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Article ; Online: Renewal equations for delayed population behaviour adaptation coupled with disease transmission dynamics: A mechanism for multiple waves of emerging infections.

Zhang, Xue / Scarabel, Francesca / Murty, Kumar / Wu, Jianhong

2023 Volume 365, Page(s) 109068

Abstract: There are many plausible reasons for recurrent outbreaks of emerging infectious diseases. In this paper, we develop a mathematical model to illustrate how population behavioural adaption and adaptation implementation delay, in response to the perceived ... ...

Abstract	There are many plausible reasons for recurrent outbreaks of emerging infectious diseases. In this paper, we develop a mathematical model to illustrate how population behavioural adaption and adaptation implementation delay, in response to the perceived infection risk, can lead to recurrent outbreak patterns. We consider the early phase of an infection outbreak when herd immunity is not reached, pathogen mutation is not considered, and seasonality is ruled out as a major contributor. We derive a transmission dynamics model coupled with the renewal equation for the disease transmission effective contacts (contact rate per unit time multiplied by the transmission probability per contact). The model incorporates two critical parameters: the population behavioural adaptation flexibility index and the behavioural change implementation delay. We show that when the behavioural change implementation delay reaches a critical value, the number of infections starts to oscillate in an equilibrium that is determined by the population behavioural adaptation flexibility. We also show that the numbers of infections at the subsequent peaks can exceed that of the first peak. This was an oblique observation globally during the early phase of the COVID-19 pandemic before variants of concern emerged, and it was an observed phenomena with the Omicron variant induced wave in areas where early interventions were successful in preventing the large outbreaks. Our model and analyses can provide partially explanation for these observations.
Language	English
Publishing date	2023-09-15
Publishing country	United States
Document type	Journal Article
ZDB-ID	1126-5
ISSN	1879-3134 ; 0025-5564
ISSN (online)	1879-3134
ISSN	0025-5564
DOI	10.1016/j.mbs.2023.109068
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Book ; Online: Approximating reproduction numbers

De Reggi, Simone / Scarabel, Francesca / Vermiglio, Rossana

a general numerical approach for age-structured models

2023

Abstract: Reproduction numbers play a fundamental role in population dynamics. For age-structured models, these quantities are typically defined as spectral radius of operators acting on infinite dimensional spaces. As a result, their analytical computation is ... ...

Abstract	Reproduction numbers play a fundamental role in population dynamics. For age-structured models, these quantities are typically defined as spectral radius of operators acting on infinite dimensional spaces. As a result, their analytical computation is hardly achievable without additional assumptions on the model coefficients (e.g., separability of age-specific transmission rates) and numerical approximations are needed. In this paper we introduce a general numerical approach, based on pseudospectral collocation of the relevant operators, for approximating the reproduction numbers of a class of age-structured models with finite life span. To our knowledge, this is the first numerical method that allows complete flexibility in the choice of the ``birth'' and ``transition'' processes, which is made possible by working with an equivalent problem for the integrated state. We discuss applications to epidemic models with continuous rates, as well as models with piecewise continuous rates estimated from real data, illustrating how the method can compute different reproduction numbers-including the basic and the type reproduction number as special cases-by considering different interpretations of the age variable (e.g., chronological age, infection age, disease age) and the transmission terms (e.g., horizontal and vertical transmission). Comment: 36 pages, 12 figures
Keywords	Quantitative Biology - Populations and Evolution ; Mathematics - Dynamical Systems ; Mathematics - Numerical Analysis ; 34L16 ; 37N25 ; 65L15 ; 65L60 ; 65P99 ; 92D25 ; 92D30
Subject code	518
Publishing date	2023-12-20
Publishing country	us
Document type	Book ; Online
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Article ; Online: A pseudospectral method for investigating the stability of linear population models with two physiological structures.

Andò, Alessia / Reggi, Simone De / Liessi, Davide / Scarabel, Francesca

Mathematical biosciences and engineering : MBE

2022 Volume 20, Issue 3, Page(s) 4493–4515

Abstract: The asymptotic stability of the null equilibrium of a linear population model with two physiological structures formulated as a first-order hyperbolic PDE is determined by the spectrum of its infinitesimal generator. In this paper, we propose a general ... ...

Abstract	The asymptotic stability of the null equilibrium of a linear population model with two physiological structures formulated as a first-order hyperbolic PDE is determined by the spectrum of its infinitesimal generator. In this paper, we propose a general numerical method to approximate this spectrum. In particular, we first reformulate the problem in the space of absolutely continuous functions in the sense of Carathéodory, so that the domain of the corresponding infinitesimal generator is defined by trivial boundary conditions. Via bivariate collocation, we discretize the reformulated operator as a finite-dimensional matrix, which can be used to approximate the spectrum of the original infinitesimal generator. Finally, we provide test examples illustrating the converging behavior of the approximated eigenvalues and eigenfunctions, and its dependence on the regularity of the model coefficients.
Language	English
Publishing date	2022-12-26
Publishing country	United States
Document type	Journal Article
ZDB-ID	2265126-3
ISSN	1551-0018 ; 1551-0018
ISSN (online)	1551-0018
ISSN	1551-0018
DOI	10.3934/mbe.2023208
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Article: Non-pharmaceutical intervention levels to reduce the COVID-19 attack ratio among children.

David, Jummy / Bragazzi, Nicola Luigi / Scarabel, Francesca / McCarthy, Zachary / Wu, Jianhong

Royal Society open science

2022 Volume 9, Issue 3, Page(s) 211863

Abstract: The attack ratio in a subpopulation is defined as the total number of infections over the total number of individuals in this subpopulation. Using a methodology based on an age-stratified transmission dynamics model, we estimated the attack ratio of ... ...

Abstract	The attack ratio in a subpopulation is defined as the total number of infections over the total number of individuals in this subpopulation. Using a methodology based on an age-stratified transmission dynamics model, we estimated the attack ratio of COVID-19 among children (individuals 0-11 years) when a large proportion of individuals eligible for vaccination (age 12 and above) are vaccinated to contain the epidemic among this subpopulation, or the
Language	English
Publishing date	2022-03-16
Publishing country	England
Document type	Journal Article
ZDB-ID	2787755-3
ISSN	2054-5703
ISSN	2054-5703
DOI	10.1098/rsos.211863
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Article: A renewal equation model to assess roles and limitations of contact tracing for disease outbreak control.

Scarabel, Francesca / Pellis, Lorenzo / Ogden, Nicholas H / Wu, Jianhong

Royal Society open science

2021 Volume 8, Issue 4, Page(s) 202091

Abstract: We propose a deterministic model capturing essential features of contact tracing as part of public health non-pharmaceutical interventions to mitigate an outbreak of an infectious disease. By incorporating a mechanistic formulation of the processes at ... ...

Abstract	We propose a deterministic model capturing essential features of contact tracing as part of public health non-pharmaceutical interventions to mitigate an outbreak of an infectious disease. By incorporating a mechanistic formulation of the processes at the individual level, we obtain an integral equation (delayed in calendar time and advanced in time since infection) for the probability that an infected individual is detected and isolated at any point in time. This is then coupled with a renewal equation for the total incidence to form a closed system describing the transmission dynamics involving contact tracing. We define and calculate basic and effective reproduction numbers in terms of pathogen characteristics and contact tracing implementation constraints. When applied to the case of SARS-CoV-2, our results show that only combinations of diagnosis of symptomatic infections and contact tracing that are almost perfect in terms of speed and coverage can attain control, unless additional measures to reduce overall community transmission are in place. Under constraints on the testing or tracing capacity, a temporary interruption of contact tracing may, depending on the overall growth rate and prevalence of the infection, lead to an irreversible loss of control even when the epidemic was previously contained.
Language	English
Publishing date	2021-04-07
Publishing country	England
Document type	Journal Article
ZDB-ID	2787755-3
ISSN	2054-5703
ISSN	2054-5703
DOI	10.1098/rsos.202091
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Article ; Online: Stability analysis of a state-dependent delay differential equation for cell maturation: analytical and numerical methods.

Getto, Philipp / Gyllenberg, Mats / Nakata, Yukihiko / Scarabel, Francesca

Journal of mathematical biology

2019 Volume 79, Issue 1, Page(s) 281–328

Abstract: We consider a mathematical model describing the maturation process of stem cells up to fully mature cells. The model is formulated as a differential equation with state-dependent delay, where maturity is described as a continuous variable. The maturation ...

Abstract	We consider a mathematical model describing the maturation process of stem cells up to fully mature cells. The model is formulated as a differential equation with state-dependent delay, where maturity is described as a continuous variable. The maturation rate of cells may be regulated by the amount of mature cells and, moreover, it may depend on cell maturity: we investigate how the stability of equilibria is affected by the choice of the maturation rate. We show that the principle of linearised stability holds for this model, and develop some analytical methods for the investigation of characteristic equations for fixed delays. For a general maturation rate we resort to numerical methods and we extend the pseudospectral discretisation technique to approximate the state-dependent delay equation with a system of ordinary differential equations. This is the first application of the technique to nonlinear state-dependent delay equations, and currently the only method available for studying the stability of equilibria by means of established software packages for bifurcation analysis. The numerical method is validated on some cases when the maturation rate is independent of maturity and the model can be reformulated as a fixed-delay equation via a suitable time transformation. We exploit the analytical and numerical methods to investigate the stability boundary in parameter planes. Our study shows some drastic qualitative changes in the stability boundary under assumptions on the model parameters, which may have important biological implications.
MeSH term(s)	Animals ; Cell Differentiation ; Cell Self Renewal ; Computer Simulation ; Models, Biological ; Stem Cells/physiology ; Time Factors
Language	English
Publishing date	2019-04-19
Publishing country	Germany
Document type	Journal Article ; Research Support, Non-U.S. Gov't
ZDB-ID	187101-8
ISSN	1432-1416 ; 0303-6812
ISSN (online)	1432-1416
ISSN	0303-6812
DOI	10.1007/s00285-019-01357-0
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Article ; Online: Canada needs to rapidly escalate public health interventions for its COVID-19 mitigation strategies.

Scarabel, Francesca / Pellis, Lorenzo / Bragazzi, Nicola Luigi / Wu, Jianhong

Infectious Disease Modelling

2020 Volume 5, Page(s) 316–322

Abstract: Background: After the declaration of COVID-19 pandemic on March 11th: Methods: We conduct data-driven and model-free estimations for the growth rates of the COVID-19 epidemics in Italy and Canada, by fitting an exponential curve to the daily reported ...

Abstract	Background: After the declaration of COVID-19 pandemic on March 11th Methods: We conduct data-driven and model-free estimations for the growth rates of the COVID-19 epidemics in Italy and Canada, by fitting an exponential curve to the daily reported cases. We use these estimates to predict epidemic trends in Canada under different scenarios of public health interventions. Results: In Italy, the initial growth rate (0.22) has reduced to 0.1 two weeks after the lockdown of the country on March 8th Interpretation: Prompt and farsighted interventions are critical to counteract the very rapid initial growth of the COVID-19 epidemic in Canada. Mitigation plans must take into account the delayed effect of interventions by up to 2-weeks and the short doubling time of 3-4 days.
Keywords	covid19
Language	English
Publishing date	2020-03-31
Publishing country	China
Document type	Journal Article
ZDB-ID	3015225-2
ISSN	2468-0427 ; 2468-2152
ISSN (online)	2468-0427
ISSN	2468-2152
DOI	10.1016/j.idm.2020.03.004
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Article ; Online: A renewal equation model to assess roles and limitations of contact tracing for disease outbreak control

Francesca Scarabel / Lorenzo Pellis / Nicholas H. Ogden / Jianhong Wu

Royal Society Open Science, Vol 8, Iss

2021 Volume 4

Abstract	We propose a deterministic model capturing essential features of contact tracing as part of public health non-pharmaceutical interventions to mitigate an outbreak of an infectious disease. By incorporating a mechanistic formulation of the processes at the individual level, we obtain an integral equation (delayed in calendar time and advanced in time since infection) for the probability that an infected individual is detected and isolated at any point in time. This is then coupled with a renewal equation for the total incidence to form a closed system describing the transmission dynamics involving contact tracing. We define and calculate basic and effective reproduction numbers in terms of pathogen characteristics and contact tracing implementation constraints. When applied to the case of SARS-CoV-2, our results show that only combinations of diagnosis of symptomatic infections and contact tracing that are almost perfect in terms of speed and coverage can attain control, unless additional measures to reduce overall community transmission are in place. Under constraints on the testing or tracing capacity, a temporary interruption of contact tracing may, depending on the overall growth rate and prevalence of the infection, lead to an irreversible loss of control even when the epidemic was previously contained.
Keywords	contact tracing ; COVID-19 ; non-pharmaceutical interventions ; renewal equation ; time since infection ; resource constraints ; Science ; Q
Subject code	612
Language	English
Publishing date	2021-04-01T00:00:00Z
Publisher	The Royal Society
Document type	Article ; Online
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Article ; Online: Shut and re-open: the role of schools in the spread of COVID-19 in Europe.

Stage, Helena B / Shingleton, Joseph / Ghosh, Sanmitra / Scarabel, Francesca / Pellis, Lorenzo / Finnie, Thomas

Philosophical transactions of the Royal Society of London. Series B, Biological sciences

2021 Volume 376, Issue 1829, Page(s) 20200277

Abstract: We investigate the effect of school closure and subsequent reopening on the transmission of COVID-19, by considering Denmark, Norway, Sweden and German states as case studies. By comparing the growth rates in daily hospitalizations or confirmed cases ... ...

Abstract	We investigate the effect of school closure and subsequent reopening on the transmission of COVID-19, by considering Denmark, Norway, Sweden and German states as case studies. By comparing the growth rates in daily hospitalizations or confirmed cases under different interventions, we provide evidence that school closures contribute to a reduction in the growth rate approximately 7 days after implementation. Limited school attendance, such as older students sitting exams or the partial return of younger year groups, does not appear to significantly affect community transmission. In countries where community transmission is generally low, such as Denmark or Norway, a large-scale reopening of schools while controlling or suppressing the epidemic appears feasible. However, school reopening can contribute to statistically significant increases in the growth rate in countries like Germany, where community transmission is relatively high. In all regions, a combination of low classroom occupancy and robust test-and-trace measures were in place. Our findings underscore the need for a cautious evaluation of reopening strategies. This article is part of the theme issue 'Modelling that shaped the early COVID-19 pandemic response in the UK'.
MeSH term(s)	Adolescent ; COVID-19/epidemiology ; COVID-19/transmission ; COVID-19/virology ; Denmark/epidemiology ; Europe/epidemiology ; Germany/epidemiology ; Humans ; Norway/epidemiology ; Pandemics ; SARS-CoV-2/pathogenicity ; Schools/trends ; Sweden/epidemiology
Language	English
Publishing date	2021-05-31
Publishing country	England
Document type	Journal Article ; Research Support, Non-U.S. Gov't
ZDB-ID	208382-6
ISSN	1471-2970 ; 0080-4622 ; 0264-3839 ; 0962-8436
ISSN (online)	1471-2970
ISSN	0080-4622 ; 0264-3839 ; 0962-8436
DOI	10.1098/rstb.2020.0277
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Article: A window of opportunity for intensifying testing and tracing efforts to prevent new COVID-19 outbreaks due to more transmissible variants.

Wu, Jianhong / Scarabel, Francesca / McCarthy, Zachary / Xiao, Yanyu / Ogden, Nicholas H

Canada communicable disease report = Releve des maladies transmissibles au Canada

2021 Volume 47, Issue 7-8, Page(s) 329–338

Abstract: Background: When public health interventions are being loosened after several days of decline in the number of coronavirus disease 2019 (COVID-19) cases, it is of critical importance to identify potential strategies to ease restrictions while mitigating ...

Abstract	Background: When public health interventions are being loosened after several days of decline in the number of coronavirus disease 2019 (COVID-19) cases, it is of critical importance to identify potential strategies to ease restrictions while mitigating a new wave of more transmissible variants of concern (VOCs). We estimated the necessary enhancements to public health interventions for a partial reopening of the economy while avoiding the worst consequences of a new outbreak, associated with more transmissible VOCs. Methods: We used a transmission dynamics model to quantify conditions that combined public health interventions must meet to reopen the economy without a large outbreak. These conditions are those that maintain the control reproduction number below unity, while accounting for an increase in transmissibility due to VOC. Results: We identified combinations of the proportion of individuals exposed to the virus who are traced and quarantined before becoming infectious, the proportion of symptomatic individuals confirmed and isolated, and individual daily contact rates needed to ensure the control reproduction number remains below unity. Conclusion: Our analysis indicates that the success of restrictive measures including lockdown and stay-at-home orders, as reflected by a reduction in number of cases, provides a narrow window of opportunity to intensify case detection and contact tracing efforts to prevent a new wave associated with circulation of more transmissible VOCs.
Language	English
Publishing date	2021-07-08
Publishing country	Canada
Document type	Journal Article
ZDB-ID	1146585-2
ISSN	1188-4169
ISSN	1188-4169
DOI	10.14745/ccdr.v47i78a06
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