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

Diagnostic Techniques ◽

P Value ◽

Contact Ratio ◽

Expiry Date ◽

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.

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

10.21203/rs.2.17927/v2 ◽

2020 ◽

Author(s):

Yan Wu ◽

Meng Huang ◽

Ximei Wang ◽

Yong Li ◽

Lei Jiang ◽

...

Keyword(s):

Dynamic Model ◽

Prevention And Control ◽

Rank Correlation ◽

Correlation Coefficients ◽

The Sustainable Development ◽

United State ◽

And Control ◽

Protection Period

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.

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 ◽

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.

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 ◽

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.

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 ◽

Reproductive Number ◽

Global Pandemic ◽

The World ◽

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.

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 ◽

Optimal Controls ◽

Modeling And Control ◽

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.

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 ◽

Elementary Model ◽

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.

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.

Stability and Global Sensitivity Analysis for an Agree-Disagree Model: Partial Rank Correlation Coefficient and Latin Hypercube Sampling Methods

International Journal of Differential Equations ◽

10.1155/2020/5051248 ◽

2020 ◽

Vol 2020 ◽

pp. 1-14 ◽

Cited By ~ 3

Author(s):

Sara Bidah ◽

Omar Zakary ◽

Mostafa Rachik

Keyword(s):

Sensitivity Analysis ◽

Correlation Coefficient ◽

Global Sensitivity Analysis ◽

Equilibrium Points ◽

Rank Correlation ◽

Latin Hypercube ◽

Global Sensitivity ◽

Existence And Stability ◽

Partial Rank Correlation

In this paper, we present a new mathematical model that describes agree-disagree opinions during polls. We first present the model and its different compartments. Then, we use the next-generation matrix method to compute thresholds of equilibrium stability. We perform the stability analysis of equilibria to determine under which conditions these equilibrium points are stable or unstable. We show that the existence and stability of these equilibria are controlled by the calculated thresholds. Finally, we also perform several computational and statistical experiments to validate the theoretical results obtained in this work. To study the influence of various parameters on these thresholds and to identify the most influential parameters, a global sensitivity analysis is carried out based on the partial rank correlation coefficient method and the Latin hypercube sampling.

Optimal Control Strategies of HFMD in Wenzhou, China

Complexity ◽

10.1155/2020/5902698 ◽

2020 ◽

Vol 2020 ◽

pp. 1-15

Author(s):

Zuqin Ding ◽

Yong Li ◽

Yongli Cai ◽

Yueping Dong ◽

Weiming Wang

Keyword(s):

Optimal Control ◽

Reproduction Number ◽

Control Strategies ◽

Rank Correlation ◽

Foot And Mouth Disease ◽

Chi Square ◽

Course Of Disease ◽

Contact Rates ◽

Partial Rank Correlation

In this paper, we investigate the dynamics and optimal control strategies of a modified hand, foot, and mouth disease (HFMD) model incorporating the EV-A71 vaccination in Wenzhou, China, analytically and numerically. We define the basic reproduction number R0 and show that it can be used to determine whether HFMD becomes extinct or not. Based on the monthly reported HFMD cases in Wenzhou for 76 months, we estimate the parameters in the dynamic model by using the method of minimum chi-square fitting, conduct the sensitivity analysis to investigate the influence of each uncertain parameter on R0 with the methods of Latin hypercube sampling and partial rank correlation coefficient, and find that the EV-A71 vaccination does not lead to the extinction of HFMD, but slightly reduces the incidence of HFMD. In order to control the spread of HFMD in Wenzhou, we need to increase the rate of EV-A71 vaccination, decrease the contact rates, and shorten the course of disease.

Epidemiological Trend of Typhoid and Paratyphoid Fevers in Zhejiang Province, China from 1953 to 2014

International Journal of Environmental Research and Public Health ◽

10.3390/ijerph15112427 ◽

2018 ◽

Vol 15 (11) ◽

pp. 2427 ◽

Cited By ~ 2

Author(s):

Hua Gu ◽

Congcong Yan ◽

Zhenggang Jiang ◽

Xiuyang Li ◽

Enfu Chen ◽

...

Keyword(s):

Prevention And Control ◽

Age Distribution ◽

Public Health Problem ◽

Epidemiological Data ◽

Zhejiang Province ◽

P Value ◽

Peak Period ◽

Circular Distribution ◽

And Control ◽

Epidemiological Characteristics

Background: The incidences of typhoid and paratyphoid remain high and these diseases still pose a public health problem in China and in Zhejiang Province in particular. This study aimed to investigate the trend of typhoid and paratyphoid in Zhejiang Province from 1953 to 2014 and to provide a theoretical basis for the prevention and control of these diseases. Methods: Included in this study were compiled epidemiological data of typhoid and paratyphoid cases in Zhejiang from 1953 to 2003 and epidemiological data of those from 2004 to 2014 registered in the China Information System for Diseases Control and Prevention. Description methods were employed to explore the epidemiological characteristics, including long-term trend, gender distribution, age distribution, and occupation distribution. Incidence maps were made to represent the annual average incidences for each municipality. Spearman’s rank correlation was performed to detect the correlation between incidence and average elevation, and circular distribution was calculated to identify the seasonality and peak days of the diseases. A p-value of <0.05 was considered statistically significant. Results: A total of 182,602 typhoid and paratyphoid cases were reported in Zhejiang Province from 1953 to 2014, and the average annual incidence was 7.89 per 100,000 population. The incidence in 2014 decreased by 93.82% compared with that in 1953 and by 95.00% compared with the highest incidence rate. The average incidence before 2003 was negatively correlated with the average elevation of each region in Zhejiang province (r < 0, p < 0.05), but there was no statistically significant correlation from 2003. The peak period of diseases fell in the months from April to October every year. The incidence among the population group aged over 35 rose gradually but declined sharply among those between 20 and 34. Conclusions: The incidence of typhoid and paratyphoid decreased in Zhejiang Province from 1953 to 2014 but remained high in some regions. Proper measures for prevention and control are warranted in the southeast coast areas and for high-risk populations.