Optimal Control Strategies of HFMD in Wenzhou, China

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.

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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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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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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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Optimal Control of a Dengue-Dengvaxia Model: Comparison Between Vaccination and Vector Control

Computational and Mathematical Biophysics ◽

10.1515/cmb-2020-0124 ◽

2021 ◽

Vol 9 (1) ◽

pp. 198-212

Author(s):

Cheryl Q. Mentuda

Keyword(s):

Optimal Control ◽

Vector Control ◽

Basic Reproduction Number ◽

Human Population ◽

Model Comparison ◽

Reproduction Number ◽

Control Strategies ◽

Minimum Principle ◽

Transmitted Disease ◽

The Basic Reproduction Number

Abstract Dengue is the most common mosquito-borne viral infection transmitted disease. It is due to the four types of viruses (DENV-1, DENV-2, DENV-3, DENV-4), which transmit through the bite of infected Aedes aegypti and Aedes albopictus female mosquitoes during the daytime. The first globally commercialized vaccine is Dengvaxia, also known as the CYD-TDV vaccine, manufactured by Sanofi Pasteur. This paper presents a Ross-type epidemic model to describe the vaccine interaction between humans and mosquitoes using an entomological mosquito growth population and constant human population. After establishing the basic reproduction number ℛ0, we present three control strategies: vaccination, vector control, and the combination of vaccination and vector control. We use Pontryagin’s minimum principle to characterize optimal control and apply numerical simulations to determine which strategies best suit each compartment. Results show that vector control requires shorter time applications in minimizing mosquito populations. Whereas vaccinating the primary susceptible human population requires a shorter time compared to the secondary susceptible human.

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Modeling the Effects of Helminth Infection on the Transmission Dynamics of Mycobacterium tuberculosis under Optimal Control Strategies

Computational and Mathematical Methods in Medicine ◽

10.1155/2020/8869377 ◽

2020 ◽

Vol 2020 ◽

pp. 1-21

Author(s):

Aristide G. Lambura ◽

Gasper G. Mwanga ◽

Livingstone Luboobi ◽

Dmitry Kuznetsov

Keyword(s):

Optimal Control ◽

Equilibrium Point ◽

Drug Administration ◽

Mass Drug Administration ◽

Helminth Infection ◽

Reproduction Number ◽

Control Strategies ◽

Active Tuberculosis ◽

Control Measures ◽

The Impact

A deterministic mathematical model for the transmission and control of cointeraction of helminths and tuberculosis is presented, to examine the impact of helminth on tuberculosis and the effect of control strategies. The equilibrium point is established, and the effective reproduction number is computed. The disease-free equilibrium point is confirmed to be asymptotically stable whenever the effective reproduction number is less than the unit. The analysis of the effective reproduction number indicates that an increase in the helminth cases increases the tuberculosis cases, suggesting that the control of helminth infection has a positive impact on controlling the dynamics of tuberculosis. The possibility of bifurcation is investigated using the Center Manifold Theorem. Sensitivity analysis is performed to determine the effect of every parameter on the spread of the two diseases. The model is extended to incorporate control measures, and Pontryagin’s Maximum Principle is applied to derive the necessary conditions for optimal control. The optimal control problem is solved numerically by the iterative scheme by considering vaccination of infants for Mtb, treatment of individuals with active tuberculosis, mass drug administration with regular antihelminthic drugs, and sanitation control strategies. The results show that a combination of educational campaign, treatment of individuals with active tuberculosis, mass drug administration, and sanitation is the most effective strategy to control helminth-Mtb coinfection. Thus, to effectively control the helminth-Mtb coinfection, we suggest to public health stakeholders to apply intervention strategies that are aimed at controlling helminth infection and the combination of vaccination of infants and treatment of individuals with active tuberculosis.

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The Dynamics and Optimal Control of a Hand-Foot-Mouth Disease Model

Computational and Mathematical Methods in Medicine ◽

10.1155/2018/9254794 ◽

2018 ◽

Vol 2018 ◽

pp. 1-11

Author(s):

Hongwu Tan ◽

Hui Cao

Keyword(s):

Optimal Control ◽

Reproduction Number ◽

Control Strategies ◽

Disease Model ◽

Mouth Disease ◽

Infected People ◽

Hand Foot Mouth Disease ◽

The Cost ◽

Existence Of Equilibria ◽

Disease Free

We build and study the transmission dynamics of a hand-foot-mouth disease model with vaccination. The reproduction number is given, the existence of equilibria is obtained, and the global stability of disease-free equilibrium is proved by constructing the Lyapunov function. We also apply optimal control theory to the hand-foot-mouth disease model. The treatment and vaccination interventions are considered in the hand-foot-mouth disease model, and the optimal control strategies based on minimizing the cost of intervention and minimizing the number of the infected people are given. Numerical results show the usefulness of the optimization strategies.

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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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Modelling the transmission dynamics of COVID-19 in six high burden countries

10.1101/2020.04.22.20075192 ◽

2020 ◽

Author(s):

Azizur Rahman ◽

Md Abdul Kuddus

Keyword(s):

Disease Transmission ◽

Compartmental Model ◽

Transmission Rate ◽

Control Strategies ◽

Rank Correlation ◽

Decision Makers ◽

High Burden ◽

Epidemic Period ◽

Partial Rank Correlation ◽

Coefficient Method

AbstractThe new coronavirus disease, officially known as COVID-19, originated in China in 2019 and has since spread around the globe. We presented a modified Susceptible-Latent-Infected-Removed (SLIR) compartmental model of COVID-19 disease transmission with nonlinear incidence during the epidemic period. We provided the model calibration to estimate parameters with day wise corona virus (COVID-19) data i.e. reported cases by worldometer from the period of 15th February to 30th March, 2020 in six high burden countries including Australia, Italy, Spain, USA, UK and Canada. We estimate transmission rates for each countries and found that the highest transmission rate country in Spain, which may be increase the new cases and deaths in Spain than the other countries. Sensitivity analysis was used to identify the most important parameters through the partial rank correlation coefficient method. We found that the transmission rate of COVID-19 had the largest influence on the prevalence. We also provides the prediction of new cases in COVID-19 until May 18, 2020 using the developed model and recommends, control strategies of COVID-19. The information that we generated from this study would be useful to the decision makers of various organizations across the world including the Ministry of Health in Australia, Italy, Spain, USA, UK and Canada to control COVID-19.

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Mathematical Modeling and Optimal Control Analysis of COVID-19 in Ethiopia

10.1101/2020.07.23.20160473 ◽

2020 ◽

Cited By ~ 1

Author(s):

Haileyesus Tessema Alemneh ◽

Getachew Teshome Telahun

Keyword(s):

Optimal Control ◽

Necessary Conditions ◽

Reproduction Number ◽

Control Strategies ◽

Equilibrium Points ◽

Control Model ◽

Control Analysis ◽

Basic Model ◽

Short Period ◽

Disease Free

In this paper we developed a deterministic mathematical model of the pandemic COVID-19 transmission in Ethiopia, which allows transmission by exposed humans. We proposed an SEIR model using system of ordinary differential equations. First the major qualitative analysis, like the disease free equilibruim point, endemic equilibruim point, basic reproduction number, stability analysis of equilibrium points and sensitivity analysis was rigorously analysed. Second, we introduced time dependent controls to the basic model and extended to an optimal control model of the disease. We then analysed using Pontryagins Maximum Principle to derive necessary conditions for the optimal control of the pandemic. The numerical simulation indicated that, an integrated strategy effective in controling the epidemic and the gvernment must apply all control strategies in combating COVID-19 at short period of time.

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OPTIMAL CONTROL ANALYSIS OF THE EFFECT OF TREATMENT, ISOLATION AND VACCINATION ON HEPATITIS B VIRUS

Journal of Biological System ◽

10.1142/s0218339020400057 ◽

2020 ◽

Vol 28 (02) ◽

pp. 351-376 ◽

Cited By ~ 5

Author(s):

MUHAMMAD ALTAF KHAN ◽

SYED AZHAR ALI SHAH ◽

SAIF ULLAH ◽

KAZEEM OARE OKOSUN ◽

MUHAMMAD FAROOQ

Keyword(s):

Optimal Control ◽

Hepatitis B ◽

Basic Reproduction Number ◽

Reproduction Number ◽

Control Strategies ◽

Control Measures ◽

Hepatitis B Infection ◽

Control Variables ◽

Effect Of Treatment ◽

The Basic Reproduction Number

Hepatitis B infection is a serious health issue and a major cause of deaths worldwide. This infection can be overcome by adopting proper treatment and control strategies. In this paper, we develop and use a mathematical model to explore the effect of treatment on the dynamics of hepatitis B infection. First, we formulate and use a model without control variables to calculate the basic reproduction number and to investigate basic properties of the model such as the existence and stability of equilibria. In the absence of control measures, we prove that the disease free equilibrium is locally asymptotically stable when the basic reproduction number is less than unity. Also, using persistent theorem, it is shown that the infection is uniformly persistent, whenever the basic reproduction number is greater than unity. Using optimal control theory, we incorporate into the model three time-dependent control variables and investigate the conditions required to curtail the spread of the disease. Finally, to illustrate the effectiveness of each of the control strategies on disease control and eradication, we perform numerical simulations. Based on the numerical results, we found that the first two strategies (treatment and isolation strategy) and (vaccination and isolation strategy) are not very effective as a long term control or eradication strategy for HBV. Hence, we recommend that in order to effectively control the disease, all the control measures (isolation, vaccination and treatment) must be implemented at the same time.

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