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 Modeling the Impact of Optimal Control Strategies on the Dynamics of Zika Virus Disease Using the Sterile Insect Technology

2020 ◽  
pp. 13-33
Author(s):  
Atokolo William ◽  
Akpa Johnson ◽  
Daniel Musa Alih ◽  
Olayemi Kehinde Samuel ◽  
C. E. Mbah Godwin
Keyword(s):  
Optimal Control ◽  
Control Strategy ◽  
Zika Virus ◽  
Human Population ◽  
Necessary Conditions ◽  
Virus Disease ◽  
Control Strategies ◽  
Control Measures ◽  
Optimal Control Strategy ◽  
The Impact

This work is aimed at formulating a mathematical model for the control of zika virus infection using Sterile Insect Technology (SIT). The model is extended to incorporate optimal control strategy by introducing three control measures. The optimal control is aimed at minimizing the number of Exposed human, Infected human and the total number of Mosquitoes in a population and as such reducing contacts between mosquitoes and human, human to human and above all, eliminates the population of Mosquitoes. The Pontryagin’s maximum principle was used to obtain the necessary conditions, find the optimality system of our model and to obtain solution to the control problem. Numerical simulations result shows that; reduction in the number of Exposed human population, Infected human population and reduction in the entire population of Mosquito population is best achieved using the optimal control strategy.

Optimal control strategy for cancer remission using combinatorial therapy: A mathematical model-based approach

2021 ◽  
Vol 145 ◽  
pp. 110789
Author(s):  
Parthasakha Das ◽  
Samhita Das ◽  
Pritha Das ◽  
Fathalla A. Rihan ◽  
Muhammet Uzuntarla ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Control Strategy ◽  
Optimal Control Strategy ◽  
Combinatorial Therapy ◽  
Model Based ◽  
Cancer Remission

scholarly journals Optimal Control Strategy Design Based on Dynamic Programming for a Dual-Motor Coupling-Propulsion System

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Shuo Zhang ◽  
Chengning Zhang ◽  
Guangwei Han ◽  
Qinghui Wang
Keyword(s):  
Optimal Control ◽  
Dynamic Programming ◽  
Energy Loss ◽  
Control Strategy ◽  
Control Strategies ◽  
Propulsion System ◽  
Dynamic Features ◽  
Optimal Control Strategy ◽  
Control Rules ◽  
Electric Bus

A dual-motor coupling-propulsion electric bus (DMCPEB) is modeled, and its optimal control strategy is studied in this paper. The necessary dynamic features of energy loss for subsystems is modeled. Dynamic programming (DP) technique is applied to find the optimal control strategy including upshift threshold, downshift threshold, and power split ratio between the main motor and auxiliary motor. Improved control rules are extracted from the DP-based control solution, forming near-optimal control strategies. Simulation results demonstrate that a significant improvement in reducing energy loss due to the dual-motor coupling-propulsion system (DMCPS) running is realized without increasing the frequency of the mode switch.

scholarly journals Estimating the Optimal Control of Zoonotic Visceral Leishmaniasis by the Use of a Mathematical Model

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Laila Massad Ribas ◽  
Vera Lucia Zaher ◽  
Helio Junji Shimozako ◽  
Eduardo Massad
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Visceral Leishmaniasis ◽  
Vector Control ◽  
Control Strategy ◽  
Control Strategies ◽  
Effective Control ◽  
Alternative Control ◽  
Alternative Strategies ◽  
Zoonotic Visceral Leishmaniasis

We argue that the strategy of culling infected dogs is not the most efficient way to control zoonotic visceral leishmaniasis (ZVL) and that, in the presence of alternative control strategies with better potential results, official programs of compulsory culling adopted by some countries are inefficient and unethical. We base our arguments on a mathematical model for the study of control strategies against ZVL, which allows the comparison of the efficacies of 5, alternative strategies. We demonstrate that the culling program, previously questioned on both theoretical and practical grounds is the less effective control strategy. In addition, we show that vector control and the use of insecticide-impregnated dog collars are, by far, more efficient at reducing the prevalence of ZVL in humans.

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 Stability and optimal control in a mathematical model of online game addiction

Filomat ◽  
2019 ◽  
Vol 33 (17) ◽  
pp. 5691-5711 ◽  
Author(s):  
Tingting Li ◽  
Youming Guo
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Maximum Principle ◽  
Control Strategy ◽  
Reproduction Number ◽  
Direct Transfer ◽  
Online Game ◽  
Optimal Control Strategy ◽  
Game Addiction ◽  
The Basic Reproduction Number

In this paper, we construct an online game addiction model(including susceptible, infective, professional and quitting compartments). We also consider that the direct transfer from the susceptible individuals to the professional individuals. Some properties of the model are derived by the basic reproduction number R0 and stability of all kinds of equilibria is obtained. Then we use Pontriagin?s maximum principle to solve the optimal control strategy. Finally, Numerical simulations are also conducted in the analytic results.

scholarly journals Dynamic modeling and optimal control of cystic echinococcosis

2021 ◽  
Author(s):  
Xinmiao Rong ◽  
Meng Fan ◽  
Huaiping Zhu ◽  
Yaohui Zheng
Keyword(s):  
Optimal Control ◽  
Numerical Simulations ◽  
Control Strategy ◽  
Cystic Echinococcosis ◽  
Control Measures ◽  
Domestic Dog ◽  
Contour Plot ◽  
Control Cost ◽  
Optimal Control Strategy ◽  
Stray Dogs

Abstract Background: Cystic echinococcosis is one of the most severe helminth zoonosis with a drastic impact on human health and livestock industry. Investigating optimal control strategy and assessing the crucial factors are essential for developing countermeasures to mitigate this disease.Methods: Two compartment models were formulated to study the dynamics of cystic echinococcosis transmission, to evaluate the effectiveness of various control measures, and to find the optimal control strategy. Sensitive analyses were conducted by obtaining PRCCs and contour plot was used to evaluate the effect of key parameters on the basic reproduction number. Based on forward-backward sweep method, numerical simulations were employed to investigate effects of key factors on the transmission of cystic echinococcosis and to obtain the optimal control strategy.Results: The food resources of stray dog and invalid sheep vaccination rate, which are always neglected, were significant to the transmission and control of cystic echinococcosis. Numerical simulations suggest that, the implementation of optimal control strategy can significantly reduce the infections. Improving the cost of health education and domestic dog deworming could not decrease human infections.Conclusions: Our study showed that only a long-term use of the optimal control measures can eliminate the disease. Meanwhile, during the intervention, sheep vaccination and stray dogs disposing should be emphasized ahead of domestic dogs deworming to minimize the control cost. Simultaneously reducing other wild intermediate hosts and strengthening the sheep vaccination as well as disposing the stray dogs would be most effective.

OPTIMAL HARVESTING PROBLEM FOR AN AGE-DEPENDENT n-DIMENSIONAL COMPETING SYSTEM WITH DIFFUSION

2008 ◽  
Vol 01 (02) ◽  
pp. 133-145 ◽  
Author(s):  
ZHIXUE LUO ◽  
ZE-RONG HE
Keyword(s):  
Optimal Control ◽  
Control Strategy ◽  
Existence And Uniqueness ◽  
Spatial Diffusion ◽  
Optimal Harvesting ◽  
Negative Solution ◽  
Optimal Control Strategy ◽  
Age Dependent ◽  
The Fixed Point Theorem ◽  
Existence Of Optimal Control

In this work, optimal harvesting policy for an age-dependent and spatial diffusion n-dimensional competing species is discussed. The existence and uniqueness of non-negative solution to the system are investigated by using the fixed point theorem. The existence of optimal control strategy is discussed and optimality conditions are obtained. Our results extend some known criteria.

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