Travelling Wave Analysis of a Diffusive COVID-19 Model

Wachira, Charle; Lawi, G. O.; Omondi, L. O.

doi:10.1155/2022/6052274

Cited by 2 publications

(2 citation statements)

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“…In this direction of epidemiological applications, in [16], the authors analyzed the role of population mobility in the transmission of coronavirus disease 2019 (COVID-19) using a nonlinear parabolic system. The authors presented alternatives to control the transmission of the virus by applying restrictions such as the closure of borders, reduction of travel, and interruption of human mobility.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we present a SAIR-type epidemiological model based on a system of partial differential equations, incorporating a discrete-time delay to mimic the virus's incubation period within a host and the time it takes for a person to become infected [10,[18][19][20][21]. The spatial effect is justified due to people's mobility and the spread of the virus [6,16,22,23]. Thus, the main contributions of this paper are the introduction of spatial effects in conjunction with the time delay due to the latent stage of individuals.…”

Section: Introductionmentioning

confidence: 99%

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Existence of Traveling Waves of a Diffusive Susceptible–Infected–Symptomatic–Recovered Epidemic Model with Temporal Delay

Miranda,

Arenas,

González-Parra

et al. 2024

Mathematics

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The aim of this article is to investigate the existence of traveling waves of a diffusive model that represents the transmission of a virus in a determined population composed of the following populations: susceptible (S), infected (I), asymptomatic (A), and recovered (R). An analytical study is performed, where the existence of solutions of traveling waves in a bounded domain is demonstrated. We use the upper and lower coupled solutions method to achieve this aim. The existence and local asymptotic stability of the endemic (Ee) and disease-free (E0) equilibrium states are also determined. The constructed model includes a discrete-time delay that is related to the incubation stage of a virus. We find the crucial basic reproduction number R0, which determines the local stability of the steady states. We perform numerical simulations of the model in order to provide additional support to the theoretical results and observe the traveling waves. The model can be used to study the dynamics of SARS-CoV-2 and other viruses where the disease evolution has a similar behavior.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Existence of Traveling Waves of a Diffusive Susceptible–Infected–Symptomatic–Recovered Epidemic Model with Temporal Delay

Miranda,

Arenas,

González-Parra

et al. 2024

Mathematics

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A deterministic transmission model for analytics-driven optimization of COVID-19 post-pandemic vaccination and quarantine strategies

Mahadhika,

Aldila

2024

MBE

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<abstract><p>This study developed a deterministic transmission model for the coronavirus disease of 2019 (COVID-19), considering various factors such as vaccination, awareness, quarantine, and treatment resource limitations for infected individuals in quarantine facilities. The proposed model comprised five compartments: susceptible, vaccinated, quarantined, infected, and recovery. It also considered awareness and limited resources by using a saturated function. Dynamic analyses, including equilibrium points, control reproduction numbers, and bifurcation analyses, were conducted in this research, employing analytics to derive insights. Our results indicated the possibility of an endemic equilibrium even if the reproduction number for control was less than one. Using incidence data from West Java, Indonesia, we estimated our model parameter values to calibrate them with the real situation in the field. Elasticity analysis highlighted the crucial role of contact restrictions in reducing the spread of COVID-19, especially when combined with community awareness. This emphasized the analytics-driven nature of our approach. We transformed our model into an optimal control framework due to budget constraints. Leveraging Pontriagin's maximum principle, we meticulously formulated and solved our optimal control problem using the forward-backward sweep method. Our experiments underscored the pivotal role of vaccination in infection containment. Vaccination effectively reduces the risk of infection among vaccinated individuals, leading to a lower overall infection rate. However, combining vaccination and quarantine measures yields even more promising results than vaccination alone. A second crucial finding emphasized the need for early intervention during outbreaks rather than delayed responses. Early interventions significantly reduce the number of preventable infections, underscoring their importance.</p></abstract>

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Travelling Wave Analysis of a Diffusive COVID-19 Model

Cited by 2 publications

References 18 publications

Existence of Traveling Waves of a Diffusive Susceptible–Infected–Symptomatic–Recovered Epidemic Model with Temporal Delay

Existence of Traveling Waves of a Diffusive Susceptible–Infected–Symptomatic–Recovered Epidemic Model with Temporal Delay

A deterministic transmission model for analytics-driven optimization of COVID-19 post-pandemic vaccination and quarantine strategies

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