An SIQ delay differential equations model for disease control via isolation

Ruschel, Stefan; Pereira, Tiago; Yanchuk, Serhiy; Young, Lai Sang

doi:10.1007/s00285-019-01356-1

Cited by 32 publications

(23 citation statements)

References 26 publications

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“…(3) and (4). The derivation of system (1)-(5) is analogous to that in [22] where we provided a detailed derivation for a simpler model. The results below pertain to the continuum limit system (1)-(5).…”

Section: Siq: An Epidemic Model With (Partial) Isolationmentioning

confidence: 99%

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Consequences of delays and imperfect implementation of isolation in epidemic control

Young

Ruschel

Yanchuk

et al. 2019

Sci Rep

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For centuries isolation has been the main control strategy of unforeseen epidemic outbreaks. When implemented in full and without delay, isolation is very effective. However, flawless implementation is seldom feasible in practice. We present an epidemic model called SIQ with an isolation protocol, focusing on the consequences of delays and incomplete identification of infected hosts. The continuum limit of this model is a system of Delay Differential Equations, the analysis of which reveals clearly the dependence of epidemic evolution on model parameters including disease reproductive number, isolation probability, speed of identification of infected hosts and recovery rates. Our model offers estimates on minimum response capabilities needed to curb outbreaks, and predictions of endemic states when containment fails. Critical response capability is expressed explicitly in terms of parameters that are easy to obtain, to assist in the evaluation of funding priorities involving preparedness and epidemics management.

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Section: Siq: An Epidemic Model With (Partial) Isolationmentioning

confidence: 99%

“…A detailed analysis will be published elsewhere. The formal limiting case α → ∞ (immediate waning of immunity) has been studied in detail [22].…”

Section: Endemic Statesmentioning

confidence: 99%

Consequences of delays and imperfect implementation of isolation in epidemic control

Young

Ruschel

Yanchuk

et al. 2019

Sci Rep

Self Cite

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“…Moreover, the definition of the so-called basic reproduction number R 0 (a parameter determining whether a infectious disease can spread or not) comes out naturally in our delay model. Actually delay models in epidemiology have been already implemented in many cases [5][6][7][8][9][10] . We consider the case where the infection period is constant and provide for the first time an analytical result for the spreading of the disease in the early stage of the infection.…”

Section: Solvable Delay Model For Epidemic Spreading: the Case Of Covmentioning

confidence: 99%

Solvable delay model for epidemic spreading: the case of Covid-19 in Italy

Dell’Anna

2020

Sci Rep

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We study a simple realistic model for describing the diffusion of an infectious disease on a population of individuals. The dynamics is governed by a single functional delay differential equation, which, in the case of a large population, can be solved exactly, even in the presence of a time-dependent infection rate. This delay model has a higher degree of accuracy than that of the so-called SIR model, commonly used in epidemiology, which, instead, is formulated in terms of ordinary differential equations. We apply this model to describe the outbreak of the new infectious disease, Covid-19, in Italy, taking into account the containment measures implemented by the government in order to mitigate the spreading of the virus and the social costs for the population.

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“…Put k ′ = handh → 0, where the expression given above takes the form as (4). The proposed technique for a susceptible compartment is , S n i+1 , and S n i−1 into the above and simplifying them, we get…”

Section: Consistency Analysismentioning

confidence: 99%

“…Models used widely to study the infectious dynamics contain non-linear differential equations without delay, but these models can be made more appropriate and comprehensive to study the viral infection in a better and more concise way. Delay mathematical models have been studied extensively by many researchers [3][4][5][6][7]. Recently, the role of delay factor has been investigated for the biological systems as many biological systems observe the time delay property [8].…”

Section: Introductionmentioning

confidence: 99%

Positivity Preserving Technique for the Solution of HIV/AIDS Reaction Diffusion Model With Time Delay

et al. 2020

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This study is concerned with finding a numerical solution to the delay epidemic model with diffusion. This is not a simple task as variables involved in the model exhibit some important physical features. We have therefore designed an efficient numerical scheme that preserves the properties acquired by the given system. We also further develop Euler's technique for a delayed epidemic reaction-diffusion model. The proposed numerical technique is also compared with the forward Euler technique, and we observe that the forward Euler technique demonstrates the false behavior at certain step sizes. On the other hand, the proposed technique preserves the true behavior of the continuous system at all step sizes. Furthermore, the effect of the delay factor is discussed graphically by using the proposed technique.

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An SIQ delay differential equations model for disease control via isolation

Cited by 32 publications

References 26 publications

Consequences of delays and imperfect implementation of isolation in epidemic control

Consequences of delays and imperfect implementation of isolation in epidemic control

Solvable delay model for epidemic spreading: the case of Covid-19 in Italy

Positivity Preserving Technique for the Solution of HIV/AIDS Reaction Diffusion Model With Time Delay

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