Modeling the spatiotemporal transmission of Ebola disease and optimal control: a regional approach

Laaroussi, Adil El Alami; Ghazzali, Rachid; Rachik, Mostafa; Benrhila, Soukaina

doi:10.1007/s40435-019-00525-w

Cited by 15 publications

(4 citation statements)

References 31 publications

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“…Our aim is to study the effect of non-local memory and vaccination strategies on the cost, needed to control the spread of infectious diseases. Our results generalize to the ABC fractional setting previous studies of classical control theory presented in [17]. The considered model there does not explain the influence of a complete memory of the system.…”

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confidence: 85%

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Necessary optimality conditions of a reaction-diffusion SIR model with ABC fractional derivatives

Ammi¹,

Tahiri²,

Torres³

2022

DCDS-S

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<p style='text-indent:20px;'>The main aim of the present work is to study and analyze a reaction-diffusion fractional version of the SIR epidemic mathematical model by means of the non-local and non-singular ABC fractional derivative operator with complete memory effects. Existence and uniqueness of solution for the proposed fractional model is proved. Existence of an optimal control is also established. Then, necessary optimality conditions are derived. As a consequence, a characterization of the optimal control is given. Lastly, numerical results are given with the aim to show the effectiveness of the proposed control strategy, which provides significant results using the AB fractional derivative operator in the Caputo sense, comparing it with the classical integer one. The results show the importance of choosing very well the fractional characterization of the order of the operators.</p>

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confidence: 85%

“…The proof of Theorem 6.1 is classical and follows exactly the same arguments as in [17], using the fact that the minimum of the objective function J is achieved at u * . For small ε such that u ε = u * + εh ∈ U ad , one can prove that…”

mentioning

confidence: 99%

Necessary optimality conditions of a reaction-diffusion SIR model with ABC fractional derivatives

Ammi¹,

Tahiri²,

Torres³

2022

DCDS-S

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“…It is well known that reaction-diffusion equations are commonly used to model a variety of physical and biological phenomena [2,4,6,16,19,21]. Such equations describe how the concentration or density distributed in space varies under the influence of two processes: (i) local interactions of species and (ii) diffusion, which causes the spread of species in space.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Analysis, Forecasting and Optimal Control of HIV/AIDS Spatiotemporal Transmission with a Reaction Diffusion SICA Model

Zine,

Adraoui,

Torres

2022

Preprint

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We propose a mathematical spatiotemporal epidemic SICA model with a control strategy. The spatial behavior is modeled by adding a diffusion term with the Laplace operator, which is justified and interpreted both mathematically and physically. By applying semigroup theory on the ordinary differential equations, we prove existence and uniqueness of the global positive spatiotemporal solution for our proposed system and some of its important characteristics. Some illustrative numerical simulations are carried out that motivate us to consider optimal control theory. A suitable optimal control problem is then posed and investigated. Using an effective method based on some properties within the weak topology, we prove existence of an optimal control and develop an appropriate set of necessary optimality conditions to find the optimal control pair that minimizes the density of infected individuals and the cost of the treatment program.

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“…The threat of COVID-19 on countries that started to count cases prompted us to develop a model to describe the evolution of the epidemic and its effects on the health care system. Mathematical models are a powerful tool that proved important in previous epidemiological disasters such as the Ebola virus [10,11], smallpox [12], or influenza [13], contributing to the understanding of the dynamics of disease and providing useful predictions about the potential transmission of a disease and the effectiveness of possible control measures, which can provide valuable information for public health policy makers [14]. SIR-type models, also known as Kermack-McKendrick model [15], consists of a set of differential equations and has been applied to a variety of infectious diseases.…”

Section: Introductionmentioning

confidence: 99%

COVID-19 pandemics modeling with SEIR(+CAQH), social distancing, and age stratification. The effect of vertical confinement and release in Brazil

Lyra

Nascimento

Belkhiria

et al. 2020

Preprint

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The ongoing COVID-19 epidemics poses a particular challenge to low and middle income countries, making some of them consider the strategy of "vertical confinement". In this strategy, contact is reduced only to specific groups (like age groups) that are at increased risk of severe disease following SARS-CoV-2 infection. We aim to assess the feasibility of this scenario as an exit strategy for the current lockdown in terms of its ability to keep the number of cases under the health care system capacity. We developed a modified SEIR model, including confinement, asymptomatic transmission, quarantine and hospitalization. The population is subdivided into 9 age groups, resulting in a system of 72 coupled nonlinear differential equations. The rate of transmission is dynamic and derived from the observed delayed fatality rate; the parameters of the epidemics are derived with a Markov chain Monte Carlo algorithm. We used Brazil as an example of middle income country, but the results are easily generalizable to other countries considering a similar strategy. We find that starting from 60% horizontal confinement, an exit strategy on May 1st of confinement of individuals older than 60 years old and full release of the younger population results in 400 000 hospitalizations, 50 000 ICU cases, and 120 000 deaths in the 50-60 years old age group alone. The health care system avoids collapse if the 50-60 years old are also confined, but our model assumes an idealized lockdown where the confined are perfectly insulated from contamination, so our numbers are a conservative lower bound. Our results discourage confinement by age as an exit strategy.April 15, 2020

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Modeling the spatiotemporal transmission of Ebola disease and optimal control: a regional approach

Cited by 15 publications

References 31 publications

Necessary optimality conditions of a reaction-diffusion SIR model with ABC fractional derivatives

Necessary optimality conditions of a reaction-diffusion SIR model with ABC fractional derivatives

Mathematical Analysis, Forecasting and Optimal Control of HIV/AIDS Spatiotemporal Transmission with a Reaction Diffusion SICA Model

COVID-19 pandemics modeling with SEIR(+CAQH), social distancing, and age stratification. The effect of vertical confinement and release in Brazil

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