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Quentin Richard

Other affiliations: University of Bordeaux
Bio: Quentin Richard is an academic researcher from Centre national de la recherche scientifique. The author has contributed to research in topics: Population & Exponential stability. The author has an hindex of 5, co-authored 14 publications receiving 55 citations. Previous affiliations of Quentin Richard include University of Bordeaux.

Papers
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Posted ContentDOI
26 Nov 2020-medRxiv
TL;DR: It is shown that the optimal control strategy strongly outperforms other strategies such as uniform constant control over the whole populations or over its younger fraction and brings new facts the debate about age-based control interventions and open promising avenues of research, for instance of age- based contact tracing.
Abstract: In an epidemic, individuals can widely differ in the way they spread the infection depending on their age or on the number of days they have been infected for In the absence of pharmaceutical interventions such as a vaccine or treatment, non-pharmaceutical interventions (eg social distancing) are essential to mitigate the pandemic We develop an original approach to identify the optimal age-stratified control strategy to implement as a function of the time since the onset of the epidemic This is based on a model with a double continuous structure in terms of host age and time since infection By applying optimal control theory to this model, we identify a solution that minimizes deaths and costs associated with the implementation of the control strategy itself We also implement this strategy to three countries with contrasted age distributions (Burkina-Faso, France, and Vietnam) Overall, the optimal strategy varies over the course of the epidemic, with a more intense control early on, and depending on host age, with a stronger control for the older population, except in the scenario where the cost associated with the control is low In the latter scenario, we find strong differences across countries because the control extends to younger population in France and Vietnam 2-3 months after the onset of the epidemic, but not in Burkina Faso Finally, we show that the optimal control strategy strongly outperforms constant uniform control of the whole population or over its younger fraction This better understanding of the effect of age-based control interventions opens new perspectives for the field, especially for age-based contact tracing

35 citations

Journal ArticleDOI
TL;DR: In this paper, the authors developed an approach to identify the optimal age-stratified control strategy to implement as a function of the time since the onset of the epidemic, based on a model with a double continuous structure in terms of host age and time since infection.
Abstract: In an epidemic, individuals can widely differ in the way they spread the infection depending on their age or on the number of days they have been infected for. In the absence of pharmaceutical interventions such as a vaccine or treatment, non-pharmaceutical interventions (e.g. physical or social distancing) are essential to mitigate the pandemic. We develop an original approach to identify the optimal age-stratified control strategy to implement as a function of the time since the onset of the epidemic. This is based on a model with a double continuous structure in terms of host age and time since infection. By applying optimal control theory to this model, we identify a solution that minimizes deaths and costs associated with the implementation of the control strategy itself. We also implement this strategy for three countries with contrasted age distributions (Burkina-Faso, France, and Vietnam). Overall, the optimal strategy varies throughout the epidemic, with a more intense control early on, and depending on host age, with a stronger control for the older population, except in the scenario where the cost associated with the control is low. In the latter scenario, we find strong differences across countries because the control extends to the younger population for France and Vietnam 2 to 3 months after the onset of the epidemic, but not for Burkina Faso. Finally, we show that the optimal control strategy strongly outperforms a constant uniform control exerted over the whole population or over its younger fraction. This improved understanding of the effect of age-based control interventions opens new perspectives for the field, especially for age-based contact tracing.

17 citations

Journal ArticleDOI
TL;DR: An age-structured model accounting for the chronological age of humans and mosquito population, the time since humans and mosquitoes are infected and humans waning immunity is formulated, which highlights the effect of above structural variables on key important epidemiological traits of the human-vector association.
Abstract: Malaria is one of the most common mosquito-borne diseases widespread in tropical and subtropical regions, causing thousands of deaths every year in the world. Few models considering a multiple structure model formulation including (i) the chronological age of human and mosquito populations, (ii) the time since they are infected, and (iii) humans waning immunity (i.e. the progressive loss of protective antibodies after recovery) have been developed. In this paper we formulate an age-structured model containing three structural variables. Using the integrated semigroups theory, we first handle the well-posedness of the model proposed. We also investigate the existence of steady-states. A disease-free equilibrium always exists while the existence of endemic equilibria is discussed. We derive the basic reproduction number R 0 which expression highlights the effect of the above structural variables on key important epidemiological traits of the human-vector association such as vectorial capacity (i.e., vector daily reproduction rate), humans transmission probability, and survival rate. The expression of R 0 obtained here generalizes the classical formula of the basic reproduction number. Next, we derive a necessary and sufficient condition that implies the bifurcation of an endemic equilibrium. In the specific case where the age-structure of the human population is neglected, we show that a bifurcation, either backward of forward, may occur at R 0 = 1 leading to the existence, or not, of multiple endemic equilibrium when 0 ≪ R 0 1 . Finally, the latter theoretical results are enlightened by numerical simulations.

13 citations

Journal ArticleDOI
TL;DR: This study shows the flexibility and robustness of PDE formalism to capture national COVID-19 dynamics and opens perspectives to study medium or long-term scenarios involving immune waning or virus evolution.
Abstract: The Covid-19 outbreak was followed by a huge amount of modelling studies in order to rapidly gain insights to implement the best public health policies. Most of these compartmental models involved ordinary differential equations (ODEs) systems. Such a formalism implicitly assumes that the time spent in each compartment does not depend on the time already spent in it, which is unrealistic. To overcome this “memoryless” issue, a widely used solution is to chain the number of compartments of a unique reality (e.g. have infected individual move between several compartments). This allows for greater heterogeneity, but also tends to make the whole model more difficult to apprehend and parameterize. We develop a non-Markovian alternative formalism based on partial differential equations (PDEs) instead of ODEs, which, by construction, provides a memory structure for each compartment. We apply our model to the French 2021 SARS-CoV-2 epidemic and we determine the major components that contributed to the Covid-19 hospital admissions. A global sensitivity analysis highlights a huge uncertainty attributable to the age-structured contact matrix. Our study shows the flexibility and robustness of PDE formalism to capture national COVID-19 dynamics and opens perspectives to study medium or long-term scenarios involving immune waning or virus evolution.

9 citations

Journal ArticleDOI
TL;DR: In this paper, the authors consider an epidemic system that models the evolution of a spore-producing pathogen within a multi-host population of plants and show that the distribution of spores converges to the singular measure concentrated on the maxima of fitness of the pathogen in each plant population.

7 citations


Cited by
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01 Jan 2020
TL;DR: Prolonged viral shedding provides the rationale for a strategy of isolation of infected patients and optimal antiviral interventions in the future.
Abstract: Summary Background Since December, 2019, Wuhan, China, has experienced an outbreak of coronavirus disease 2019 (COVID-19), caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Epidemiological and clinical characteristics of patients with COVID-19 have been reported but risk factors for mortality and a detailed clinical course of illness, including viral shedding, have not been well described. Methods In this retrospective, multicentre cohort study, we included all adult inpatients (≥18 years old) with laboratory-confirmed COVID-19 from Jinyintan Hospital and Wuhan Pulmonary Hospital (Wuhan, China) who had been discharged or had died by Jan 31, 2020. Demographic, clinical, treatment, and laboratory data, including serial samples for viral RNA detection, were extracted from electronic medical records and compared between survivors and non-survivors. We used univariable and multivariable logistic regression methods to explore the risk factors associated with in-hospital death. Findings 191 patients (135 from Jinyintan Hospital and 56 from Wuhan Pulmonary Hospital) were included in this study, of whom 137 were discharged and 54 died in hospital. 91 (48%) patients had a comorbidity, with hypertension being the most common (58 [30%] patients), followed by diabetes (36 [19%] patients) and coronary heart disease (15 [8%] patients). Multivariable regression showed increasing odds of in-hospital death associated with older age (odds ratio 1·10, 95% CI 1·03–1·17, per year increase; p=0·0043), higher Sequential Organ Failure Assessment (SOFA) score (5·65, 2·61–12·23; p Interpretation The potential risk factors of older age, high SOFA score, and d-dimer greater than 1 μg/mL could help clinicians to identify patients with poor prognosis at an early stage. Prolonged viral shedding provides the rationale for a strategy of isolation of infected patients and optimal antiviral interventions in the future. Funding Chinese Academy of Medical Sciences Innovation Fund for Medical Sciences; National Science Grant for Distinguished Young Scholars; National Key Research and Development Program of China; The Beijing Science and Technology Project; and Major Projects of National Science and Technology on New Drug Creation and Development.

4,408 citations

01 Jan 2016
TL;DR: The methods of modern mathematical physics is universally compatible with any devices to read and is available in the digital library an online access to it is set as public so you can download it instantly.
Abstract: Thank you very much for reading methods of modern mathematical physics. Maybe you have knowledge that, people have look numerous times for their favorite novels like this methods of modern mathematical physics, but end up in harmful downloads. Rather than reading a good book with a cup of tea in the afternoon, instead they are facing with some infectious virus inside their desktop computer. methods of modern mathematical physics is available in our digital library an online access to it is set as public so you can download it instantly. Our books collection saves in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Merely said, the methods of modern mathematical physics is universally compatible with any devices to read.

1,536 citations

01 Jan 2016
TL;DR: The nonlinear functional analysis and its applications is universally compatible with any devices to read and is available in the book collection an online access to it is set as public so you can get it instantly.
Abstract: nonlinear functional analysis and its applications is available in our book collection an online access to it is set as public so you can get it instantly. Our books collection hosts in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Merely said, the nonlinear functional analysis and its applications is universally compatible with any devices to read.

581 citations

Journal ArticleDOI
TL;DR: An optimal control analysis of a mathematical model of SARS-CoV-2 transmission found that a major factor that differentiates strategies that prioritize lives saved versus reduced time under control is how quickly control is relaxed once social distancing restrictions expire in May 2020.

127 citations