Deterministic Epidemic Models For Ebola Infection With Time-dependent Controls

Okyere, Eric; Ankamah, Johnson De-Graft; Hunkpe, Anthony Kodzo; Mensah, D.

doi:10.48550/arxiv.1908.07974

Cited by 2 publications

(3 citation statements)

References 31 publications

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“…In this section, we present the numerical solutions for our optimality problem using the fourth-order runge-kutta forward-backward sweep method. This numerical scheme is very efficient and has been widely used by several authors in simulating their optimal control problems [1,8,[15][16][17]. The details of this scheme can be found in the monograph [10].…”

Section: Numerical Results Of the Optimal Control Model And Discussionmentioning

confidence: 99%

“…A detailed comprehensive literature of optimal control models in epidemiological modeling and numerical approximation techniques can be found in [10,24]. Several works in literature reveals that epidemic models that are constructed with optimal control problems are appropriate and very useful for suggesting control strategies to curb disease spread, see, e.g., [1,13,17,18].…”

Section: Introductionmentioning

confidence: 99%

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Controlling the Transmission Dynamics of COVID-19

Moore¹,

Okyere²

2020

Preprint

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The outbreak of COVID-19 caused by SARS-CoV-2 in Wuhan and other cities in China in 2019 has become a global pandemic as declared by World Health Organization (WHO) in the first quarter of 2020 [19]. The delay in diagnosis, limited hospital resources and other treatment resources leads to rapid spread of COVID-19. In this article, we consider an optimal control COVID-19 transmission model and assess the impact of some control measures that can lead to the reduction of exposed and infectious individuals in the population. We investigate three control strategies for this deadly infectious disease using personal protection, treatment with early diagnosis, treatment with delay diagnosis and spraying of virus in the environment as time-dependent control functions in our dynamical model to curb the disease spread.

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Section: Numerical Results Of the Optimal Control Model And Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Controlling the Transmission Dynamics of COVID-19

Moore¹,

Okyere²

2020

Preprint

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show abstract

“…They developed a fourth-order Runge-Kutta method and a nonstandard finite difference scheme for the proposed model and demonstrated that the RK-4 method failed at certain step sizes, while the NSFD scheme conserved all the dynamical properties of the model at large step sizes. Okyere et al examined the optimal control analysis of epidemiological models such as SIR and SEIR using vaccination, treatment, and educational campaigns as time-dependent control functions [29]. They used the forward-backward sweep method with the RK-4 method to explain the optimal system for different control strategies.…”

Section: Introductionmentioning

confidence: 99%

Analysis of a Modified System of Infectious Disease in a Closed and Convex Subset of a Function Space with Numerical Study

Shaikh

Akgül

Rehman

et al. 2023

Axioms

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In this article, the transmission dynamical model of the deadly infectious disease named Ebola is investigated. This disease originated in the Democratic Republic of Congo (DRC) and Sudan (now South Sudan) and was identified in 1976. The novelty of the model under discussion is the inclusion of advection and diffusion in each compartmental equation. The addition of these two terms makes the model more general. Similar to a simple population dynamic system, the prescribed model also has two equilibrium points and an important threshold, known as the basic reproductive number. The current work comprises the existence and uniqueness of the solution, the numerical analysis of the model, and finally, the graphical simulations. In the section on the existence and uniqueness of the solutions, the optimal existence is assessed in a closed and convex subset of function space. For the numerical study, a nonstandard finite difference (NSFD) scheme is adopted to approximate the solution of the continuous mathematical model. The main reason for the adoption of this technique is delineated in the form of the positivity of the state variables, which is necessary for any population model. The positivity of the applied scheme is verified by the concept of M-matrices. Since the numerical method gives a discrete system of difference equations corresponding to a continuous system, some other relevant properties are also needed to describe it. In this respect, the consistency and stability of the designed technique are corroborated by using Taylor's series expansion and Von Neumann's stability criteria, respectively. To authenticate the proposed NSFD method, two other illustrious techniques are applied for the sake of comparison. In the end, numerical simulations are also performed that show the efficiency of the prescribed technique, while the existing techniques fail to do so.

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Deterministic Epidemic Models For Ebola Infection With Time-dependent Controls

Cited by 2 publications

References 31 publications

Controlling the Transmission Dynamics of COVID-19

Controlling the Transmission Dynamics of COVID-19

Analysis of a Modified System of Infectious Disease in a Closed and Convex Subset of a Function Space with Numerical Study

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