A dynamic model for tuberculosis transmission and optimal treatment strategies in South Korea

Examining operational efficiency with prudent risks of Covid-19: a contextual DEA analysis with an undesirable intermediate measure

In the wake of the losses of human lives and disruption to the world economy caused by the spread of the COVID-19 pandemic, it has become imperative to assess the effectiveness of containment strategies adopted by countries. The success of any containment strategy of achieving low mortality and high recovery rate depends on the efficient utilization of available but limited resources, such as number of hospital beds and healthcare workers. While the spreading pattern of the pandemic has been researched heavily, there is limited research that comprehensively focuses on the efficient utilization of available resources to achieve the desired aims of low mortality and high recovery. In order to close this research gap, we employ a two-stage network data envelopment analysis (DEA) to identify the inefficiency in the process and resolve the resource constraints by considering medical and non-medical (administrative) interventions as two serial stages. The number of infected people is treated as the intermediate product, which is an undesirable output of the first stage and subsequently enters the second stage as an input. This network DEA model successfully addresses the conflict between the two stages over the handling of infected people and assesses the vulnerabilities of the countries against the transmission rates of the disease in the respective countries. Thus, the objective of this study is to develop a well-coordinated plan for different government agencies to jointly mitigate the risk under constrained resources. The findings reveal that almost 60 % of the Organization for Economic Cooperation and Development (OECD) countries have used their resources suboptimally and are producing, on average, almost half the amount of the maximum possible outputs. As a sizeable amount of inefficiency can be explained by varying economic and demographic factors, such as health expenditure and the proportion of the aged population, the efficiency evaluation has been revisited with adjustments for unfavorable externalities. The analysis and its implications can help policymakers formulate optimal resource plans and identify potential areas for improvement.

Dynamics and control strategy for a delayed viral infection model

In this paper, we derive a delayed epidemic model to describe the characterization of cytotoxic T lymphocyte (CTL)-mediated immune response against virus infection. The stability of equilibria and the existence of Hopf bifurcation are analysed. Theoretical results reveal that if the basic reproductive number is greater than 1, the positive equilibrium may lose its stability and the bifurcated periodic solution occurs when time delay is taken as the bifurcation parameter. Furthermore, we investigate an optimal control problem according to the delayed model based on the available therapy for hepatitis B infection. With the aim of minimizing the infected cells and viral load with consideration for the treatment costs, the optimal solution is discussed analytically. For the case when periodic solution occurs, numerical simulations are performed to suggest the optimal therapeutic strategy and compare the model-predicted consequences.

Demographic Control Measure Implications of Tuberculosis Infection for Migrant Workers across Taiwan Regions

A sharp increase in migrant workers has raised concerns for TB epidemics, yet optimal TB control strategies remain unclear in Taiwan regions. This study assessed intervention efforts on reducing tuberculosis (TB) infection among migrant workers. We performed large-scale data analyses and used them to develop a control-based migrant worker-associated susceptible-latently infected-infectious-recovered (SLTR) model. We used the SLTR model to assess potential intervention strategies such as social distancing, early screening, and directly observed treatment, short-course (DOTS) for TB transmission among migrant workers and locals in three major hotspot cities from 2018 to 2023. We showed that social distancing was the best single strategy, while the best dual measure was social distancing coupled with early screening. However, the effectiveness of the triple strategy was marginally (1-3%) better than that of the dual measure. Our study provides a mechanistic framework to facilitate understanding of TB transmission dynamics between locals and migrant workers and to recommend better prevention strategies in anticipation of achieving WHO's milestones by the next decade. Our work has implications for migrant worker-associated TB infection prevention on a global scale and provides a knowledge base for exploring how outcomes can be best implemented by alternative control measure approaches.

Review of fractional epidemic models

The global impact of corona virus (COVID-19) has been profound, and the public health threat it represents is the most serious seen in a respiratory virus since the 1918 influenza A(H1N1) pandemic. In this paper, we have focused on reviewing the results of epidemiological modelling especially the fractional epidemic model and summarized different types of fractional epidemic models including fractional Susceptible-Infective-Recovered (SIR), Susceptible-Exposed-Infective-Recovered (SEIR), Susceptible-Exposed-Infective-Asymptomatic-Recovered (SEIAR) models and so on. Furthermore, we propose a general fractional SEIAR model in the case of single-term and multi-term fractional differential equations. A feasible and reliable parameter estimation method based on modified hybrid Nelder-Mead simplex search and particle swarm optimisation is also presented to fit the real data using fractional SEIAR model. The effective methods to solve the fractional epidemic models we introduced construct a simple and effective analytical technique that can be easily extended and applied to other fractional models, and can help guide the concerned bodies in preventing or controlling, even predicting the infectious disease outbreaks.

Analysis of an age-structured tuberculosis model with treatment and relapse

A new tuberculosis model consisting of ordinary differential equations and partial differential equations is established in this paper. The model includes latent age (i.e., the time elapsed since the individual became infected but not infectious) and relapse age (i.e., the time between cure and reappearance of symptoms of tuberculosis). We identify 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 for this model, and show that 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 determines the global dynamics of the model. If \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {R}_{0}<1$$\end{document}R0<1, the disease-free equilibrium is globally asymptotically stable, which means that tuberculosis will disappear, and if \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {R}_{0}>1$$\end{document}R0>1, there exists a unique endemic equilibrium that attracts all solutions that can cause the spread of tuberculosis. Based on the tuberculosis data in China from 2007 to 2018, we use Grey Wolf Optimizer algorithm to find the optimal parameter values and initial values of the model. Furthermore, we perform uncertainty and sensitivity analysis to identify the parameters that have significant impact on the basic reproduction number. Finally, we give an effective measure to reach the goal of WHO of reducing the incidence of tuberculosis by 80% by 2030 compared to 2015.

State Feedback and Synergetic controllers for tuberculosis in infected population

Tuberculosis (TB) is a contagious disease which can easily be disseminated in a society. A five state Susceptible, exposed, infected, recovered and resistant (SEIRs) epidemiological mathematical model of TB has been considered along with two non-linear controllers: State Feedback (SFB) and Synergetic controllers have been designed for the control and prevention of the TB in a population. Using the proposed controllers, the infected individuals have been reduced/controlled via treatment, and susceptible individuals have been prevented from the disease via vaccination. A mathematical analysis has been carried out to prove the asymptotic stability of proposed controllers by invoking the Lyapunov control theory. Simulation results using MATLAB/Simulink manifest that the non-linear controllers show fast convergence of the system states to their respective desired levels. Comparison shows that proposed SFB controller performs better than Synergetic controller in terms of convergence time, steady state error and oscillations.

Optimal control on a mathematical model to pattern the progression of coronavirus disease 2019 (COVID-19) in Indonesia

Background

Understanding the pattern of COVID-19 infection progression is critical for health policymakers. Reaching the exponential peak of cases, flattening the curve, and treating all of the active cases are the keys to success in reducing outbreak transmission. The objective of this study was to determine the most effective model for predicting the peak of COVID-19 in Indonesia, using a deterministic model.

Methods

The SEI2RS model considers five strategies for control, namely: large-scale social restriction ( u1 ), contact tracing ( u2 ), mass testing ( u3 ) , case detection and treatment ( u4 ), and the wearing of face masks ( u5 ). Three scenarios were developed, each differentiated by the controls. The model used April 10, 2020, and December 31, 2020, as the initial and final times.

Results

The simulation results indicated that the peak of COVID-19 cases for scenarios 1, 2, and 3 occur on the 59th day with 33,151 cases, on the 38th day with 37,908 cases, and on the 40th day with 39,305 cases. For all of the scenarios, the decline phase shows a slow downward slope and about 8000 cases of COVID-19 still active by the end of 2020.

Conclusion

The study concludes that scenario 2, which consists of large-scale social restriction (u1), contact tracing (u2), case detection and treatment (u4), and the wearing of face masks (u5), is the most rational scenario to control COVID-19 spreading in Indonesia.

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.

Modeling drug-resistant tuberculosis amplification rates and intervention strategies in Bangladesh

Tuberculosis (TB) is the seventh leading cause of morbidity and mortality in Bangladesh. Although the National TB control program (NTP) of Bangladesh is implementing its nationwide TB control strategies, more specific and effective single or combination interventions are needed to control drug-susceptible (DS) and multi-drug resistant (MDR) TB. In this study, we developed a two strain TB mathematical model with amplification and fit it to the Bangladesh TB data to understand the transmission dynamics of DS and MDR TB. Sensitivity analysis was used to identify important parameters. We evaluated the cost-effectiveness of varying combinations of four basic control strategies including distancing, latent case finding, case holding and active case finding, all within the optimal control framework. From our fitting, the model with different transmission rates between DS and MDR TB best captured the Bangladesh TB reported case counts. The estimated basic reproduction number for DS TB was 1.14 and for MDR TB was 0.54, with an amplification rate of 0.011 per year. The sensitivity analysis also indicated that the transmission rates for both DS and MDR TB had the largest influence on prevalence. To reduce the burden of TB (both DS and MDR), our finding suggested that a quadruple control strategy that combines distancing control, latent case finding, case holding and active case finding is the most cost-effective. Alternative strategies can be adopted to curb TB depending on availability of resources and policy makers’ decisions.

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.

Strategies in regulating glioblastoma signaling pathways and anti-invasion therapy

Glioblastoma multiforme is one of the most invasive type of glial tumors, which rapidly grows and commonly spreads into nearby brain tissue. It is a devastating brain cancer that often results in death within approximately 12 to 15 months after diagnosis. In this work, optimal control theory was applied to regulate intracellular signaling pathways of miR-451–AMPK–mTOR–cell cycle dynamics via glucose and drug intravenous administration infusions. Glucose level is controlled to activate miR-451 in the up-stream pathway of the model. A potential drug blocking the inhibitory pathway of mTOR by AMPK complex is incorporated to explore regulation of the down-stream pathway to the cell cycle. Both miR-451 and mTOR levels are up-regulated inducing cell proliferation and reducing invasion in the neighboring tissues. Concomitant and alternating glucose and drug infusions are explored under various circumstances to predict best clinical outcomes with least administration costs.

Mathematical model and intervention strategies for mitigating tuberculosis in the Philippines

Tuberculosis (TB) is the sixth leading cause of morbidity and mortality in the Philippines. Although significant progress has been made in the detection and cure of TB under the Directly Observed Treatment Short Course, battling against the disease is still a burdensome task. It demands a concerted effort for specific and effective interventions. In this work, a mathematical TB model fitted to the Philippine data is developed to understand its transmission dynamics. Different control strategies such as distancing, latent case finding, case holding, active case finding controls, and combinations thereof are investigated within the framework of optimal control theory. This study proposes optimal control strategies for reducing the number of high-risk latent and infectious TB patients with minimum intervention implementation costs. Results suggest that distancing control is the most efficient control strategy when a single intervention is utilized. However, full scale employment of the distancing control measure is a daunting task. This burden can be circumvented by the combination of other control interventions. Our noble finding in this study is that enhancing active case finding control instead of case holding control together with distancing and latent case finding control is shown to have significant potential for curtailing the spread of TB in the Philippines.

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.

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.

On the analysis of a multi-regions discrete SIR epidemic model: an optimal control approach

In this paper, we devise a discrete time SIR model depicting the spread of infectious diseases in various geographical regions that are connected by any kind of anthropological movement, which suggests disease-affected people can propagate the disease from one region to another via travel. In fact, health policy-makers could manage the problem of the regional spread of an epidemic, by organizing many vaccination campaigns, or by suggesting other defensive strategies such as blocking movement of people coming from borders of regions at high-risk of infection and entering very controlled regions or with insignificant infection rate. Further, we introduce in the discrete SIR systems, two control variables which represent the effectiveness rates of vaccination and travel-blocking operation. We focus in our study to control the outbreaks of an epidemic that affects a hypothetical population belonging to a specific region. Firstly, we analyze the epidemic model when the control strategy is based on the vaccination control only, and secondly, when the travel-blocking control is added. The multi-points boundary value problems, associated to the optimal control problems studied here, are obtained based on a discrete version of Pontryagin's maximum principle, and resolved numerically using a progressive-regressive discrete scheme that converges following an appropriate test related to the Forward-Backward Sweep Method on optimal control.

Optimal control strategies of eradicating invisible glioblastoma cells after conventional surgery

Glioblastoma, the most aggressive type of brain cancer, has median survival time of 1 year after diagnosis. It is characterized by alternating modes of rapid proliferation and aggressive invasion in response to metabolic stress in the microenvironment. A particular microRNA, miR-451, and its downstream signalling molecules, AMPK complex, are known to be key determinants in switching cell fate. These components form a core control system determining a balance between cell growth and migration which is regulated by fluctuating glucose levels in the microenvironment. An important factor from the treatment point of view is that low levels of glucose affect metabolism and activate cell migration through the miR-451-AMPK control system, creating 'invisible' migratory cells and making them inaccessible by conventional surgery. In this work, we apply optimal control theory to deal with the problem of maintaining upregulated miR-451 levels that prevent cell infiltration to surrounding brain tissue and thus induce localization of these cancer cells at the surgical site. The model also considers the effect of a drug that blocks inhibitive pathways of miR-451 from AMPK complex. Glucose infusion control and drug infusion control are chosen to represent dose rates of glucose and drug intravenous administrations, respectively. The characteristics of optimal control lead us to investigate the structure of optimal intravenous infusion regimen under various circumstances and predict best clinical outcomes with minimum expense possible.

Optimal tuberculosis prevention and control strategy from a mathematical model based on real data

A mathematical control model for the transmission dynamics of tuberculosis (TB) in South Korea is developed on the basis of the reported active-TB and relapse-TB incidence data. In this work, optimal control theory is used to propose optimal TB prevention and control strategy and rearrange the government TB budget for the best TB elimination plan. The impact of distancing, case finding, and/or case holding controls are investigated when the number of infected and infectious individuals are minimized, while the intervention costs are kept low. The implementation of optimal control measures shows that the distancing control, such as isolation of infectious people, early TB patient detection, and educational program/campaign for healthy control, is the most effective control factor for the prevention of TB transmission in South Korea.

What does a mathematical model tell about the impact of reinfection in korean tuberculosis infection?

OBJECTIVES

According to the Korea Centers for Disease Control and Prevention, new active tuberculosis (TB) cases have increased since 2001. Some key factors explain and characterize the transmission dynamics of Korean TB infection, such as a higher ratio of latent individuals and a new reporting system implemented in 2001, among others.

METHODS

We propose a mathematical TB model that includes exogenous reinfection to gain a better understanding of the recent trend for TB incidence. We divide the simulation time window into two periods, 1970-2000 and 2001-2012, according to the implementation date of a new TB detection system.

RESULTS

Two sets of parameters, including the transmission rate, the latent period, the recovery rate, and the proportion of exogenous reinfection, are estimated using the least-squares method and calibrated to data on the incidence of active TB.

CONCLUSION

Among some key parameters in the model, the case finding effort turned out to be the most significant impacting component on the reduction in the active TB cases.