scholarly journals Optimal Containment Control Strategy of the Second Phase of the COVID-19 Lockdown in Morocco

2020 ◽  
Vol 10 (21) ◽  
pp. 7559
Author(s):  
Mustapha Lhous ◽  
Omar Zakary ◽  
Mostafa Rachik ◽  
El Mostafa Magri ◽  
Abdessamad Tridane
Keyword(s):  
Optimal Control ◽  
Least Squares Method ◽  
Control Strategies ◽  
Nonlinear Least Squares ◽  
Real Data ◽  
Contact Tracing ◽  
Second Phase ◽  
Containment Control ◽  
Treatment Measures ◽  
The Impact

This work investigates the optimal control of the second phase of the COVID-19 lockdown in Morocco. The model consists of susceptible, exposed, infected, recovered, and quarantine compartments (SEIRQD model), where we take into account contact tracing, social distancing, quarantine, and treatment measures during the nationwide lockdown in Morocco. First, we present different components of the model and their interactions. Second, to validate our model, the nonlinear least-squares method is used to estimate the model’s parameters by fitting the model outcomes to real data of the COVID-19 in Morocco. Next, to investigate the impact of optimal control strategies on this pandemic in the country. We also give numerical simulations to illustrate and compare the obtained results with the actual situation in Morocco.

scholarly journals Mathematical Modeling of Public Opinions: Parameter Estimation, Sensitivity Analysis, and Model Uncertainty Using an Agree-Disagree Opinion Model

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Sara Bidah ◽  
Omar Zakary ◽  
Mostafa Rachik ◽  
Hanane Ferjouchia
Keyword(s):  
Sensitivity Analysis ◽  
Control Strategies ◽  
Nonlinear Least Squares ◽  
Real Data ◽  
Outcome Variable ◽  
Polling System ◽  
Least Squares Regression ◽  
Approval Rating ◽  
Statistical Experiments ◽  
The Stability

In this paper, we present a mathematical model that describes agree-disagree opinions during polls. We first present the different compartments of the model. Then, using the next-generation matrix method, we derive thresholds of the stability of equilibria. We consider two sets of data from the Reuters polling system regarding the approval rating of the U.S presidential in two terms. These two weekly polls data track the percentage of Americans who approve and disapprove of the way the President manages his work. To validate the reality of the underlying model, we use nonlinear least-squares regression to fit the model to actual data. In the first poll, we consider only 31 weeks to estimate the parameters of the model, and then, we compare the rest of the data with the outcome of the model over the remaining 21 weeks. We show that our model fits correctly the real data. The second poll data is collected for 115 weeks. We estimate again the parameters of the model, and we show that our model can predict the poll outcome in the next weeks, thus, whether the need for some control strategies or not. Finally, we also perform several computational and statistical experiments to validate the proposed model in this paper. To study the influence of various parameters on these thresholds and to identify the most influential parameters, sensitivity analysis is carried out to investigate the effect of the small perturbation near a parameter value on the value of the threshold. An uncertainty analysis is performed to evaluate the forecast inaccuracy in the outcome variable due to uncertainty in the estimation of the parameters.

scholarly journals Modeling the Effects of Helminth Infection on the Transmission Dynamics of Mycobacterium tuberculosis under Optimal Control Strategies

2020 ◽  
Vol 2020 ◽  
pp. 1-21
Author(s):  
Aristide G. Lambura ◽  
Gasper G. Mwanga ◽  
Livingstone Luboobi ◽  
Dmitry Kuznetsov
Keyword(s):  
Optimal Control ◽  
Equilibrium Point ◽  
Drug Administration ◽  
Mass Drug Administration ◽  
Helminth Infection ◽  
Reproduction Number ◽  
Control Strategies ◽  
Active Tuberculosis ◽  
Control Measures ◽  
The Impact

A deterministic mathematical model for the transmission and control of cointeraction of helminths and tuberculosis is presented, to examine the impact of helminth on tuberculosis and the effect of control strategies. The equilibrium point is established, and the effective reproduction number is computed. The disease-free equilibrium point is confirmed to be asymptotically stable whenever the effective reproduction number is less than the unit. The analysis of the effective reproduction number indicates that an increase in the helminth cases increases the tuberculosis cases, suggesting that the control of helminth infection has a positive impact on controlling the dynamics of tuberculosis. The possibility of bifurcation is investigated using the Center Manifold Theorem. Sensitivity analysis is performed to determine the effect of every parameter on the spread of the two diseases. The model is extended to incorporate control measures, and Pontryagin’s Maximum Principle is applied to derive the necessary conditions for optimal control. The optimal control problem is solved numerically by the iterative scheme by considering vaccination of infants for Mtb, treatment of individuals with active tuberculosis, mass drug administration with regular antihelminthic drugs, and sanitation control strategies. The results show that a combination of educational campaign, treatment of individuals with active tuberculosis, mass drug administration, and sanitation is the most effective strategy to control helminth-Mtb coinfection. Thus, to effectively control the helminth-Mtb coinfection, we suggest to public health stakeholders to apply intervention strategies that are aimed at controlling helminth infection and the combination of vaccination of infants and treatment of individuals with active tuberculosis.

scholarly journals State-Based Switching for Optimal Control of Computer Virus Propagation with External Device Blocking

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Qingyi Zhu ◽  
Seng W. Loke ◽  
Ye Zhang
Keyword(s):  
Optimal Control ◽  
Control Strategies ◽  
Minimum Principle ◽  
Optimal Solution ◽  
Computer Virus ◽  
Numerical Results ◽  
Difference Approximation ◽  
External Device ◽  
Virus Propagation ◽  
The Impact

The rapid propagation of computer virus is one of the greatest threats to current cybersecurity. This work deals with the optimal control problem of virus propagation among computers and external devices. To formulate this problem, two control strategies are introduced: (a) external device blocking, which means prohibiting a fraction of connections between external devices and computers, and (b) computer reconstruction, which includes updating or reinstalling of some infected computers. Then the combination of both the impact of infection and the cost of controls is minimized. In contrast with previous works, this paper takes into account a state-based cost weight index in the objection function instead of a fixed one. By using Pontryagin’s minimum principle and a modified forward-backward difference approximation algorithm, the optimal solution of the system is investigated and numerically solved. Then numerical results show the flexibility of proposed approach compared to the regular optimal control. More numerical results are also given to evaluate the performance of our approach with respect to various weight indexes.

CONTROL STRATEGIES FOR CHAOTIC NEUROMODULES

1996 ◽  
Vol 06 (04) ◽  
pp. 693-703 ◽  
Author(s):  
NICO STOLLENWERK ◽  
FRANK PASEMANN
Keyword(s):  
Least Squares ◽  
Chaotic Dynamics ◽  
Chaotic Systems ◽  
Least Squares Method ◽  
Control Strategies ◽  
Nonlinear Least Squares ◽  
The Neural Network ◽  
One Step ◽  
Nonlinear Least Squares Method ◽  
The One

Different strategies for control of chaotic systems are discussed: The well known Ott-Grebogi-Yorke algorithm and two alternative algorithms based on least-squares minimisation of the one step future deviation. To compare their effectiveness in the neural network context they are applied to a minimal two neuron module with discrete chaotic dynamics. The best method with respect to calculation effort, to neural implementation, and to controlling properties is the nonlinear least squares method. Furthermore, it is observed in simulations that one can stabilise a whole periodic orbit by applying the control signals only to one of its periodic points, which lies in a distinguished region of phase space.

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.

scholarly journals Modeling, Estimation, and Optimal Control of Anti-COVID-19 Multi-dose Vaccine Administration

2021 ◽  
Author(s):  
Paolo Scarabaggio ◽  
Raffaele Carli ◽  
Graziana Cavone ◽  
Nicola Epicoco ◽  
Mariagrazia Dotoli
Keyword(s):  
Optimal Control ◽  
Disease Transmission ◽  
Linear Time ◽  
Real Data ◽  
Science And Engineering ◽  
Vaccine Administration ◽  
Control Approach ◽  
International Conference ◽  
The Impact ◽  
Dose Vaccine

The recent trends of the COVID-19 research are being devoted to disease transmission modeling in presence of vaccinated individuals, while the emerging needs are being focused on developing effective strategies for the optimal distribution of vaccine between population. <br>In this context, we propose a novel non-linear time-varying model that effectively supports policy-makers in predicting and analyzing the dynamics of COVID-19 when partially and fully immune individuals are included in the population. Specifically, this paper proposes an accurate SIRUCQHE epidemiological model, with eight compartments (namely, Susceptible, Infected, Removed, Unsusceptible, Contagious, Quarantined, Hospitalized, and Extinct). <br>Differently from the related literature, where the common strategies typically rely on the prioritization of the different classes of individuals, we propose a novel Model Predictive Control approach to optimally control the multi-dose vaccine administration in the case the available number of doses is not sufficient to cover the whole population. Focusing on the minimization of the expected number of deaths, the approach discriminates between the number of first and second doses, thus considering also the possibility that some individuals may receive only one injection if the resulting expected fatalities are low. <br><div>To show the effectiveness of the resulting strategies, we first calibrate the model on the Israeli scenario using real data to get reliable predictions on the pandemic dynamics. Lastly, we estimate the impact of the vaccine administration on the virus dynamics and, in particular, based on validated model, we assess the impact of the first dose of the Pfitzer's vaccine confirming the results of clinical tests.</div><div><br></div><div><br></div><div>Extended version of the paper published in <i>Proceedings of the IEEE 16th International Conference on Automation Science and Engineering (CASE) </i><br> </div><div><b>How to cite:</b> Scarabaggio, P., Carli, R., Cavone, G., Epicoco, N., & Dotoli, M. "Modeling, Estimation, and Optimal Control of Anti-COVID-19 Multi-dose Vaccine Administration." In <i>2021 IEEE 17th International Conference on Automation Science and Engineering</i> (CASE) (pp. 990-995). IEEE.<br></div><div><br></div><div>DOI: <u>https://doi.org/10.1109/CASE49439.2021.9551418</u></div><div><br></div><div><br> </div>

scholarly journals Maximizing and evaluating the impact of test-trace-isolate programs: A modeling study

PLoS Medicine ◽  
2021 ◽  
Vol 18 (4) ◽  
pp. e1003585
Author(s):  
Kyra H. Grantz ◽  
Elizabeth C. Lee ◽  
Lucy D’Agostino McGowan ◽  
Kyu Han Lee ◽  
C. Jessica E. Metcalf ◽  
...  
Keyword(s):  
Control Strategies ◽  
R Package ◽  
Sensitivity Analyses ◽  
Contact Tracing ◽  
Reproductive Number ◽  
Case Detection ◽  
Modeling Framework ◽  
Online Application ◽  
Almost All ◽  
The Impact

Background Test-trace-isolate programs are an essential part of Coronavirus Disease 2019 (COVID-19) control that offer a more targeted approach than many other nonpharmaceutical interventions. Effective use of such programs requires methods to estimate their current and anticipated impact. Methods and findings We present a mathematical modeling framework to evaluate the expected reductions in the reproductive number, R, from test-trace-isolate programs. This framework is implemented in a publicly available R package and an online application. We evaluated the effects of completeness in case detection and contact tracing and speed of isolation and quarantine using parameters consistent with COVID-19 transmission (R0: 2.5, generation time: 6.5 days). We show that R is most sensitive to changes in the proportion of cases detected in almost all scenarios, and other metrics have a reduced impact when case detection levels are low (<30%). Although test-trace-isolate programs can contribute substantially to reducing R, exceptional performance across all metrics is needed to bring R below one through test-trace-isolate alone, highlighting the need for comprehensive control strategies. Results from this model also indicate that metrics used to evaluate performance of test-trace-isolate, such as the proportion of identified infections among traced contacts, may be misleading. While estimates of the impact of test-trace-isolate are sensitive to assumptions about COVID-19 natural history and adherence to isolation and quarantine, our qualitative findings are robust across numerous sensitivity analyses. Conclusions Effective test-trace-isolate programs first need to be strong in the “test” component, as case detection underlies all other program activities. Even moderately effective test-trace-isolate programs are an important tool for controlling the COVID-19 pandemic and can alleviate the need for more restrictive social distancing measures.

scholarly journals Control of snakebite envenoming: A mathematical modeling study

2021 ◽  
Vol 15 (8) ◽  
pp. e0009711
Author(s):  
Shuaibu Ahijo Abdullahi ◽  
Abdulrazaq Garba Habib ◽  
Nafiu Hussaini
Keyword(s):  
Public Health ◽  
Cost Effectiveness ◽  
Control Strategies ◽  
Real Data ◽  
Disability Adjusted Life Years ◽  
Health Awareness ◽  
Data Set ◽  
Disability Adjusted Life ◽  
Life Years ◽  
The Impact

A mathematical model is designed to assess the impact of some interventional strategies for curtailing the burden of snakebite envenoming in a community. The model is fitted with real data set. Numerical simulations have shown that public health awareness of the susceptible individuals on snakebite preventive measures could reduce the number of envenoming and prevent deaths and disabilities in the population. The simulations further revealed that if at least fifty percent of snakebite envenoming patients receive early treatment with antivenom a substantial number of deaths will be averted. Furthermore, it is shown using optimal control that combining public health awareness and antivenom treatment averts the highest number of snakebite induced deaths and disability adjusted life years in the study area. To choose the best strategy amidst limited resources in the study area, cost effectiveness analysis in terms of incremental cost effectiveness ratio is performed. It has been established that the control efforts of combining public health awareness of the susceptible individuals and antivenom treatment for victims of snakebite envenoming is the most cost effective strategy. Approximately the sum of US$72,548 is needed to avert 117 deaths or 2,739 disability adjusted life years that are recorded within 21 months in the study area. Thus, the combination of these two control strategies is recommended.

scholarly journals Fractional Optimal Control with Fish Consumption to Prevent the Risk of Coronary Heart Disease

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13 ◽  
Author(s):  
I. Ameen ◽  
M. Hidan ◽  
Z. Mostefaoui ◽  
H.M. Ali
Keyword(s):  
Optimal Control ◽  
Heart Disease ◽  
Fish Consumption ◽  
Control Function ◽  
Real Data ◽  
World Health ◽  
Susceptible Population ◽  
Fractional Optimal Control ◽  
The World ◽  
The Impact

According to the World Health Organization (WHO), Chronic Heart Disease (CHD) is one of the greatest defies currently confronting humankind which is sweeping the whole globe, with an expanding trend in developing countries. In this paper, a mathematical model (MM) was proposed to study the connection between fish consumption and CHD mortality in Egypt, by considering a system of ordinary differential equations (ODEs) involving time-fractional derivative (FD). We considered here the study on Egypt for the ease of obtaining real data, but the method and approach adopted here is not limited to Egypt only and can be applied to any country in the world with the information of the real data related to the subject of the study. Additionally, the control function which represents the metabolic and the behavioural risk factors of CHD that help to reduce the number of mortality due to CHD is incorporated in the proposed MM. A fractional optimal control problem (FOCP) with a proposed control is formulated and studied theoretically using the Pontryagin maximum principle, to minimize the susceptible population and also to decrease the mortality rate of CHD. Moreover, firstly we discussed the positivity and boundedness of solutions; then, the model equilibria are determined and their local stability analysis was investigated; furthermore, we use the improved forward-backward sweep method (FBSM) based on the predictor-corrector method (PCM) in order to obtain the solution of proposed FOCP. In addition, some numerical simulations were performed to show the effect of the proposed optimal control (OC) besides the impact of fish consumption on the mortality of CHD.

scholarly journals Transmission Dynamics of Hepatitis C with Control Strategies

2014 ◽  
Vol 2014 ◽  
pp. 1-18 ◽  
Author(s):  
Adnan Khan ◽  
Sultan Sial ◽  
Mudassar Imran
Keyword(s):  
Optimal Control ◽  
Hepatitis C ◽  
Deterministic Model ◽  
Control Strategies ◽  
Endemic Equilibrium ◽  
Transmission Dynamics ◽  
Critical Parameters ◽  
Optimal Controls ◽  
Infected Population ◽  
The Impact

We present a rigorous mathematical analysis of a deterministic model, for the transmission dynamics of hepatitis C, using a standard incidence function. The infected population is divided into three distinct compartments featuring two distinct infection stages (acute and chronic) along with an isolation compartment. It is shown that for basic reproduction number R0≤1, the disease-free equilibrium is locally and globally asymptotically stable. The model also has an endemic equilibrium for R0>1. Uncertainty and sensitivity analyses are carried out to identify and study the impact of critical parameters on R0. In addition, we have presented the numerical simulations to investigate the influence of different important parameters on R0. Since we have a locally stable endemic equilibrium, optimal control is applied to the deterministic model to reduce the total infected population. Two different optimal control strategies (vaccination and isolation) are designed to control the disease and reduce the infected population. Pontryagin’s Maximum Principle is used to characterize the optimal controls in terms of an optimality system which is solved numerically. Numerical results for the optimal controls are compared against the constant controls and their effectiveness is discussed.

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