OPTIMAL CONTROL APPLIED IN AN ANTHRAX EPIZOOTIC MODEL

2016 ◽  
Vol 24 (04) ◽  
pp. 495-517 ◽  
Author(s):  
BUDDHI PANTHA ◽  
JUDY DAY ◽  
SUZANNE LENHART
Keyword(s):  
Optimal Control ◽  
National Parks ◽  
Animal Species ◽  
Control Measure ◽  
Population Decline ◽  
Model Parameters ◽  
Carcass Disposal ◽  
The Cost ◽  
Wildlife Reserve ◽  
Proper Disposal

Anthrax is a rapidly fatal, infectious disease which occurs in many animal species, particularly herbivore mammals, and is one of the main causes of population decline in several national parks worldwide. As the infected animals face inevitable death and each infected carcass contributes spores to the surrounding environment, infected carcasses and the infected animals are the main sources of new infections. Thus any control measure should focus on vaccinating susceptible animals and the proper disposal of infected carcasses. In this paper, a system of ordinary differential equations modeling an anthrax epizootic in a wildlife reserve is formulated. Two controls representing vaccination of the susceptible animals and disposal of the infected carcasses are investigated in order to minimize the number of infected animals, the number of infected carcasses and the cost of vaccination and carcass disposal. Model parameters are estimated by using outbreak data from Malilangwe Wildlife Reserve, Zimbabwe, and some numerical results for the optimal control problem are presented.

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 An Optimal Control Problem by a Hybrid System of Hyperbolic and Ordinary Differential Equations

Games ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 23
Author(s):  
Alexander Arguchintsev ◽  
Vasilisa Poplevko
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Ordinary Differential Equations ◽  
Hyperbolic Equations ◽  
Control Methods ◽  
The Right ◽  
The Cost ◽  
Optimal Control Methods

This paper deals with an optimal control problem for a linear system of first-order hyperbolic equations with a function on the right-hand side determined from controlled bilinear ordinary differential equations. These ordinary differential equations are linear with respect to state functions with controlled coefficients. Such problems arise in the simulation of some processes of chemical technology and population dynamics. Normally, general optimal control methods are used for these problems because of bilinear ordinary differential equations. In this paper, the problem is reduced to an optimal control problem for a system of ordinary differential equations. The reduction is based on non-classic exact increment formulas for the cost-functional. This treatment allows to use a number of efficient optimal control methods for the problem. An example illustrates the approach.

scholarly journals Accommodating Taste and Scale Heterogeneity for Front-Seat Passenger’ Choice of Seat Belt Usage

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 460 ◽  
Author(s):  
Mahdi Rezapour ◽  
Khaled Ksaibati
Keyword(s):  
Mixed Model ◽  
Seat Belt ◽  
Model Fit ◽  
Model Parameters ◽  
Extended Model ◽  
Random Parameters ◽  
Front Seat ◽  
Scale Heterogeneity ◽  
Error Terms ◽  
The Cost

There is growing interest in implementation of the mixed model to account for heterogeneity across population observations. However, it has been argued that the assumption of independent and identically distributed (i.i.d) error terms might not be realistic, and for some observations the scale of the error is greater than others. Consequently, that might result in the error terms’ scale to be varied across those observations. As the standard mixed model could not account for the aforementioned attribute of the observations, extended model, allowing for scale heterogeneity, has been proposed to relax the equal error terms across observations. Thus, in this study we extended the mixed model to the model with heterogeneity in scale, or generalized multinomial logit model (GMNL), to see if accounting for the scale heterogeneity, by adding more flexibility to the distribution, would result in an improvement in the model fit. The study used the choice data related to wearing seat belt across front-seat passengers in Wyoming, with all attributes being individual-specific. The results highlighted that although the effect of the scale parameter was significant, the scale effect was trivial, and accounting for the effect at the cost of added parameters would result in a loss of model fit compared with the standard mixed model. Besides considering the standard mixed and the GMNL, the models with correlated random parameters were considered. The results highlighted that despite having significant correlation across the majority of the random parameters, the goodness of fits favors more parsimonious models with no correlation. The results of this study are specific to the dataset used in this study, and due to the possible fact that the heterogeneity in observations related to the front-seat passengers seat belt use might not be extreme, and do not require extra layer to account for the scale heterogeneity, or accounting for the scale heterogeneity at the cost of added parameters might not be required. Extensive discussion has been made in the content of this paper about the model parameters’ estimations and the mathematical formulation of the methods.

scholarly journals Dynamical Analysis and Optimal Control for a SEIR Model Based on Virus Mutation in WSNs

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 929
Author(s):  
Guiyun Liu ◽  
Jieyong Chen ◽  
Zhongwei Liang ◽  
Zhimin Peng ◽  
Junqiang Li
Keyword(s):  
Optimal Control ◽  
Rapid Development ◽  
Hamiltonian Function ◽  
Propagation Model ◽  
Dynamical Analysis ◽  
Optimal Control Strategy ◽  
Epidemic Dynamics ◽  
Optimization Control ◽  
The Cost ◽  
The Pontryagin Maximum Principle

With the rapid development of science and technology, the application of wireless sensor networks (WSNs) is more and more widely. It has been widely concerned by scholars. Viruses are one of the main threats to WSNs. In this paper, based on the principle of epidemic dynamics, we build a SEIR propagation model with the mutated virus in WSNs, where E nodes are infectious and cannot be repaired to S nodes or R nodes. Subsequently, the basic reproduction number R0, the local stability and global stability of the system are analyzed. The cost function and Hamiltonian function are constructed by taking the repair ratio of infected nodes and the repair ratio of mutated infected nodes as optimization control variables. Based on the Pontryagin maximum principle, an optimal control strategy is designed to effectively control the spread of the virus and minimize the total cost. The simulation results show that the model has a guiding significance to curb the spread of mutated virus in WSNs.

scholarly journals Cost-effectiveness of TAS-102 plus bevacizumab versus TAS-102 monotherapy in patients with metastatic colorectal cancer

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Kiyoaki Sugiura ◽  
Yuki Seo ◽  
Takayuki Takahashi ◽  
Hideyuki Tokura ◽  
Yasuhiro Ito ◽  
...  
Keyword(s):  
Colorectal Cancer ◽  
Health Care ◽  
Sensitivity Analysis ◽  
Cost Effectiveness ◽  
Combination Therapy ◽  
Metastatic Colorectal Cancer ◽  
Cost Effective ◽  
Model Parameters ◽  
Combination Regimen ◽  
The Cost

Abstract Background TAS-102 plus bevacizumab is an anticipated combination regimen for patients who have metastatic colorectal cancer. However, evidence supporting its use for this indication is limited. We compared the cost-effectiveness of TAS-102 plus bevacizumab combination therapy with TAS-102 monotherapy for patients with chemorefractory metastatic colorectal cancer. Method Markov decision modeling using treatment costs, disease-free survival, and overall survival was performed to examine the cost-effectiveness of TAS-102 plus bevacizumab combination therapy and TAS-102 monotherapy. The Japanese health care payer’s perspective was adopted. The outcomes were modeled on the basis of published literature. The incremental cost-effectiveness ratio (ICER) between the two treatment regimens was the primary outcome. Sensitivity analysis was performed and the effect of uncertainty on the model parameters were investigated. Results TAS-102 plus bevacizumab had an ICER of $21,534 per quality-adjusted life-year (QALY) gained compared with TAS-102 monotherapy. Sensitivity analysis demonstrated that TAS-102 monotherapy was more cost-effective than TAS-102 and bevacizumab combination therapy at a willingness-to-pay of under $50,000 per QALY gained. Conclusions TAS-102 and bevacizumab combination therapy is a cost-effective option for patients who have metastatic colorectal cancer in the Japanese health care system.

scholarly journals Protocol for the health economic evaluation of increasing the weekend specialist to patient ratio in hospitals in England

BMJ Open ◽  
2018 ◽  
Vol 8 (2) ◽  
pp. e015561 ◽  
Author(s):  
Samuel I Watson ◽  
Yen-Fu Chen ◽  
Julian F Bion ◽  
Cassie P Aldridge ◽  
Alan Girling ◽  
...  
Keyword(s):  
Health Economic Evaluation ◽  
Care Quality ◽  
Expert Elicitation ◽  
Weekend Effect ◽  
Model Parameters ◽  
Risk Of Death ◽  
Causal Processes ◽  
Key Policy ◽  
The Uk ◽  
The Cost

IntroductionThis protocol concerns the evaluation of increased specialist staffing at weekends in hospitals in England. Seven-day health services are a key policy for the UK government and other health systems trying to improve use of infrastructure and resources. A particular motivation for the 7-day policy has been the observed increase in the risk of death associated with weekend admission, which has been attributed to fewer hospital specialists being available at weekends. However, the causes of the weekend effect have not been adequately characterised; many of the excess deaths associated with the ‘weekend effect’ may not be preventable, and the presumed benefits of improved specialist cover might be offset by the cost of implementation.Methods/designThe Bayesian-founded method we propose will consist of four major steps. First, the development of a qualitative causal model. Specialist presence can affect multiple, interacting causal processes. One or more models will be developed from the results of an expert elicitation workshop and probabilities elicited for each model and relevant model parameters. Second, systematic review of the literature. The model from the first step will provide search limits for a review to identify relevant studies. Third, a statistical model for the effects of specialist presence on care quality and patient outcomes. Fourth, valuation of outcomes. The expected net benefits of different levels of specialist intensity will then be evaluated with respect to the posterior distributions of the parameters.Ethics and disseminationThe study was approved by the Review Subcommittee of the South West Wales REC on 11 November 2013. Informed consent was not required for accessing anonymised patient case records from which patient identifiers had been removed. The findings of this study will be published in peer-reviewed journals; the outputs from this research will also form part of the project report to the HS&DR Programme Board.

scholarly journals The barasingha, or swamp deer, in Suklaphanta Wildlife Reserve, Nepal

Oryx ◽  
1994 ◽  
Vol 28 (3) ◽  
pp. 199-206 ◽  
Author(s):  
J. Henshaw
Keyword(s):  
Environmental Impact ◽  
Field Study ◽  
National Parks ◽  
Wildlife Conservation ◽  
Irrigation Canal ◽  
Protective Measures ◽  
Deer Species ◽  
The World ◽  
Wildlife Reserve ◽  
Swamp Deer

Between 1988 and 1993 six periods of field study were undertaken to investigate the environmental impact of the construction of a main irrigation canal and other works in the proposed extension of Suklaphanta Wildlife Reserve and to recommend protective measures. Suklaphanta is administered by His Majesty's Government of Nepal through the Department of National Parks and Wildlife Conservation. Special emphasis was placed upon the barasingha Cervus duvauceli population because it is the largest remaining group of this endangered deer species in the world. This paper presents recommendations for the management of the barasingha and its habitat.

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 Estimation and optimal control of the multi-scale dynamics of the Covid-19

2021 ◽  
Author(s):  
David Jaurès Fotsa-Mbogne ◽  
Stéphane Yanick Tchoumi ◽  
Yannick Kouakep-Tchaptchie ◽  
Vivient Corneille Kamla ◽  
Jean-Claude Kamgang ◽  
...  
Keyword(s):  
Optimal Control ◽  
Human Population ◽  
Virus Transmission ◽  
Scale Model ◽  
Model Parameters ◽  
Optimal Control Strategy ◽  
Or Efficiency ◽  
Human Virus ◽  
Multi Scale ◽  
Human Density

AbstractThis work aims at a better understanding and the optimal control of the spread of the new severe acute respiratory corona virus 2 (SARS-CoV-2). We first propose a multi-scale model giving insights on the virus population dynamics, the transmission process and the infection mechanism. We consider 10 compartments in the human population in order to take into accounts the effects of different specific mitigation policies: susceptible, infected, infectious, quarantined, hospitalized, treated, recovered, non-infectious dead, infectious dead, buried. The population of viruses is also partitioned into 10 compartments corresponding respectively to each of the first nine human population compartments and the free viruses available in the environment. Indeed, we have human to human virus transmission, human to environment virus transmission, environment to human virus transmission and self infection by susceptible individuals. We show the global stability of the disease free equilibrium if a given threshold 𝒯0 is less or equal to 1 and we provide how to compute the basic reproduction number ℛ0. A convergence index 𝒯1 is also defined in order to estimate the speed at which the disease extincts and an upper bound to the time of extinction is given. The existence of the endemic equilibrium is conditional and its description is provided. We evaluate the sensitivity of ℛ0, 𝒯0 and 𝒯1 to control parameters such as the maximal human density allowed per unit of surface, the rate of disinfection both for people and environment, the mobility probability, the wearing mask probability or efficiency, and the human to human contact rate which results from the previous one. Except the maximal human density allowed per unit of surface, all those parameters have significant effects on the qualitative dynamics of the disease. The most significant is the probability of wearing mask followed by the probability of mobility and the disinfection rate. According to a functional cost taking into consideration economic impacts of SARS-CoV-2, we determine and discuss optimal fighting strategies. The study is applied to real available data from Cameroon and an estimation of model parameters is done. After several simulations, social distancing and the disinfection frequency appear as the main elements of the optimal control strategy.

High-order relaxation approaches for adjoint-based optimal control problems governed by nonlinear hyperbolic systems of conservation laws

2016 ◽  
Vol 24 (1) ◽  
Author(s):  
Elimboto M. Yohana ◽  
Mapundi K. Banda
Keyword(s):  
Optimal Control ◽  
Conservation Laws ◽  
Optimal Control Problems ◽  
Initial Conditions ◽  
Hyperbolic Systems ◽  
Control Problems ◽  
Computational Investigation ◽  
Backward Problem ◽  
Systems Of Conservation Laws ◽  
The Cost

AbstractA computational investigation of optimal control problems which are constrained by hyperbolic systems of conservation laws is presented. The general framework is to employ the adjoint-based optimization to minimize the cost functional of matching-type between the optimal and the target solution. Extension of the numerical schemes to second-order accuracy for systems for the forward and backward problem are applied. In addition a comparative study of two relaxation approaches as solvers for hyperbolic systems is undertaken. In particular optimal control of the 1-D Riemann problem of Euler equations of gas dynamics is studied. The initial values are used as control parameters. The numerical flow obtained by optimal initial conditions matches accurately with observations.

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