Mathematical model and intervention strategies for mitigating tuberculosis in the Philippines

Unraveling the influence of the objective functional on epidemic optimal control: Insights from the SIR model

In the application of optimal control theory to medical and biological problems, the dependence of the objective functional on the control variable is often subject to uncertainty. This study examines the effects of this dependency on the outcomes of optimal control problems in the context of disease control using the SIR model. We formulate two distinct optimal control problems: one for the control of disease spread through prophylactic vaccination, and another for the treatment of infected individuals. For each scenario, we propose four variations of the objective functional to capture the cost of control interventions, namely, quadratic state-independent, quadratic state-dependent, linear state-independent, and linear state-dependent. We also conduct numerical simulations to compare optimal control solutions across different weight parameters. While some qualitative characteristics of the control profiles are similar in certain scenarios, there are also notable differences suggesting that the choice of objective functional can substantially alter the resulting control profiles. Consequently, when there is uncertainty regarding the functional form of the objective and its relationship to the control parameter, it is recommended to evaluate multiple objectives and subsequently identify which solution is most suitable for practical implementation.

Vaccination strategies in a pair formation model for human papillomavirus infection: An optimal control approach

Human papillomavirus (HPV) infection is a widespread sexually transmitted infection responsible for several cancers including anal, oropharyngeal, penile, vaginal, and cervical cancer. Despite HPV vaccines have been available for almost 20 years and are incredibly effective in preventing infection, the scale-up of vaccination has been slow in many low and middle-income countries. This analysis uses a pair model that explicitly accounts for sexual partnership formation to investigate HPV immunization programs. The optimality of vaccine interventions is analyzed using optimal control theory. We give formal proof of the existence of optimal control solutions and obtain first-order optimality conditions via Pontryagin's Maximum Principle. Extensive numerical simulations are used to investigate plausible what-if scenarios to understand under which conditions the inclusion of males should be recommended in addition to female vaccination. The results suggest that a gender-neutral vaccination program should be recommended in regions where vaccination uptake in women is still low whereas for an already existing female-only program with high uptake, it is more effective to keep increasing coverage in females.

A six-compartment model for COVID-19 with transmission dynamics and public health strategies

The global crisis of the COVID-19 pandemic has highlighted the need for mathematical models to inform public health strategies. The present study introduces a novel six-compartment epidemiological model that uniquely incorporates a higher isolation rate for unreported symptomatic cases of COVID-19 compared to reported cases, aiming to enhance prediction accuracy and address the challenge of initial underreporting. Additionally, we employ optimal control theory to assess the cost-effectiveness of interventions and adapt these strategies to specific epidemiological scenarios, such as varying transmission rates and the presence of asymptomatic carriers. By applying this model to COVID-19 data from India (30 January 2020 to 24 November 2020), chosen to capture the initial outbreak and subsequent waves, we calculate a basic reproduction number of 2.147, indicating the high transmissibility of the virus during this period in India. A sensitivity analysis reveals the critical impact of detection rates and isolation measures on disease progression, showing the robustness of our model in estimating the basic reproduction number. Through optimal control simulations, we demonstrate that increasing isolation rates for unreported cases and enhancing detection reduces the spread of COVID-19. Furthermore, our cost-effectiveness analysis establishes that a combined strategy of isolation and treatment is both more effective and economically viable. This research offers novel insights into the efficacy of non-pharmaceutical interventions, providing a tool for strategizing public health interventions and advancing our understanding of infectious disease dynamics.

Optimal vaccination strategies for a heterogeneous population using multiple objectives: The case of L1- and L2-formulations

The choice of the objective functional in optimization problems coming from biomedical and epidemiological applications plays a key role in optimal control outcomes. In this study, we investigate the role of the objective functional on the structure of the optimal control solution for an epidemic model for sexually transmitted infections that includes a core group with higher sexual activity levels than the rest of the population. An optimal control problem is formulated to find a targeted vaccination program able to control the spread of the infection with minimum vaccine deployment. Both L1- and L2-objectives are considered as an attempt to explore the trade-offs between control dynamics and the functional form characterizing optimality. The results show that the optimal vaccination policies for both the L1- and the L2-formulation share one important qualitative property, that is, immunization of the core group should be prioritized by policymakers to achieve a fast reduction of the epidemic. However, quantitative aspects of this result can be significantly affected depending on the choice of the control weights between formulations. Overall, the results suggest that with appropriate weight constants, the optimal control outcomes are reasonably robust with respect to the L1- or L2-formulation. This is particularly true when the monetary cost of the control policy is substantially lower than the cost associated with the disease burden. Under these conditions, even if the L1-formulation is more realistic from a modeling perspective, the L2-formulation can be used as an approximation and yield qualitatively comparable outcomes.

COVID-19 transmission dynamics and the impact of vaccination: modelling, analysis and simulations

Despite the lifting of COVID-19 restrictions, the COVID-19 pandemic and its effects remain a global challenge including the sub-Saharan Africa (SSA) region. Knowledge of the COVID-19 dynamics and its potential trends amidst variations in COVID-19 vaccine coverage is therefore crucial for policy makers in the SSA region where vaccine uptake is generally lower than in high-income countries. Using a compartmental epidemiological model, this study aims to forecast the potential COVID-19 trends and determine how long a wave could be, taking into consideration the current vaccination rates. The model is calibrated using South African reported data for the first four waves of COVID-19, and the data for the fifth wave are used to test the validity of the model forecast. The model is qualitatively analysed by determining equilibria and their stability, calculating the basic reproduction number R 0 and investigating the local and global sensitivity analysis with respect to R 0 . The impact of vaccination and control interventions are investigated via a series of numerical simulations. Based on the fitted data and simulations, we observed that massive vaccination would only be beneficial (deaths averting) if a highly effective vaccine is used, particularly in combination with non-pharmaceutical interventions. Furthermore, our forecasts demonstrate that increased vaccination coverage in SSA increases population immunity leading to low daily infection numbers in potential future waves. Our findings could be helpful in guiding policy makers and governments in designing vaccination strategies and the implementation of other COVID-19 mitigation strategies.

Co-dynamics of COVID-19 and TB with COVID-19 vaccination and exogenous reinfection for TB: An optimal control application

COVID-19 and Tuberculosis (TB) are among the major global public health problems and diseases with major socioeconomic impacts. The dynamics of these diseases are spread throughout the world with clinical similarities which makes them difficult to be mitigated. In this study, we formulate and analyze a mathematical model containing several epidemiological characteristics of the co-dynamics of COVID-19 and TB. Sufficient conditions are derived for the stability of both COVID-19 and TB sub-models equilibria. Under certain conditions, the TB sub-model could undergo the phenomenon of backward bifurcation whenever its associated reproduction number is less than one. The equilibria of the full TB-COVID-19 model are locally asymptotically stable, but not globally, due to the possible occurrence of backward bifurcation. The incorporation of exogenous reinfection into our model causes effects by allowing the occurrence of backward bifurcation for the basic reproduction number R₀ < 1 and the exogenous reinfection rate greater than a threshold (η > η∗). The analytical results show that reducing R₀ < 1 may not be sufficient to eliminate the disease from the community. The optimal control strategies were proposed to minimize the disease burden and related costs. The existence of optimal controls and their characterization are established using Pontryagin's Minimum Principle. Moreover, different numerical simulations of the control induced model are carried out to observe the effects of the control strategies. It reveals the usefulness of the optimization strategies in reducing COVID-19 infection and the co-infection of both diseases in the community.

Quantitative Assessment of a Dual Epidemic Caused by Tuberculosis and HIV in the Philippines

Tuberculosis (TB) and human immunodeficiency virus (HIV) are the two major public health emergencies in the Philippines. The country is ranked fourth worldwide in TB incidence cases despite national efforts and initiatives to mitigate the disease. Concurrently, the Philippines has the fastest-growing HIV epidemic in Asia and the Pacific region. The TB-HIV dual epidemic forms a lethal combination enhancing each other's progress, driving the deterioration of immune responses. In order to understand and describe the transmission dynamics and epidemiological patterns of the co-infection, a compartmental model for TB-HIV is developed. A class of people living with HIV (PLHIV) who did not know their HIV status is incorporated into the model. These unaware PLHIV who do not seek medical treatment are potential sources of new HIV infections that could significantly influence the disease transmission dynamics. Sensitivity analysis using the partial rank correlation coefficient is performed to assess model parameters that are influential to the output of interests. The model is calibrated using available Philippine data on TB, HIV, and TB-HIV. Parameters that are identified include TB and HIV transmission rates, progression rates from exposed to active TB, and from TB-latent with HIV to active infectious TB with HIV in the AIDS stage. Uncertainty analysis is performed to identify the degree of accuracy of the estimates. Simulations predict an alarming increase of 180% and 194% in new HIV and TB-HIV infections in 2025, respectively, relative to 2019 data. These projections underscore an ongoing health crisis in the Philippines that calls for a combined and collective effort by the government and the public to take action against the lethal combination of TB and HIV.

The prevalence of tuberculosis infection in India: A systematic review and meta-analysis

Background & objectives

The National Prevalence Survey of India (2019-2021) estimated 31 per cent tuberculosis infection (TBI) burden among individuals above 15 years of age. However, so far little is known about the TBI burden among the different risk groups in India. Thus, this systematic review and meta-analysis, aimed to estimate the prevalence of TBI in India based on geographies, sociodemographic profile, and risk groups.

Methods

To identify the prevalence of TBI in India, data sources such as MEDLINE, EMBASE, CINAHL, and Scopus were searched for articles reporting data between 2013-2022, irrespective of the language and study setting. TBI data were extracted from 77 publications and pooled prevalence was estimated from the 15 community-based cohort studies. Articles were reviewed in accordance with the Preferred Reporting Items for Systematic Reviews and Meta-Analysis guidelines and were sourced using a predefined search strategy from different databases.

Results

Out of 10,521 records, 77 studies (46 cross-sectional and 31 cohort studies) were included. The pooled TBI prevalence for India based on the community-based cohort studies was estimated as 41 per cent [95% confidence interval (CI) 29.5-52.6%] irrespective of the risk of acquiring it, while the estimation was 36 per cent (95% CI 28-45%) prevalence observed among the general population excluding high-risk groups. Regions with high active TB burden were found to have a high TBI prevalence such as Delhi and Tamil Nadu. An increasing trend of TBI was observed with increasing age in India.

Interpretation & conclusions

This review demonstrated a high prevalence of TBI in India. The burden of TBI was commensurate with active TB prevalence suggesting possible conversion of TBI to active TB. A high burden was recorded among people residing in the northern and southern regions of the country. Such local epidemiologic variation need to be considered to reprioritize and implement-tailored strategies for managing TBI in India.

Innovating tuberculosis prevention to achieve universal health coverage in the Philippines

To contribute to tuberculosis (TB) elimination, TB preventive treatment (TPT) should integrate innovative approaches including tele-contact investigation (TCI), mathematical modelling, and participatory governance. Aligning with the World Health Organisation's primary health care framework, supply is provided by the provincial health system, demand is cultivated by the community, while governance is represented by the governor, who oversees the health leadership structure, local policies, and allocation of resources. A healthy dynamic between these three components is required to achieve universal health coverage (UHC). Because of their potential to integrate health systems and engage communities, primary health care principles underpin an effective approach to TB prevention. First, the provincial health system should connect with the community through TCI to transform the status quo of passive service delivery. Second, community participation should strengthen the linkage between the health system and governance, which ensures that community action plans are aligned with provincial TPT targets. Third, governance should leverage mathematical modelling to allocate resources to those with greatest need. Central to this is a reliable TB information system that should validate a robust mathematical model to measure cost-effectiveness of the intervention. Collectively, this holistic approach to TB prevention could provide a proof-of-concept that investing in primary health care is the key to UHC.

COVID-19 outbreak: a predictive mathematical study incorporating shedding effect

In this paper, a modified SEIR epidemic model incorporating shedding effect is proposed to analyze transmission dynamics of the COVID-19 virus among different individuals' classes. The direct impact of pathogen concentration over susceptible populations through the shedding of COVID-19 virus into the environment is investigated. Moreover, the threshold value of shedding parameters is computed which gives information about their significance in decreasing the impact of the disease. The basic reproduction number ( R 0 ) is calculated using the next-generation matrix method, taking shedding as a new infection. In the absence of disease, the condition for the equilibrium point to be locally and globally asymptotically stable withR 0 < 1 are established. It has been shown that the unique endemic equilibrium point is globally asymptotically stable under the conditionR 0 > 1 . Bifurcation theory and center manifold theorem imply that the system exhibit backward bifurcation atR 0 = 1 . The sensitivity indices of R 0 are computed to investigate the robustness of model parameters. The numerical simulation is demonstrated to illustrate the results.

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.

Tuberculosis in Ethiopia: Optimal Intervention Strategies and Cost-Effectiveness Analysis

This paper searches for optimal strategies for the minimization of the number of high-risk latent and active tuberculosis (TB) infectious individuals using real data from Ethiopia. Optimal control theory is harnessed for investigation and analysis of the optimal combination of interventions for controlling the transmission of TB using distancing, case finding, and case holding as controls. We calculate and compare the incremental cost-effectiveness ratio (ICER) for each of the strategies to determine the most effective combination of interventions for curbing the spread of the disease. Our findings suggest that, for optimal cost-effective management of the TB disease, the government of Ethiopia must focus more on prevention strategies such as isolation of infectious people, early TB patient detection, treatment, and educational programs. The optimal strategy is quantified through simulation.

An efficient nonstandard computer method to solve a compartmental epidemiological model for COVID-19 with vaccination and population migration

BACKGROUND AND OBJECTIVE

In this manuscript, we consider a compartmental model to describe the dynamics of propagation of an infectious disease in a human population. The population considers the presence of susceptible, exposed, asymptomatic and symptomatic infected, quarantined, recovered and vaccinated individuals. In turn, the mathematical model considers various mechanisms of interaction between the sub-populations in addition to population migration.

METHODS

The steady-state solutions for the disease-free and endemic scenarios are calculated, and the local stability of the equilibium solutions is determined using linear analysis, Descartes' rule of signs and the Routh-Hurwitz criterion. We demonstrate rigorously the existence and uniqueness of non-negative solutions for the mathematical model, and we prove that the system has no periodic solutions using Dulac's criterion. To solve this system, a nonstandard finite-difference method is proposed.

RESULTS

As the main results, we show that the computer method presented in this work is uniquely solvable, and that it preserves the non-negativity of initial approximations. Moreover, the steady-state solutions of the continuous model are also constant solutions of the numerical scheme, and the stability properties of those solutions are likewise preserved in the discrete scenario. Furthermore, we establish the consistency of the scheme and, using a discrete form of Gronwall's inequality, we prove theoretically the stability and the convergence properties of the scheme. For convenience, a Matlab program of our method is provided in the appendix.

CONCLUSIONS

The computer method presented in this work is a nonstandard scheme with multiple dynamical and numerical properties. Most of those properties are thoroughly confirmed using computer simulations. Its easy implementation make this numerical approach a useful tool in the investigation on the propagation of infectious diseases. From the theoretical point of view, the present work is one of the few papers in which a nonstandard scheme is fully and rigorously analyzed not only for the dynamical properties, but also for consistently, stability and convergence.

Mathematical modeling for COVID-19 transmission dynamics: A case study in Ethiopia

In this paper, we proposed a nonlinear deterministic mathematical model for the transmission dynamics of COVID-19. First, we analyzed the system properties such as boundedness of the solutions, existence of disease-free and endemic equilibria, local and global stability of equilibrium points. Besides, we computed the basic reproduction number R 0 and studied its normalized sensitivity for model parameters to identify the most influencing parameter. The local stability of the disease-free equilibrium point is also verified via the help of the Jacobian matrix and Routh Hurwitz criteria. Moreover, the global stability of the disease-free equilibrium point is proved by using the approach of Castillo-Chavez and Song. We also proved the existence of the forward bifurcation using the center manifold theory. Then the model is fitted with COVID-19 infected cases reported from March 13, 2020, to July 31, 2021, in Ethiopia. The values of model parameters are then estimated from the data reported using the least square method together with the fminsearch function in the MATLAB optimization toolbox. Finally, different simulation cases were performed using PYTHON software to compare with analytical results. The simulation results suggest that the spread of COVID-19 can be managed via minimizing the contact rate of infected and increasing the quarantine of exposed individuals.

An efficient numerical simulation and mathematical modeling for the prevention of tuberculosis

The main purpose of this research is to use a fractional-mathematical model including Atangana–Baleanu derivatives to explore the clinical associations and dynamical behavior of the tuberculosis. Herein, we used a lately introduced fractional operator having Mittag-Leffler kernel. The existence and inimitability problems to the relevant model were examined through the fixed-point theory. To verify the significance of the arbitrary fractional-order derivative, numerical outcomes were explored from the biological and mathematical viewpoints using the values of model parameters. The graphical simulations show the comparison of the predictor–corrector method (PCM) and Caputo method (CM) for different fractional orders and the results indicated the significant preference of PCM over CM.

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.

A mathematical model of the dynamics of lymphatic filariasis in Caraga Region, the Philippines

Despite being one of the first countries to implement mass drug administration (MDA) for elimination of lymphatic filariasis (LF) in 2001 after a pilot study in 2000, the Philippines is yet to eliminate the disease as a public health problem with 6 out of the 46 endemic provinces still implementing MDA for LF as of 2018. In this work, we propose a mathematical model of the transmission dynamics of LF in the Philippines and a control strategy for its elimination using MDA. Sensitivity analysis using the Latin hypercube sampling and partial rank correlation coefficient methods suggests that the infected human population is most sensitive to the treatment parameters. Using the available LF data in Caraga Region from the Philippine Department of Health, we estimate the treatment rates r ₁ and r ₂ using the least-squares parameter estimation technique. Parameter bootstrapping showed small variability in the parameter estimates. Finally, we apply optimal control theory with the objective of minimizing the infected human population and the corresponding implementation cost of MDA, using the treatment coverage γ as the control parameter. Simulation results highlight the importance of maintaining a high MDA coverage per year to effectively minimize the infected population by the year 2030.

Modelling the Transmission Dynamics of COVID-19 in Six High-Burden Countries

The new Coronavirus Disease 19, officially known as COVID-19, originated in China in 2019 and has since spread worldwide. We presented an age-structured Susceptible-Latent-Mild-Critical-Removed (SLMCR) compartmental model of COVID-19 disease transmission with nonlinear incidence during the pandemic period. We provided the model calibration to estimate parameters with day-wise COVID-19 data, i.e., reported cases by worldometer from 15^th February to 30^th March 2020 in six high-burden countries, including Australia, Italy, Spain, the USA, the UK, and Canada. We estimate transmission rates for each country and found that the country with the highest transmission rate is Spain, which may increase the new cases and deaths than the other countries. We found that saturation infection negatively impacted the dynamics of COVID-19 cases in all the six high-burden countries. The study used a sensitivity analysis to identify the most critical parameters through the partial rank correlation coefficient method. We found that the transmission rate of COVID-19 had the most significant influence on prevalence. The prediction of new cases in COVID-19 until 30^th April 2020 using the developed model was also provided with recommendations to control strategies of COVID-19. We also found that adults are more susceptible to infection than both children and older people in all six countries. However, in Italy, Spain, the UK, and Canada, older people show more susceptibility to infection than children, opposite to the case in Australia and the USA. The information generated from this study would be helpful to the decision-makers of various organisations across the world, including the Ministry of Health in Australia, Italy, Spain, the USA, the UK, and Canada, to control COVID-19.

Scenario analysis for programmatic tuberculosis control in Bangladesh: a mathematical modelling study

Tuberculosis (TB) is a major public health problem in Bangladesh. Although the National TB control program of Bangladesh is implementing a comprehensive expansion of TB control strategies, logistical challenges exist, and there is significant uncertainty concerning the disease burden. Mathematical modelling of TB is considered one of the most effective ways to understand the dynamics of infection transmission and allows quantification of parameters in different settings, including Bangladesh. In this study, we present a two-strain mathematical modelling framework to explore the dynamics of drug-susceptible (DS) and multidrug-resistant (MDR) TB in Bangladesh. We calibrated the model using DS and MDR-TB annual incidence data from Bangladesh from years 2001 to 2015. Further, we performed a sensitivity analysis of the model parameters and found that the contact rate of both strains had the largest influence on the basic reproduction numbers [Formula: see text] and [Formula: see text] of DS and MDR-TB, respectively. Increasingly powerful intervention strategies were developed, with realistic impact and coverage determined with the help of local staff. We simulated for the period from 2020 to 2035. Here, we projected the DS and MDR-TB burden (as measured by the number of incident cases and mortality) under a range of intervention scenarios to determine which of these scenario is the most effective at reducing burden. Of the single-intervention strategies, enhanced case detection is the most effective and prompt in reducing DS and MDR-TB incidence and mortality in Bangladesh and that with GeneXpert testing was also highly effective in decreasing the burden of MDR-TB. Our findings also suggest combining additional interventions simultaneously leads to greater effectiveness, particularly for MDR-TB, which we estimate requires a modest investment to substantially reduce, whereas DS-TB requires a strong sustained investment.

Analysis of COVID-19 Prevention and Control Effects Based on the SEITRD Dynamic Model and Wuhan Epidemic Statistics

Since December 2019, millions of people worldwide have been diagnosed with COVID-19, which has caused enormous losses. Given that there are currently no effective treatment or prevention drugs, most countries and regions mainly rely on quarantine and travel restrictions to prevent the spread of the epidemic. How to find proper prevention and treatment methods has been a hot topic of discussion. The key to the problem is to understand when these intervention measures are the best strategies for disease control and how they might affect disease dynamics. In this paper, we build a transmission dynamic model in combination with the transmission characteristics of COVID-19. We thoroughly study the dynamical behavior of the model and analyze how to determine the relevant parameters, and how the parameters influence the transmission process. Furthermore, we subsequently compare the impact of different control strategies on the epidemic, the variables include intervention time, control duration, control intensity, and other model parameters. Finally, we can find a better control method by comparing the results under different schemes and choose the proper preventive control strategy according to the actual epidemic stage and control objectives.

Spatiotemporal characteristics and the epidemiology of tuberculosis in China from 2004 to 2017 by the nationwide surveillance system

Background

China has always been one of the countries with the most serious Tuberculosis epidemic in the world. Our study was to observe the Spatial-temporal characteristics and the epidemiology of Tuberculosis in China from 2004 to 2017 with Joinpoint regression analysis, Seasonal Autoregressive integrated moving average (SARIMA) model, geographic cluster, and multivariate time series model.

Methods

The data of TB from January 2004 to December 2017 were obtained from the notifiable infectious disease reporting system supplied by the Chinese Center for Disease Control and Prevention. The incidence trend of TB was observed by the Joinpoint regression analysis. The Seasonal autoregressive integrated moving average (SARIMA) model was used to predict the monthly incidence. Geographic clusters was employed to analyze the spatial autocorrelation. The relative importance component of TB was detected by the multivariate time series model.

Results

We included 13,991,850 TB cases from January 2004 to December 2017, with a yearly average morbidity of 999,417 cases. The final selected model was the 0 Joinpoint model (P = 0.0001) with an annual average percent change (AAPC) of − 3.3 (95% CI: − 4.3 to − 2.2, P < 0.001). A seasonality was observed across the 14 years, and the seasonal peaks were in January and March every year. The best SARIMA model was (0, 1, 1) X (0, 1, 1)₁₂ which can be written as (1-B) (1-B¹²) X_t = (1–0.42349B) (1–0.43338B¹²) ε_t, with a minimum AIC (880.5) and SBC (886.4). The predicted value and the original incidence data of 2017 were well matched. The MSE, RMSE, MAE, and MAPE of the modelling performance were 201.76, 14.2, 8.4 and 0.06, respectively. The provinces with a high incidence were located in the northwest (Xinjiang, Tibet) and south (Guangxi, Guizhou, Hainan) of China. The hotspot of TB transmission was mainly located at southern region of China from 2004 to 2008, including Hainan, Guangxi, Guizhou, and Chongqing, which disappeared in the later years. The autoregressive component had a leading role in the incidence of TB which accounted for 81.5–84.5% of the patients on average. The endemic component was about twice as large in the western provinces as the average while the spatial-temporal component was less important there. Most of the high incidences (> 70 cases per 100,000) were influenced by the autoregressive component for the past 14 years.

Conclusion

In a word, China still has a high TB incidence. However, the incidence rate of TB was significantly decreasing from 2004 to 2017 in China. Seasonal peaks were in January and March every year. Obvious geographical clusters were observed in Tibet and Xinjiang Province. The relative importance component of TB driving transmission was distinguished from the multivariate time series model. For every provinces over the past 14 years, the autoregressive component played a leading role in the incidence of TB which need us to enhance the early protective implementation.

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.

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.

Primary Esophageal Tuberculosis Without Dysphagia or Odynophagia in a Patient Without HIV

We report a case of primary esophageal tuberculosis in a 35-year-old woman without HIV who presented with a month's history of epigastric and chest pain without dysphagia or odynophagia and was found to have histologic evidence of multiple caseating granulomata on esophageal biopsy, which was confirmed positive for Mycobacterium tuberculosis complex DNA and cultures.

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.