Prevention and Control of Tuberculosis Relying on a Tuberculosis Dynamic Model Based on the Cases of American

Abstract Background: Tuberculosis (TB) which is a preventable and curable disease, is claimed as the second largest number of fatalities and there are 9,025 cases reported in the United State in 2018. Many researches have done a lot of research and achieved remarkable results, but TB is also a serious problem for human being.The study is a further exploration. Methods: In the paper, we propose a new dynamic model to study the transmission dynamics of TB, 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 (R0) and the total infectious (including the diagnosed, undiagnosed and incomplete treatment infectious), respectively. Results: By the research, the basic reproduction is computed as 2.3597 which means TB will be epidemic in US. The diagnosed rate is 0.6082 which means the undiagnosed will be diagnosed after 1.6442 years. The diagnosed will be recovered with an average of 1.9912 years, especially, some diagnosed will end the treatment after 1.7550 years, for some reasons. By the study, it’s shown that there are 2.4% of the recovered will be reactivated and 13.88% of the newborn will be vaccination. However, the immunity will be lose 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 State, 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 prevention and control of TB and treatment after illness; isolation treatment for the infected to reduce the spread of TB. According to the latest report, in the announcement came at the first WHO Global Ministerial Conference on Ending Tuberculosis in the Sustainable Development Era, we predict that it’s difficult to control TB in 2030.

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The Prevention and Control of Tuberculosis: An Analysis Based On a Tuberculosis Dynamic Model Derived from the Cases of Americans

10.21203/rs.2.17927/v3 ◽

2020 ◽

Author(s):

Yan Wu ◽

Meng Huang ◽

Ximei Wang ◽

Yong Li ◽

Lei Jiang ◽

...

Keyword(s):

United States ◽

Dynamic Model ◽

Prevention And Control ◽

Rank Correlation ◽

Correlation Coefficients ◽

Latin Hypercube Sampling ◽

The United States ◽

Human Beings ◽

Severe Problem ◽

And Control

Abstract 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 to the 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 (R0) and the total infectious (including the diagnosed, undiagnosed and incomplete treatment infectious), respectively.Results: According to the research, the basic reproduction is computed as 2.3597, which means TB will be 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 2.4% 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 in 2030.

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Prevention and Control of Tuberculosis Relying on a Tuberculosis Dynamic Model Based on the Cases of American

10.21203/rs.2.17927/v1 ◽

2019 ◽

Author(s):

Yan Wu ◽

Yong Li

Keyword(s):

Dynamic Model ◽

Rank Correlation ◽

Latin Hypercube Sampling ◽

Diagnostic Techniques ◽

P Value ◽

Contact Ratio ◽

Expiry Date ◽

Partial Rank Correlation ◽

And Control ◽

Epidemiological Characteristics

Abstract Background: Tuberculosis (TB) which is a preventable and curable disease, is claimed as the second largest number of fatalities and there are 9,029 cases of American in 2018. Many researches have done many study to control TB and had evident e_ects, but TB is also a serious problem for human being. So the study is always improving. Methods: In the paper, we propose a new dynamic model to study the transmission dynamic and prevalence of TB, then use global di_erential evolution and local sequential quadratic programming (DESQP) optimization algorithm to estimate parameters of the model. Next, we use Latin hypercube sampling (LHS) to sample and partial rank correlation coe_cients (PRCC) to analyze the inuence of parameters on the basic reproduction number (R0) and the total infectious (including the diagnosed, undiagnosed and incomplete treatment infectious), respectively. Results: With the PRCC and p-value of the parameters, we _nd how the factors a_ect the outbreaks of TB. Chemoprophylaxis, treatment and vaccination have positive e_ects, relatively, the vaccine expiry date, diagnostic techniques and the contact ratio have negative e_ects. Especially, chemoprophylaxis is the most sensitive factors controlling TB. Conclusion: With results, we give some suggestions to control the prevalence of TB, such as prolonging the duration of the vaccine by researching new and better vaccines to prevent TB, persuading people infected with TB in the latent stage to use chemoprophylaxis to treat and do not contact with the infected and instructing people take care of themselves and be treated in time when they are infected with TB. By doing these, we can e_ectively control and prevent the prevalence of TB according to the epidemiological characteristics of tuberculosis transmission.

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Uncertainty and Sensitivity Analysis of the In-Vessel Hydrogen Generation for Gen-III PWR and Phebus FPT-1 with MELCOR 2.2

Energies ◽

10.3390/en14164884 ◽

2021 ◽

Vol 14 (16) ◽

pp. 4884

Author(s):

Piotr Darnowski ◽

Piotr Mazgaj ◽

Mateusz Włostowski

Keyword(s):

Sensitivity Analysis ◽

Hydrogen Generation ◽

Rank Correlation ◽

Correlation Coefficients ◽

Latin Hypercube Sampling ◽

Severe Accident ◽

Sensitivity Analyses ◽

Pressurized Water ◽

Water Reactor ◽

Best Estimate

In this study, uncertainty and sensitivity analyses were performed with MELCOR 2.2.18 to study the hydrogen generation (figure-of-merit (FoM)) during the in-vessel phase of a severe accident in a light water reactor. The focus of this work was laid on a large generation-III pressurized water reactor (PWR) and a double-ended hot leg (HL) large break loss of coolant accident (LB-LOCA) without a safety injection (SI). The FPT-1 Phebus integral experiment emulating LOCA was studied, where the experiment outcomes were applied for the plant scale modelling. The best estimate calculations were supplemented with an uncertainty analysis (UA) based on 400 input-decks and Latin hypercube sampling (LHS). Additionally, the sensitivity analysis (SA) utilizing the linear regression and linear and rank correlation coefficients was performed. The study was prepared with a new open-source MELCOR sensitivity and uncertainty tool (MelSUA), which was supplemented with this work. The FPT-1 best-estimate model results were within the 10% experimental uncertainty band for the final FoM. It was shown that the hydrogen generation uncertainties in PWR were similar to the FPT-1, with the 95% percentile being covered inside a ~50% band and the 50% percentile inside a ~25% band around the FoM median. Two different power profiles for PWR were compared, indicating its impact on the uncertainty but also on the sensitivity results. Despite a similar setup, different uncertainty parameters impacted FoM, showing the difference between scales but also a significant impact of boundary conditions on the sensitivity analysis.

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Quantifying the dose-dependent impact of intracellular amyloid beta in a mathematical model of calcium regulation in xenopus oocyte

PLoS ONE ◽

10.1371/journal.pone.0246116 ◽

2021 ◽

Vol 16 (1) ◽

pp. e0246116

Author(s):

Joseph Minicucci ◽

Molly Alfond ◽

Angelo Demuro ◽

David Gerberry ◽

Joe Latulippe

Keyword(s):

Mathematical Model ◽

Amyloid Beta ◽

Rank Correlation ◽

Correlation Coefficients ◽

Dependent Manner ◽

Partial Rank Correlation ◽

Dose Dependent ◽

Detrimental Impact ◽

Oligomeric Forms

Alzheimer’s disease (AD) is a devastating illness affecting over 40 million people worldwide. Intraneuronal rise of amyloid beta in its oligomeric forms (iAβOs), has been linked to the pathogenesis of AD by disrupting cytosolic Ca2+ homeostasis. However, the specific mechanisms of action are still under debate and intense effort is ongoing to improve our understanding of the crucial steps involved in the mechanisms of AβOs toxicity. We report the development of a mathematical model describing a proposed mechanism by which stimulation of Phospholipase C (PLC) by iAβO, triggers production of IP3 with consequent abnormal release of Ca2+ from the endoplasmic reticulum (ER) through activation of IP3 receptor (IP3R) Ca2+ channels. After validating the model using experimental data, we quantify the effects of intracellular rise in iAβOs on model solutions. Our model validates a dose-dependent influence of iAβOs on IP3-mediated Ca2+ signaling. We investigate Ca2+ signaling patterns for small and large iAβOs doses and study the role of various parameters on Ca2+ signals. Uncertainty quantification and partial rank correlation coefficients are used to better understand how the model behaves under various parameter regimes. Our model predicts that iAβO alter IP3R sensitivity to IP3 for large doses. Our analysis also shows that the upstream production of IP3 can influence Aβ-driven solution patterns in a dose-dependent manner. Model results illustrate and confirm the detrimental impact of iAβOs on IP3 signaling.

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Stability and global sensitivity analysis of the transmission dynamics of malaria with relapse and ignorant infected humans

Physica Scripta ◽

10.1088/1402-4896/ac4862 ◽

2022 ◽

Author(s):

Yves Tinda Mangongo ◽

Joseph-Désiré Kyemba Bukweli ◽

Justin Dupar Busili Kampempe ◽

Rostin Matendo Mabela ◽

Justin Manango Wazute Munganga

Keyword(s):

Sensitivity Analysis ◽

Recovery Rate ◽

Global Sensitivity Analysis ◽

Rank Correlation ◽

Latin Hypercube Sampling ◽

Transmission Dynamics ◽

Asymptotically Stable ◽

Globally Asymptotically Stable ◽

Global Sensitivity ◽

Partial Rank Correlation

Abstract In this paper we present a more realistic mathematical model for the transmission dynamics of malaria by extending the classical SEIRS scheme and the model of Hai-Feng Huo and Guang-Ming Qiu [21] by adding the ignorant infected humans compartment. We analyze the global asymptotically stabilities of the model by the use of the basic reproduction number R_0 and we prove that when R_0≦1, the disease-free equilibrium is globally asymptotically stable. That is malaria dies out in the population. When R_0>1, there exists a co-existing unique endemic equilibrium which is globally asymptotically stable. The global sensitivity analysis have been done through the partial rank correlation coefficient using the samples generated by the use of latin hypercube sampling method and shows that the most influence parameters in the spread of malaria are the proportion θ of infectious humans who recover and the recovery rate γ of infectious humans. In order to eradicate malaria, we have to decrease the number of ignorant infected humans by testing peoples and treat them. Numerical simulations show that malaria can be also controlled or eradicated by increasing the recovery rate γ of infectious humans, decreasing the number of ignorant infected humans and decreasing the average number n of mosquito bites.

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Mathematical Modeling to Estimate the Reproductive Number and the Outbreak Size of COVID-19: The case of India and the World

10.21203/rs.3.rs-26261/v1 ◽

2020 ◽

Author(s):

Durgesh Nandini Sinha

Keyword(s):

Mathematical Model ◽

Reproduction Number ◽

Model Fitting ◽

Rank Correlation ◽

Latin Hypercube Sampling ◽

Reproductive Number ◽

Global Pandemic ◽

The World ◽

Partial Rank Correlation ◽

Coefficient Method

Abstract Coronavirus disease (COVID-19) has become a global pandemic with more than 218,000 deaths in 211 different countries around the world. Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the virus responsible for this deadliest disease. This paper describes a mathematical model for India, a country with the second highest population in the world with an extremely high population density of about 464 people per km2. This disease has multiphasic actions and reaction mode and our model SEIAQIm is based on six compartmental groups in the form of susceptible, exposed, infectious, asymptomatic, quarantine, and recovered immune factions. Latin Hypercube Sampling Partial Rank Correlation Coefficient method was used for the data analysis and model fitting. According to our model, India would reach its basic reproduction number R0=0.97 on May 14, 2020 with a total number of 73,800 estimated cases. Further, this study also equates the world's situation using the same model system and predicts by May 7, 2020 with a total number of 3,772,000 estimated confirmed cases. Moreover, the current mathematical model highlights the importance of social distancing as an effective method of containing spread of COVID-19.

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Modeling and Control of the Public Opinion: An Agree-Disagree Opinion Model

International Journal of Differential Equations ◽

10.1155/2020/5864238 ◽

2020 ◽

Vol 2020 ◽

pp. 1-15

Author(s):

Sara Bidah ◽

Omar Zakary ◽

Mostafa Rachik

Keyword(s):

Optimal Control ◽

Control Problem ◽

Initial Conditions ◽

Control Strategies ◽

Rank Correlation ◽

Latin Hypercube Sampling ◽

Optimal Controls ◽

Modeling And Control ◽

Partial Rank Correlation ◽

Objective Functional

In this paper, we aim to investigate optimal control to a new mathematical model that describes agree-disagree opinions during polls, which we presented and analyzed in Bidah et al., 2020. We first present the model and recall its different compartments. We formulate the optimal control problem by supplementing our model with a objective functional. Optimal control strategies are proposed to reduce the number of disagreeing people and the cost of interventions. We prove the existence of solutions to the control problem, we employ Pontryagin’s maximum principle to find the necessary conditions for the existence of the optimal controls, and Runge–Kutta forward-backward sweep numerical approximation method is used to solve the optimal control system, and we perform numerical simulations using various initial conditions and parameters to investigate several scenarios. Finally, a global sensitivity analysis is carried out based on the partial rank correlation coefficient method and the Latin hypercube sampling to study the influence of various parameters on the objective functional and to identify the most influential parameters.

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HUMAN POPULATION EFFECTS ON THE ULSOOR LAKE FISH SURVIVAL

Journal of Biological System ◽

10.1142/s0218339018500274 ◽

2018 ◽

Vol 26 (04) ◽

pp. 603-632 ◽

Cited By ~ 2

Author(s):

PANKAJ KUMAR TIWARI ◽

IULIA MARTINA BULAI ◽

FRANCESCA BONA ◽

EZIO VENTURINO ◽

ARVIND KUMAR MISRA

Keyword(s):

Human Population ◽

Rank Correlation ◽

Correlation Coefficients ◽

Organic Pollution ◽

Fish Population ◽

Fish Mortality ◽

Human Populations ◽

Sewage Farm ◽

Fish Survival ◽

Partial Rank Correlation

In this paper, we introduce a model to study the effects of human populations on fish survival in aquatic media. Directly, this occurs by fishing. Indirectly instead this is related to other human actions that lead to organic pollution and consequently low dissolved oxygen(DO) levels, thereby harming the aquatic fauna. Mathematically, we consider various nonlinear processes involving human population, organic pollutants, bacteria, DO and fish population. In the present study, our aim is to investigate the effect of depleted level of DO on the survival of fish populations in such an aquatic system. The case study in consideration is represented by the Ulsoor lake, Bengaluru, India. Into it, huge amounts of sewage were discharged and resulted in reduction of DO level and massive fish mortality. Equilibria are analyzed for feasibility and stability, substantiated via numerical simulations. Global sensitivity analysis identifies the important parameters having a significant impact on the fish population. The Partial Rank Correlation Coefficients (PRCCs) values of fish population in the lake with respect to input parameters of the system show that the growth rate of humans in the lake watershed has maximum negative correlation while the growth in the fish population due to DO has maximum positive correlation with the density of fish population in the lake. The results show that increase in human population may decrease fish population in the system to very low values. However, by controlling additional dissolved organic loads coming from domestic sewage, farm waste and many other sources, the level of DO can be brought back to values that allow fish survival. Maintaining it at these levels would preserve the ecosystem.

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Epidemic model formulation and analysis for diarrheal infections caused by salmonella

SIMULATION ◽

10.1177/0037549716685409 ◽

2017 ◽

Vol 93 (7) ◽

pp. 543-552 ◽

Cited By ~ 1

Author(s):

Ojaswita Chaturvedi ◽

Mandu Jeffrey ◽

Edward Lungu ◽

Shedden Masupe

Keyword(s):

Parameter Estimation ◽

Basic Reproduction Number ◽

Reproduction Number ◽

Rank Correlation ◽

Latin Hypercube Sampling ◽

Elementary Model ◽

Partial Rank Correlation ◽

Parameter Values ◽

Working Out ◽

Disease Free

Epidemic modeling can be used to gain better understanding of infectious diseases, such as diarrhea. In the presented research, a continuous mathematical model has been formulated for diarrhea caused by salmonella. This model has been analyzed and simulated to be established in a functioning form. Elementary model analysis, such as working out the disease-free state and basic reproduction number, has been done for this model. The basic reproduction number has been calculated using the next generation matrix method. Stability analysis of the model has been done using the Routh–Hurwitz method. Sensitivity analysis and parameter estimation have been completed for the system too using MATLAB packages that work on the Latin Hypercube Sampling and Partial Rank Correlation Coefficient methods. It was established that as long as R0 < 1, there will be no epidemic. Upon simulation using assumed parameter values, the results produced comprehended the epidemic theory and practical situations. The system was proven stable using the Routh–Hurwitz criterion and parameter estimation was successfully completed. Salmonella diarrhea has been successfully modeled and analyzed in this research. This model has been flexibly built and it can be integrated onto certain platforms to be used as a predictive system to prevent further infections of salmonella diarrhea.

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Research about the optimal strategies for prevention and control of varicella outbreak in a school in a central city of China: based on an SEIR dynamic model

Epidemiology and Infection ◽

10.1017/s0950268819002188 ◽

2020 ◽

Vol 148 ◽

Cited By ~ 8

Author(s):

Wen-ting Zha ◽

Feng-rui Pang ◽

Nan Zhou ◽

Bin Wu ◽

Ying Liu ◽

...

Keyword(s):

Dynamic Model ◽

Prevention And Control ◽

Model Simulation ◽

Central City ◽

Control Measures ◽

Peak Time ◽

Cumulative Number ◽

And Control ◽

Epidemiological Characteristics ◽

Combined Interventions

Abstract Varicella is an acute respiratory infectious diseases, with high transmissibility and quick dissemination. In this study, an SEIR (susceptible-exposed-infected-recovered) dynamic model was established to explore the optimal prevention and control measures according to the epidemiological characteristics about varicella outbreak in a school in a central city of China. Berkeley Madonna 8.3.18 and Microsoft Office Excel 2010 software were employed for the model simulation and data management, respectively. The result showed that the simulated result of SEIR model agreed well with the reported data when β (infected rate) equal to 0.067. Models showed that the cumulative number of cases was only 13 when isolation adopted when the infected individuals were identified (assuming isolation rate was up to 100%); the cumulative number of cases was only two and the TAR (total attack rate) was 0.56% when the vaccination coefficient reached 50%. The cumulative number of cases did not change significantly with the change of efficiency of ventilation and disinfection, but the peak time was delayed; when δ (vaccination coefficient) = 0.1, m (ventilation efficiency) = 0.7 or δ = 0.2, m = 0.5 or δ = 0.3, m = 0.1 or δ = 0.4 and above, the cumulative number of cases would reduce to one case and TAR would reduce to 0.28% with combined interventions. Varicella outbreak in school could be controlled through strict isolation or vaccination singly; combined interventions have been adopted when the vaccination coefficient was low.

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