A New Simple Epidemic Discrete-Time Model Describing the Dissemination of Information with Optimal Control Strategy

Boutayeb, Hamza; Bidah, Sara; Zakary, Omar; Rachik, Mostafa

doi:10.1155/2020/7465761

Cited by 12 publications

(4 citation statements)

References 18 publications

(25 reference statements)

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“…Pontryagin's maximum principle [23][24][25][26][27], we derive necessary conditions for our optimal control problem. For this purpose, we define the Hamiltonian as:…”

Section: Necessary Conditions By Using a Discrete Version Ofmentioning

confidence: 99%

Mathematical Model to Estimate and Predict the COVID-19 Infections in Morocco: Optimal Control Strategy

Zakary

Bidah

Rachik

et al. 2020

Journal of Applied Mathematics

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In this paper, we aim to estimate and predict the situation of the new coronavirus pandemic (COVID-19) in countries under quarantine measures. First, we present a new discrete-time mathematical model describing the evolution of the COVID-19 in a population under quarantine. We are motivated by the growing numbers of infections and deaths in countries under quarantine to investigate potential causes. We consider two new classes of people, those who respect the quarantine and stay at home, and those who do not respect the quarantine and leave their homes for one or another reason. Second, we use real published data to estimate the parameters of the model, and then, we estimate these populations in Morocco. We investigate the impact of people who underestimate the quarantine by considering an optimal control strategy to reduce this category and then reducing the number of the population at risk in Morocco. We provide several simulations to support our findings.

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“…Pontryagin's maximum principle [23][24][25][26][27], we derive necessary conditions for our optimal control problem. For this purpose, we define the Hamiltonian as:…”

Section: Necessary Conditions By Using a Discrete Version Ofmentioning

confidence: 99%

Mathematical Model to Estimate and Predict the COVID-19 Infections in Morocco: Optimal Control Strategy

Zakary

Bidah

Rachik

et al. 2020

Journal of Applied Mathematics

Self Cite

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“…Several epidemic models exist, from basic to developed ones with application to Ebola, Influenza (Amiri Mehra et al 2019 ), HIV, and other epidemic diseases. These epidemic models can be stochastic, deterministic, discrete (Boutayeb et al 2020 ), or continuous (Amiri Mehra et al 2019 ), used for the COVID-19 pandemic by changing the parameters and adding or subtracting some states. There are also several epidemiological models (e.g., within-host type (Abbasi et al 2022 ), SIR (Cooper et al 2020 ), SEIAR (Chen et al 2020 ), SQAIR (Amiri Mehra et al 2020 ), SQEIAR (Abbasi et al 2020 ), SIQHRE (Badfar et al 2022 ), SEIAQRDT (Kumari et al 2020 ), and SIDARTHE (Giordano et al 2020 )) being used to control and predict the evolution of COVID-19 in different countries across the world.…”

Section: Introductionmentioning

confidence: 99%

Vaccination and isolation based control design of the COVID-19 pandemic based on adaptive neuro fuzzy inference system optimized with the genetic algorithm

et al. 2022

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The study of the COVID-19 pandemic is of pivotal importance due to its tremendous global impacts. This paper aims to control this disease using an optimal strategy comprising two methods: isolation and vaccination. In this regard, an optimized Adaptive Neuro-Fuzzy Inference System (ANFIS) is developed using the Genetic Algorithm (GA) to control the dynamic model of the COVID-19 termed SIDARTHE (Susceptible, Infected, Diagnosed, Ailing, Recognized, Threatened, Healed, and Extinct). The number of diagnosed and recognized people is reduced by isolation, and the number of susceptible people is reduced by vaccination. The GA generates optimal control efforts related to the random initial number of each chosen group as the input data for ANFIS to train Takagi–Sugeno (T–S) fuzzy structure coefficients. Also, three theorems are presented to indicate the positivity, boundedness, and existence of the solutions in the presence of the controller. The performance of the proposed system is evaluated through the mean squared error (MSE) and the root-mean-square error (RMSE). The simulation results show a significant decrease in the number of diagnosed, recognized, and susceptible individuals by employing the proposed controller, even with a 70% increase in transmissibility caused by various variants.

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“…Also, in [23], a new epidemic model (called SIDARTHE) is studied that considers the distinction between diagnosed and nondiagnosed infected individuals with and without symptoms detected acutely symptomatic infected ones. Besides, the discrete-time SEIR epidemic models can be used in such studies instead of continuous ones [25,26], to name a few. To further study about optimal control with time delay, readers refer to [27][28][29][30][31] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Optimal Allocation of Vaccine and Antiviral Drugs for Influenza Containment over Delayed Multiscale Epidemic Model considering Time-Dependent Transmission Rate

Abbasi

Zamani

Mehra

et al. 2021

Computational and Mathematical Methods in Medicine

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In this study, two types of epidemiological models called “within host” and “between hosts” have been studied. The within-host model represents the innate immune response, and the between-hosts model signifies the SEIR (susceptible, exposed, infected, and recovered) epidemic model. The major contribution of this paper is to break the chain of infectious disease transmission by reducing the number of susceptible and infected people via transferring them to the recovered people group with vaccination and antiviral treatment, respectively. Both transfers are considered with time delay. In the first step, optimal control theory is applied to calculate the optimal final time to control the disease within a host’s body with a cost function. To this end, the vaccination that represents the effort that converts healthy cells into resistant-to-infection cells in the susceptible individual’s body is used as the first control input to vaccinate the susceptible individual against the disease. Moreover, the next control input (antiviral treatment) is applied to eradicate the concentrations of the virus and convert healthy cells into resistant-to-infection cells simultaneously in the infected person’s body to treat the infected individual. The calculated optimal time in the first step is considered as the delay of vaccination and antiviral treatment in the SEIR dynamic model. Using Pontryagin’s maximum principle in the second step, an optimal control strategy is also applied to an SEIR mathematical model with a nonlinear transmission rate and time delay, which is computed as optimal time in the first step. Numerical results are consistent with the analytical ones and corroborate our theoretical results.

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A New Simple Epidemic Discrete-Time Model Describing the Dissemination of Information with Optimal Control Strategy

Cited by 12 publications

References 18 publications

Mathematical Model to Estimate and Predict the COVID-19 Infections in Morocco: Optimal Control Strategy

Mathematical Model to Estimate and Predict the COVID-19 Infections in Morocco: Optimal Control Strategy

Vaccination and isolation based control design of the COVID-19 pandemic based on adaptive neuro fuzzy inference system optimized with the genetic algorithm

Optimal Allocation of Vaccine and Antiviral Drugs for Influenza Containment over Delayed Multiscale Epidemic Model considering Time-Dependent Transmission Rate

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