Mathematical models for the economic allocation of tuberculosis control activities in developing nations

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.

The prevention and control of tuberculosis: an analysis based on a tuberculosis dynamic model derived from the cases of Americans

Background

Tuberculosis (TB), a preventable and curable disease, is claimed as the second largest number of fatalities, and there are 9,025 cases reported in the United States in 2018. Many researchers have done a lot of research and achieved remarkable results, but TB is still a severe problem for human beings. The study is a further exploration of the prevention and control of tuberculosis.

Methods

In the paper, we propose a new dynamic model to study the transmission dynamics of TB, and then use global differential evolution and local sequential quadratic programming (DESQP) optimization algorithm to estimate parameters of the model. Finally, we use Latin hypercube sampling (LHS) and partial rank correlation coefficients (PRCC) to analyze the influence of parameters on 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}$\mathcal R_{0}$\end{document}R0) and the total infectious (including the diagnosed, undiagnosed and incomplete treatment infectious), respectively.

Results

According to the research, the basic reproduction number is computed as 2.3597 from 1984 to 2018, which means TB is also an epidemic in the US. The diagnosed rate is 0.6082, which means the undiagnosed will be diagnosed after 1.6442 years. The diagnosed will recover after an average of 1.9912 years. Moreover, some diagnosed will end the treatment after 1.7550 years for some reason. From the study, it’s shown that 2.40% of the recovered will be reactivated, and 13.88% of the newborn will be vaccinated. However, the immune system will be lost after about 19.6078 years.

Conclusion

Through the results of this study, we give some suggestions to help prevent and control the TB epidemic in the United States, such as prolonging the protection period of the vaccine by developing new and more effective vaccines to prevent TB; using the Chemoprophylaxis for incubation patients to prevent their conversion into active TB; raising people’s awareness of the prevention and control of TB and treatment after illness; isolating the infected to reduce the spread of TB. According to the latest report in the announcement that came at the first WHO Global Ministerial Conference on Ending tuberculosis in the Sustainable Development Era, we predict that it is challenging to control TB by 2030.

Country-specific intervention strategies for top three TB burden countries using mathematical model

Tuberculosis (TB) is one of the top 10 causes of death globally and the leading cause of death by a single infectious pathogen. The World Health Organization (WHO) has declared the End TB Strategy, which targets a 90% reduction in the incidence rate by the year 2035 compared to the level in the year 2015. In this work, a TB model is considered to understand the transmission dynamics in the top three TB burden countries-India, China, and Indonesia. Country-specific epidemiological parameters were identified using data reported by the WHO. If India and Indonesia succeed in enhancing their treatment protocols and increase treatment and treatment success rate to that of China, the incidence rate could be reduced by 65.99% and 68.49%, respectively, by the end of 2035. Evidently, complementary interventions are essential to achieve the WHO target. Our analytical approach utilizes optimal control theory to obtain time-dependent nonpharmaceutical and latent case finding controls. The objective functional of the optimal control problem includes a payoff term reflecting the goal set by WHO. Appropriate combinations of control strategies are investigated. Based on the results, gradual enhancement and continuous implementation of intervention measures are recommended in each country.

Optimizing influenza vaccine policies for controlling 2009-like pandemics and regular outbreaks

Background

This study examined the effectiveness of various vaccine policies against influenza. The transmission rate was calculated by use of the time-series influenza-like illness case during the year of 2009 and recent epidemics in Taiwan.

Methods

We developed a stochastic compartmental model to analyze the transmission of influenza, where the population was stratified by location and age group, and the vaccine distribution was considered using the current policy. The simulation study compared the previous vaccine policy and a new policy with expanded coverage and various lengths of the vaccination campaign. The sensitivity analysis investigated different levels of vaccine efficacy to confirm the robustness of the recommended policies.

Results

Doubling vaccine coverage can decrease the number of infections effectively in the regular epidemic scenario. However, a peak of infections occurs if the duration of implementing vaccination is too long. In the 2009-like pandemic scenario, both increasing vaccine doses and reducing the program’s duration can mitigate infections, although the early outbreak restricts the effectiveness of vaccination programs.

Conclusions

The finding indicates that only increasing vaccine coverage can reduce influenza infections. To avoid the peak of infections, it is also necessary to execute the vaccination activity immediately. Vaccine efficacy significantly impacts the vaccination policy’s performance. When vaccine efficacy is low, neither increasing vaccination doses nor reducing vaccination timeframe prevents infections. Therefore, the variation in vaccine efficacy should be taken into account when making immunization policies against influenza.

Systematic review of mathematical models exploring the epidemiological impact of future TB vaccines

Mathematical models are useful for assessing the potential epidemiological impact of future tuberculosis (TB) vaccines. We conducted a systematic review of mathematical models estimating the epidemiological impact of future human TB vaccines. PubMed, Embase and WHO Global Health Library were searched, 3-stage manual sifted, and citation- and reference-tracked, identifying 23 papers. An adapted quality assessment tool was developed, with a resulting median study quality score of 20/28. The literature remains divided as to whether vaccines effective pre- or post-infection would provide greatest epidemiological impact. However, all-age or adolescent/adult targeted prevention of disease vaccines achieve greater and more rapid impact than neonatal vaccines. Mass campaigns alongside routine neonatal vaccination can have profound additional impact. Economic evaluations found TB vaccines overwhelmingly cost-effective, particularly when targeted to adolescents/adults. The variability of impact by setting, age group and vaccine characteristics must be accounted for in the development and delivery of future TB vaccines.

Modeling historical tuberculosis epidemics among Canadian First Nations: effects of malnutrition and genetic variation

Late 19th century epidemics of tuberculosis (TB) in Western Canadian First Nations resulted in peak TB mortality rates more than six times the highest rates recorded in Europe. Using a mathematical modeling approach and historical TB mortality time series, we investigate potential causes of high TB mortality and rapid epidemic decline in First Nations from 1885 to 1940. We explore two potential causes of dramatic epidemic dynamics observed in this setting: first, we explore effects of famine prior to 1900 on both TB and population dynamics. Malnutrition is recognized as an individual-level risk factor for TB progression and mortality; its population-level effects on TB epidemics have not been explored previously. Second, we explore effects of heterogeneity in susceptibility to TB in two ways: modeling heterogeneity in susceptibility to infection, and heterogeneity in risk of developing disease once infected. Our results indicate that models lacking famine-related changes in TB parameters or heterogeneity result in an implausibly poor fit to both the TB mortality time series and census data; the inclusion of these features allows for the characteristic decline and rise in population observed in First Nations during this time period and confers improved fits to TB mortality data.

Parameter identification in a tuberculosis model for Cameroon

A deterministic model of tuberculosis in Cameroon is designed and analyzed with respect to its transmission dynamics. The model includes lack of access to treatment and weak diagnosis capacity as well as both frequency- and density-dependent transmissions. It is shown that the model is mathematically well-posed and epidemiologically reasonable. Solutions are non-negative and bounded whenever the initial values are non-negative. A sensitivity analysis of model parameters is performed and the most sensitive ones are identified by means of a state-of-the-art Gauss-Newton method. In particular, parameters representing the proportion of individuals having access to medical facilities are seen to have a large impact on the dynamics of the disease. The model predicts that a gradual increase of these parameters could significantly reduce the disease burden on the population within the next 15 years.

Epidemiological models of Mycobacterium tuberculosis complex infections

The resurgence of tuberculosis in the 1990s and the emergence of drug-resistant tuberculosis in the first decade of the 21st century increased the importance of epidemiological models for the disease. Due to slow progression of tuberculosis, the transmission dynamics and its long-term effects can often be better observed and predicted using simulations of epidemiological models. This study provides a review of earlier study on modeling different aspects of tuberculosis dynamics. The models simulate tuberculosis transmission dynamics, treatment, drug resistance, control strategies for increasing compliance to treatment, HIV/TB co-infection, and patient groups. The models are based on various mathematical systems, such as systems of ordinary differential equations, simulation models, and Markov Chain Monte Carlo methods. The inferences from the models are justified by case studies and statistical analysis of TB patient datasets.

Multivariate Markovian modeling of tuberculosis: forecast for the United States

We have developed a computer-implemented, multivariate Markov chain model to project tuberculosis (TB) incidence in the United States from 1980 to 2010 in disaggregated demographic groups. Uncertainty in model parameters and in the projections is represented by fuzzy numbers. Projections are made under the assumption that current TB control measures will remain unchanged for the projection period. The projections of the model demonstrate an intermediate increase in national TB incidence (similar to that which actually occurred) followed by continuing decline. The rate of decline depends strongly on geographic, racial, and ethnic characteristics. The model predicts that the rate of decline in the number of cases among Hispanics will be slower than among white non-Hispanics and black non-Hispanics a prediction supported by the most recent data.

Experimental chemotherapy of tuberculosis

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