scholarly journals Optimization of spatial control strategies for population replacement, application to Wolbachia

2021 ◽  
Author(s):  
Yannick Privat ◽  
Michel Duprez ◽  
Nicolas Vauchelet ◽  
Romane Hélie
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Control Strategies ◽  
Mosquito Population ◽  
Infected Mosquito ◽  
Asymptotic Model ◽  
Population Replacement ◽  
Replacement Technique ◽  
Very High

In this article, we are interested in the analysis and simulation of solutions to an optimal control problem motivated by population dynamics issues. In order to control the spread of mosquito-borne arboviruses, the population replacement technique consists in releasing into the environment mosquitoes infected with the Wolbachia bacterium, which greatly reduces the trans- mission of the virus to the humans. Spatial releases are then sought in such a way that the infected mosquito population invades the uninfected mosquito population. Assuming very high mosquito fecundity rates, we first introduce an asymptotic model on the proportion of infected mosquitoes and then an optimal control problem to determine the best spatial strategy to achieve these releases. We then analyze this problem, including the optimality of natural candidates and carry out first numerical simulations in one dimension of space to illustrate the relevance of our approach.

scholarly journals Optimal Control of HIV/AIDS in the Workplace in the Presence of Careless Individuals

2014 ◽  
Vol 2014 ◽  
pp. 1-19 ◽  
Author(s):  
Baba Seidu ◽  
Oluwole D. Makinde
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Control Strategies ◽  
Nonlinear Dynamical System ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Nonlinear Dynamical ◽  
Basic Model ◽  
Hiv Aids

A nonlinear dynamical system is proposed and qualitatively analyzed to study the dynamics of HIV/AIDS in the workplace. The disease-free equilibrium point of the model is shown to be locally asymptotically stable if the basic reproductive number,R0, is less than unity and the model is shown to exhibit a unique endemic equilibrium when the basic reproductive number is greater than unity. It is shown that, in the absence of recruitment of infectives, the disease is eradicated whenR0<1, whiles the disease is shown to persist in the presence of recruitment of infected persons. The basic model is extended to include control efforts aimed at reducing infection, irresponsibility, and nonproductivity at the workplace. This leads to an optimal control problem which is qualitatively analyzed using Pontryagin’s Maximum Principle (PMP). Numerical simulation of the resulting optimal control problem is carried out to gain quantitative insights into the implications of the model. The simulation reveals that a multifaceted approach to the fight against the disease is more effective than single control strategies.

scholarly journals Optimal Control Problem for Cholera Disease and Cost-Effectiveness Analysis

2021 ◽  
Vol 53 (2) ◽  
pp. 200-2017
Author(s):  
Jhoana Patricia Romero-Leiton ◽  
Muhammad Ozair ◽  
Takasar Hussaing
Keyword(s):  
Optimal Control ◽  
Cost Effectiveness ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Control Strategies ◽  
Cost Effectiveness Analysis ◽  
Effectiveness Analysis ◽  
Using Data ◽  
Theoretical Results

Cholera is a disease that continues to be a threat to public health globally and is an indicator of inequity and lack of social development in countries. For this reason, strategies for its control need to be investigated. In this work, an optimal control problem related to cholera disease was formulated by introducing personal protection, drug treatment and water sanitation as control strategies. First, the existence and characterization of controls to minimize the performance index or cost function was proved by using classic control theory. Then, the theoretical results were validated with numerical experiments by using data reported in the literature. Finally, the effectiveness and efficiency of the proposed controls were determined through a cost-effectiveness analysis. The results showed that the use of the three controls simultaneously is the cheapest and most effective strategy to control the disease.

scholarly journals Optimal control problem on COVID-19 disease transmission model considering medical mask, disinfectants and media campaign

2020 ◽  
Vol 202 ◽  
pp. 12009
Author(s):  
Dipo Aldila
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Disease Transmission ◽  
Control Strategies ◽  
Population Based ◽  
Transmission Model ◽  
Media Campaign ◽  
Free Virus ◽  
Final State

In this paper, a system of ordinary differential equation approach is developed to understand the spread of COVID-19. We first formulate the dynamic model by dividing the human population based on their health status, awareness status, and also including the free virus on the environment. We provide a basic analysis of the model regarding the well-posed properties and how the basic reproduction number can be used to determine the final state of COVID-19 in the population. A Pontryagin Maximum’s Principle used to construct the model as an optimal control problem in a purpose to determine the most effective strategies against the spread of COVID-19. Three control strategies involved in the model, such as media campaign to develop an awareness of individuals, medical masks to prevent direct transmission, and use of disinfectant to reduce the number of free virus in the environment. Through numerical simulations, we find that the time-dependent control succeeds in reducing the outbreak of COVID-19. Furthermore, if the intervention should be implemented as a single intervention, then the media campaign gives the most effective cost strategy.

scholarly journals Optimal control problem for a tuberculosis model with multiple infectious compartments and time delays

2021 ◽  
Vol 11 (1) ◽  
pp. 75-91
Author(s):  
Mohamed Elhia ◽  
Omar Balatif ◽  
Lahoucine Boujallal ◽  
Mostafa Rachik
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Time Delays ◽  
Control Strategies ◽  
Multiple Time ◽  
Optimal Controls ◽  
Loss To Follow Up ◽  
Tuberculosis Model

In this paper, we formulate an optimal control problem based on a tuberculosis model with multiple infectious compartments and time delays. In order to have a more realistic model that allows highlighting the role of detection, loss to follow-up and treatment in TB transmission, we propose an extension of the classical SEIR model by dividing infectious patients in the compartment (I) into three categories: undiagnosed infected (I), diagnosed patients who are under treatment (T) and diagnosed patients who are lost to follow-up (L). We incorporate in our model delays representing the incubation period and the time needed for treatment. We also introduce three control variables in our delayed system which represent prevention, detection and the efforts that prevent the failure of treatment. The purpose of our control strategies is to minimize the number of infected individuals and the cost of intervention. The existence of the optimal controls is investigated, and a characterization of the three controls is given using the Pontryagin's maximum principle with delays. To solve numerically the optimality system with delays, we present an adapted iterative method based on the iterative Forward-Backward Sweep Method (FBSM). Numerical simulations performed using Matlab are also provided. They indicate that the prevention control is the most effective one. To the best of our knowledge, it is the first work to apply optimal control theory to a TB model which considers infectious patients diagnosis, loss to follow-up phenomenon and multiple time delays.

scholarly journals A Quantitative Analysis of Preventive Measures to Mitigate the Infectious Diseases Using SIR model by Optimal Control Technique

2018 ◽  
Vol 5 (1) ◽  
pp. 11-19
Author(s):  
Jakia Sultana ◽  
Samiha Islam Tanni ◽  
Shamima Islam
Keyword(s):  
Optimal Control ◽  
Infectious Diseases ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Transmission Rate ◽  
Control Strategies ◽  
Sir Model ◽  
The State ◽  
Control Technique ◽  
State Equations

Optimal Control Problem with the state equations which describes the standard SIR Model is studied here. We considered the SIR Model with vaccination and without vaccination. We formulated an optimal control problem and derived necessary conditions. Existence of the state and the objective functional are also verified. We also characterized the optimal control by Pontryagin’s maximum principle which minimizes the number of infected individuals and cost of vaccination over some finite period. Whenever the vaccination is carried out for a long period of time, the simulated result effectively works for disease with high transmission rate. Observations from the numerical simulation revels that the infectious diseases are most successfully controlled whenever control strategies were adopted at early stages. GUB JOURNAL OF SCIENCE AND ENGINEERING, Vol 5(1), Dec 2018 P 11-19

REDUCED MODEL OF PLASMA DISCHARGE CONTROL IN TOKAMAK WITH IRON CORE

2020 ◽  
Vol 7 (3) ◽  
pp. 11-22
Author(s):  
VALERY ANDREEV ◽  
◽  
ALEXANDER POPOV
Keyword(s):  
Optimal Control ◽  
Inverse Problem ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Nonlinear Behavior ◽  
Plasma Discharge ◽  
Reduced Model ◽  
Iron Core ◽  
Power Sources ◽  
Real Power

A reduced model has been developed to describe the time evolution of a discharge in an iron core tokamak, taking into account the nonlinear behavior of the ferromagnetic during the discharge. The calculation of the discharge scenario and program regime in the tokamak is formulated as an inverse problem - the optimal control problem. The methods for solving the problem are compared and the analysis of the correctness and stability of the control problem is carried out. A model of “quasi-optimal” control is proposed, which allows one to take into account real power sources. The discharge scenarios are calculated for the T-15 tokamak with an iron core.

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