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 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 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 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 for Multistage Nonlinear Dynamic System of Microbial Bioconversion in Batch Culture

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Lei Wang ◽  
Zhilong Xiu ◽  
Yuduo Zhang ◽  
Enmin Feng
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Batch Culture ◽  
Control Function ◽  
Nonlinear Dynamical System ◽  
Control Model ◽  
Optimization Techniques ◽  
Terminal Time ◽  
Continuous State

In batch culture of glycerol biodissimilation to 1,3-propanediol (1,3-PD), the aim of adding glycerol is to obtain as much 1,3-PD as possible. Taking the yield intensity of 1,3-PD as the performance index and the initial concentration of biomass, glycerol, and terminal time as the control vector, we propose an optimal control model subject to a multistage nonlinear dynamical system and constraints of continuous state. A computational approach is constructed to seek the solution of the above model. Firstly, we transform the optimal control problem into the one with fixed terminal time. Secondly, we transcribe the optimal control model into an unconstrained one based on the penalty functions and an extension of the state space. Finally, by approximating the control function with simple functions, we transform the unconstrained optimal control problem into a sequence of nonlinear programming problems, which can be solved using gradient-based optimization techniques. The convergence analysis and optimality function of the algorithm are also investigated. Numerical results show that, by employing the optimal control, the concentration of 1,3-PD at the terminal time can be increased, compared with the previous results.

scholarly journals Optimal Control and Cost Effectiveness Analysis of SIRS Malaria Disease Model with Temperature Variability Factor

2021 ◽  
Vol 53 (1) ◽  
pp. 134-163
Author(s):  
Temesgen Duressa Keno ◽  
Oluwole Daniel Makinde ◽  
Legesse Lemecha Obsu
Keyword(s):  
Optimal Control ◽  
Cost Effectiveness ◽  
Initial Conditions ◽  
Control Strategies ◽  
Disease Model ◽  
Temperature Variability ◽  
Control Measures ◽  
Basic Reproductive Number ◽  
Bed Nets ◽  
Reproductive Number

In this study, we proposed and analyzed the optimal control and cost-effectiveness strategies for malaria epidemics model with impact of temperature variability. Temperature variability strongly determines the transmission of malaria. Firstly, we proved that all solutions of the model are positive and bounded within a certain set with initial conditions. Using the next-generation matrix method, the basic reproductive number at the present malaria-free equilibrium point was computed. The local stability and global stability of the malaria-free equilibrium were depicted applying the Jacobian matrix and Lyapunov function respectively when the basic reproductive number is smaller than one. However, the positive endemic equilibrium occurs when the basic reproductive number is greater than unity. A sensitivity analysis of the parameters was conducted; the model showed forward and backward bifurcation. Secondly, using Pontryagin’s maximum principle, optimal control interventions for malaria disease reduction are described involving three control measures, namely use of insecticide-treated bed nets, treatment of infected humans using anti-malarial drugs, and indoor residual insecticide spraying. An analysis of cost-effectiveness was also conducted. Finally, based on the simulation of different control strategies, the combination of treatment of infected humans and insecticide spraying was proved to be the most efficient and least costly strategy to eradicate the disease.

scholarly journals Multiobjective optimization to a TB-HIV/AIDS coinfection optimal control problem

2017 ◽  
Vol 37 (2) ◽  
pp. 2112-2128 ◽  
Author(s):  
Roman Denysiuk ◽  
Cristiana J. Silva ◽  
Delfim F. M. Torres
Keyword(s):  
Optimal Control ◽  
Multiobjective Optimization ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Hiv Aids

scholarly journals Application and Optimal Control for an HBV Model with Vaccination and Treatment

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Jing Zhang ◽  
Suxia Zhang
Keyword(s):  
Optimal Control ◽  
Hepatitis B ◽  
Least Squares Method ◽  
Control Strategies ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Optimal Theory ◽  
B Virus ◽  
The Stability ◽  
Hbv Model

In this study, we formulate a model for hepatitis B virus with control strategies of newborn vaccination and treatment. Mathematical analysis is done theoretically and numerically. The results indicate that the stability of equilibria and persistence of the disease are determined by the basic reproductive number R0. Using the least squares method, the model is applied to simulate yearly new infected cases of hepatitis B in China from 2004 to 2016. Moreover, optimal control problem with newborn vaccination and treatment appearing as functions of time is analyzed by classical optimal theory. The existence of the solution to optimality system is proved, and the simulations are conducted to show the results when optimal control or current intervention is used.

scholarly journals Modeling Optimal Control of Cholera Disease Under the Interventions of Vaccination, Treatment and Education Awareness

2018 ◽  
Vol 10 (5) ◽  
pp. 137
Author(s):  
Hellen Namawejje ◽  
Emmanuel Obuya ◽  
Livingstone S. Luboobi
Keyword(s):  
Optimal Control ◽  
Control Strategies ◽  
Care Service ◽  
Equilibrium Points ◽  
Health Care Service ◽  
Medical Science ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Education Campaigns ◽  
Global Threat

Cholera is virulent disease that affects both children and adults and can kill within hours. It has long been, and continues to be, a global threat to public health regardless of the advancement of medical science and health care service available. In this paper we formulate and analyze a mathematical model of the dynamics and optimal con- trol strategies for cholera epidemic. We present and analyze a cholera model with controls: u1 for vaccination of the human population, u2 for treatment and u3 for health education campaigns. The basic reproductive number R0; the effective reproductive number Re; as well as disease free equilibrium and endemic equilibrium points are derived. We establish the conditions for optimal control of the cholera disease using the Pontryagin&#39;s maximum principle and simulate the model for different control strategies. The results show that vaccination and education campaigns should be applied from start of the epidemic in any community faced with cholera disease.

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

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