
The number of newly diagnosed pulmonary tuberculosis patients and the adequate contact rate show seasonal fluctuations, as is seen in many respiratory infections such as influenza and measles [
22‐
25]. The number of confirmed patients in February was slightly lower, probably due to a decrease in the number of hospital visits during the one-week Spring Festival holiday. Since the adequate contact rate is estimated based on official data, it was also slightly lower at the corresponding time in February, and this effect cannot be eliminated by the model. The peak in the adequate contact rate was observed in November, indicating that pulmonary tuberculosis is most contagious in autumn and winter. This is consistent with the results of previously published studies [
9]. Therefore, we should focus on strengthening prevention and control in autumn and winter, and the government should increase publicity and education on pulmonary tuberculosis in this season, strengthen management measures, and encourage the public to pay attention to personal protection. The peak in the number of patients newly diagnosed with pulmonary tuberculosis lagged behind the peak in the adequate contact rate by 2 months. The reason is that when some infected persons are re-infected with
M. tuberculosis and develop active tuberculosis, it takes an average of 72 days between disease onset and confirmation of the diagnosis. According to the algorithm described in the Additional file
1, the probability of being diagnosed is greatest at 2–3 months after symptom onset. The adequate contact rate has increased yearly since 2010. This may be due to increased population mobility due to urbanization in China, mutations of pathogenic bacteria leading to increased infectiousness and increased urban population density. Our findings suggest that the efficiency of pulmonary tuberculosis transmission has actually increased.
According to the results of the Fourth National Survey of Pulmonary Tuberculosis Epidemiology, the prevalence of active pulmonary tuberculosis in China in 2000 was 367 per 100,000 [
26]. Since the prevalence is decreasing every year, we adjusted the prevalence of active pulmonary tuberculosis in early 2004 to 340 per 100,000 according to the annual rate of decline. Based on this calculation, the annual rate of decline in active pulmonary tuberculosis in 2004–2015 was 5.3%. Comparison of the prevalence in 1990 with that in 2000 showed an annual decline of 5.4% [
26], indicating that the model estimation results are in line with the actual survey results. The Fifth National Survey of Pulmonary Tuberculosis Epidemiology conducted in 2010 did not include people under the age of 15 years. Therefore, since 2000, no actual survey data have been available to compare with the prevalence estimated by the model. The overall rate of
M. tuberculosis infection has also been decreasing, but the rate of decline is relatively slow. The fluctuation range of the infection rate is very narrow, indicating that changes in the model parameters have little effect on the model. Based on the decline in the prevalence and infection rate, it can be clearly determined that the epidemic of tuberculosis in China is being effectively controlled and that comprehensive prevention and control measures implemented by the government have achieved significant results.
The number of newly diagnosed patients released by the government does not represent the actual numbers of new patients and new infections. The latter two values reflect the severity of the pulmonary tuberculosis epidemic in real time and are important criteria for measuring prevalence. However, they cannot be directly observed. Using the mathematical model, we found that these indicators also exhibited significant seasonal changes, and trends over time were similar to those observed for the adequate contact rate. This can be explained by the fact that when the adequate contact rate is high, pulmonary tuberculosis spreads rapidly, which leads to a corresponding increase in the growth rate of infected persons. In addition, the growth rate of new patients is also affected by the adequate contact rate because as the adequate contact rate increases, more infected people in state E develop secondary pulmonary tuberculosis due to increased re-exposure to M. tuberculosis. A high adequate contact rate also increases the number of individuals in state Ep, leading to an increase in the number of new primary pulmonary tuberculosis patients.
We distinguished MDR-TB and non-MDR-TB in our analyses. The treatment cycle and cure rate of the two types of M. tuberculosis are different. To ensure that the model’s analysis of pulmonary tuberculosis treatment is as realistic as possible, we considered MDR-TB and non-MDR-TB separately. The mortality associated with pulmonary tuberculosis is not considered in the model. We made this choice because the mortality rate of patients seeking initial treatment and that of patients seeking repeat treatment are different, and the mortality rates of MDR-TB and non-MDR-TB infection are also different. There is currently not enough literature to determine the parameters needed to assess the mortality rate of pulmonary tuberculosis.
Parameter κs is negatively correlated with the infection rate because the sum of the cure rate and the treatment failure rate is less than 1. A higher cure rate results in a lower treatment failure rate, and fewer patients convert to state E after treatment. Similarly, κf is positively correlated with the infection rate. τ is positively correlated with the infection rate such that a larger increase in the number of patients with primary pulmonary tuberculosis results in a greater number of conversions to state E after spontaneous recovery. The positive correlation effect of df and the infection rate gradually decreases because as more patients with secondary tuberculosis die and survival decreases, fewer people become infected due to exposure to M. tuberculosis. Thus, the number of individuals in state E increases, and as time goes by, this effect gradually diminishes. λ is positively correlated with the infection rate because as the number of asymptomatic infections grows faster, the number of individuals in state E increases. δ is positively correlated with the infection rate because when the number of patients who undergo spontaneous recovery from primary pulmonary tuberculosis is larger, the number of individuals in state E is greater. θ is negatively correlated with the infection rate because as the number of infected individuals who experience reactivation due to reduced immunity increases, the number of individuals in state E decreases. ν is negatively correlated with the infection rate because as the number of patients seeking treatment increases, the number of patients undergoing spontaneous recovery and entering state E decreases, and the reduction in the number of infectious patients also reduces the number of new infections. dh is positively correlated with the infection rate because as the number of spontaneous recovery individuals increases, the number of individuals in state E increases. The PRCC of other parameters is near 0, indicating that their influence on the infection rate is very weak.
MDR-TB and non-MDR-TB should be distinguished throughout all stages because both forms of tuberculosis are found among infected individuals and patients. However, certain relevant parameters, such as the rate of reactivation and the incubation period, among others, have not been proven to differ between MDR-TB and non-MDR-TB based on available reports. We are restricted to using approximations of these parameters based on literature sources to integratively represent their characteristics. This limitation may have affected the accuracy of the results to a certain extent.
Since most of the parameters in the model are obtained directly from literature searches, they are all set at a fixed value. However, many parameters change with time, and we cannot accurately obtain the values of these changing parameters, which affects the model’s estimated results to some extent. Our model does not cover all situations that manifest in reality. For example, we did not consider the immune effects of the Bacille Calmette-Guerin vaccine, tuberculin test screening, centralized diagnosis and treatment for military, student and other special populations, as well as the differences between age groups, because we did not have enough data to include these parameters in a model. Nevertheless, the model estimates are consistent with the national surveys of pulmonary tuberculosis and the conclusions of available studies, indicating that the model faithfully reflects the epidemiological patterns of pulmonary tuberculosis in China since 2004.