scholarly journals Fractional-Order Modelling and Optimal Control of Cholera Transmission

2021 ◽  
Vol 5 (4) ◽  
pp. 261
Author(s):  
Silvério Rosa ◽  
Delfim F. M. Torres
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Sensitivity Analysis ◽  
Fractional Order ◽  
Control Measures ◽  
Time Interval ◽  
Variable Order ◽  
Effectiveness Analysis ◽  
The Cost ◽  
Derivative Order

A Caputo-type fractional-order mathematical model for “metapopulation cholera transmission” was recently proposed in [Chaos Solitons Fractals 117 (2018), 37–49]. A sensitivity analysis of that model is done here to show the accuracy relevance of parameter estimation. Then, a fractional optimal control (FOC) problem is formulated and numerically solved. A cost-effectiveness analysis is performed to assess the relevance of studied control measures. Moreover, such analysis allows us to assess the cost and effectiveness of the control measures during intervention. We conclude that the FOC system is more effective only in part of the time interval. For this reason, we propose a system where the derivative order varies along the time interval, being fractional or classical when more advantageous. Such variable-order fractional model, that we call a FractInt system, shows to be the most effective in the control of the disease.

scholarly journals Stability Analysis and Optimal Control of a Vector-Borne Disease with Nonlinear Incidence

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Muhammad Ozair ◽  
Abid Ali Lashari ◽  
Il Hyo Jung ◽  
Kazeem Oare Okosun
Keyword(s):  
Optimal Control ◽  
Sensitivity Analysis ◽  
Control Measures ◽  
Basic Reproductive Number ◽  
Control Technique ◽  
Global Dynamics ◽  
Nonlinear Incidence ◽  
Vector Borne Disease ◽  
Vector Borne ◽  
The Impact

The paper considers a model for the transmission dynamics of a vector-borne disease with nonlinear incidence rate. It is proved that the global dynamics of the disease are completely determined by the basic reproduction number. In order to assess the effectiveness of disease control measures, the sensitivity analysis of the basic reproductive numberR0and the endemic proportions with respect to epidemiological and demographic parameters are provided. From the results of the sensitivity analysis, the model is modified to assess the impact of three control measures; the preventive control to minimize vector human contacts, the treatment control to the infected human, and the insecticide control to the vector. Analytically the existence of the optimal control is established by the use of an optimal control technique and numerically it is solved by an iterative method. Numerical simulations and optimal analysis of the model show that restricted and proper use of control measures might considerably decrease the number of infected humans in a viable way.

scholarly journals Cost-Effectiveness Analysis of Optimal Control Measures for Tuberculosis

2014 ◽  
Vol 76 (10) ◽  
pp. 2627-2645 ◽  
Author(s):  
Paula Rodrigues ◽  
Cristiana J. Silva ◽  
Delfim F. M. Torres
Keyword(s):  
Optimal Control ◽  
Cost Effectiveness ◽  
Cost Effectiveness Analysis ◽  
Control Measures ◽  
Effectiveness Analysis

scholarly journals Cost-Effectiveness Analysis of Direct Oral Anticoagulants Versus Vitamin K Antagonists for Venous Thromboembolism in China

2021 ◽  
Vol 12 ◽  
Author(s):  
Ke-Xin Sun ◽  
Bin Cui ◽  
Shan-Shan Cao ◽  
Qi-Xiang Huang ◽  
Ru-Yi Xia ◽  
...  
Keyword(s):  
Decision Making ◽  
Sensitivity Analysis ◽  
Cost Effectiveness ◽  
Markov Model ◽  
Clinical Decision Making ◽  
Cost Effective ◽  
Clinical Decision ◽  
Base Case ◽  
Effectiveness Analysis ◽  
The Cost

Background: The drug therapy of venous thromboembolism (VTE) presents a significant economic burden to the health-care system in low- and middle-income countries. To understand which anticoagulation therapy is most cost-effective for clinical decision-making , the cost-effectiveness of apixaban (API) versus rivaroxaban (RIV), dabigatran (DAB), and low molecular weight heparin (LMWH), followed by vitamin K antagonist (VKA), in the treatment of VTE in China was assessed.Methods: To access the quality-adjusted life-years (QALYs) and incremental cost-effectiveness ratios (ICERs), a long-term cost-effectiveness analysis was constructed using a Markov model with 5 health states. The Markov model was developed using patient data collected from the Xijing Hospital from January 1, 2016 to January 1, 2021. The time horizon was set at 30 years, and a 6-month cycle length was used in the model. Costs and ICERs were reported in 2020 U.S. dollars. One-way sensitivity analysis and probabilistic sensitivity analysis (PSA) were used to test the uncertainties. A Chinese health-care system perspective was used.Results: In the base case, the data of 231 VTE patients were calculated in the base case analysis retrospectively. The RIV group resulted in a mean VTE attributable to 95% effective treatment. API, DAB, and VKA have a negative ICER (−187017.543, −284,674.922, and −9,283.339, respectively) and were absolutely dominated. The Markov model results confirmed this observation. The ICER of the API and RIV was negative (−216176.977), which belongs to the absolute inferiority scheme, and the ICER value of the DAB and VKA versus RIV was positive (110,577.872 and 836,846.343). Since the ICER of DAB and VKA exceeds the threshold, RIV therapy was likely to be the best choice for the treatment of VTE within the acceptable threshold range. The results of the sensitivity analysis revealed that the model output varied mostly with the cost in the DAB on-treatment therapy. In a probabilistic sensitivity analysis of 1,000 patients for 30 years, RIV has 100% probability of being cost-effective compared with other regimens when the WTP is $10973 per QALY. When WTP exceeded $148,000, DAB was more cost-effective than RIV.Conclusions: Compared with LMWH + VKA and API, the results proved that RIV may be the most cost-effective treatment for VTE patients in China. Our findings could be helpful for physicians in clinical decision-making to select the appropriate treatment option for VTE.

scholarly journals Control measures of malaria transmission in Rwanda based on SEIR SEI mathematical model

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Emmanuel Hakizimana ◽  
Jean Marie Ntaganda
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Malaria Transmission ◽  
Optimal Control Problems ◽  
Control Strategies ◽  
Control Measures ◽  
Bed Nets ◽  
Infected People ◽  
Insecticide Treated Bed Nets ◽  
Malaria Model

This research paper investigated the dynamics of malaria transmission in Rwanda using the nonlinear forces of infections which are included in SEIR-SEI mathematical model for human and mosquito populations. The mathematical modeling of malaria studies the interaction among the human and mosquito populations in controlling malaria transmission and eventually eliminating malaria infection. This work investigates the optimal control strategies for minimizing the rate of malaria transmission by applying three control variables through Caputo fractional derivative. The optimal control problems for malaria model found the control parameters which minimize infection. The numerical simulation showed that the number of exposed and infected people and mosquito population are decreased due to the control strategies. Finally, this work found out that the transmission of malaria in Rwanda can be minimized by using the combination of controls like Insecticide Treated bed Nets (ITNs), Indoor Residual Spray (IRS) and Artemisinin based Combination Therapies (ACTs).

scholarly journals Optimal Control Techniques on a Mathematical Model for the Dynamics of Tungiasis in a Community

2017 ◽  
Vol 2017 ◽  
pp. 1-19 ◽  
Author(s):  
Jairos Kahuru ◽  
Livingstone S. Luboobi ◽  
Yaw Nkansah-Gyekye
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Control Strategy ◽  
Control Strategies ◽  
Control Process ◽  
Control Measures ◽  
Human Beings ◽  
Optimal Control Strategy ◽  
Control Techniques ◽  
Existence Of Optimal Control

Tungiasis is a permanent penetration of female sand flea“Tunga penetrans”into the epidermis of its host. It affects human beings and domestic and sylvatic animals. In this paper, we apply optimal control techniques to a Tungiasis controlled mathematical model to determine the optimal control strategy in order to minimize the number of infested humans, infested animals, and sand flea populations. In an attempt to reduce Tungiasis infestation in human population, the control strategies based on personal protection, personal treatment, educational campaign, environmental sanitation, and insecticidal treatments on the affected parts as well as on animal fur are considered. We prove the existence of optimal control problem, determine the necessary conditions for optimality, and then perform numerical simulations. The numerical results showed that the control strategy comprises all five control measures and that which involves the three control measures of insecticide control, insecticidal dusting on animal furs, and environmental hygiene has the significant impact on Tungiasis transmission. Therefore, fighting against Tungiasis infestation in endemic settings, multidimensional control process should be employed in order to achieve the maximum benefits.

scholarly journals A dynamic optimal control model for COVID-19 and cholera co-infection in Yemen

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ibrahim M. Hezam ◽  
Abdelaziz Foul ◽  
Adel Alrasheedi
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Preventive Measures ◽  
Control Model ◽  
Model Parameters ◽  
System Of Differential Equations ◽  
Model Framework ◽  
Social Distancing ◽  
Infected People ◽  
The Cost

AbstractIn this work, we propose a new dynamic mathematical model framework governed by a system of differential equations that integrates both COVID-19 and cholera outbreaks. The estimations of the model parameters are based on the outbreaks of COVID-19 and cholera in Yemen from January 1, 2020 to May 30, 2020. Moreover, we present an optimal control model for minimizing both the number of infected people and the cost associated with each control. Four preventive measures are to be taken to control the outbreaks: social distancing, lockdown, the number of tests, and the number of chlorine water tablets (CWTs). Under the current conditions and resources available in Yemen, various policies are simulated to evaluate the optimal policy. The results obtained confirm that the policy of providing resources for the distribution of CWTs, providing sufficient resources for testing with an average social distancing, and quarantining of infected individuals has significant effects on flattening the epidemic curves.

scholarly journals Optimal Control and Cost-Effectiveness Analysis of HIV Model with Educational Campaigns and Therapy

MATEMATIKA ◽  
2019 ◽  
Vol 35 (4) ◽  
pp. 123-138
Author(s):  
. Marsudi ◽  
Noor Hidayat ◽  
Ratno Bagus Edy Wibowo
Keyword(s):  
Optimal Control ◽  
Cost Effectiveness ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Necessary Conditions ◽  
Cost Effectiveness Analysis ◽  
Control Measures ◽  
Hiv Model ◽  
Effectiveness Analysis ◽  
Educational Campaigns

In this paper, we present a deterministic model for the transmission dynamics of HIV, in which educational campaigns and therapy are both important for disease management. We propose and analyze an optimal control problem to investigate the effectiveness and cost-effectiveness of three control measures (educational campaigns, therapy on infected individuals in the asymptomatic stage, and therapy on infected individuals in the pre-AIDS class). We formulate the appropriate optimal control problem and investigate the necessary conditions for disease control in order to determine the role of asymptomatic infection, pre-AIDS, and full-blown AIDS in the spread of HIV. Pontryagin’s Maximum Principle was employed to derive the necessary conditions for the existence of optimal control. The fourth-order Runge-Kutta forward-backwards sweep numerical approximation method was used to solve the optimal control system. The Incremental Cost-Effectiveness Ratio (ICER) was calculated to investigate the cost-effectiveness of all possible combinations of the three control measures. Using cost-effectiveness analysis, we showed that control of therapy on pre-AIDS and a combination of control of educational campaigns and therapy on pre-AIDS provides the most cost-effective strategy to control the disease.

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