Age-structured non-pharmaceutical interventions for optimal control of COVID-19 epidemic.
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.
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TL;DR: In this paper, an extended SEIR (susceptible-exposed-infectious-recovered) model and continuous-time optimal control theory are used to compute the optimal non-pharmaceutical intervention strategy for the case that a vaccine is never found and complete containment (eradication of the epidemic) is impossible.
Abstract: When effective medical treatment and vaccination are not available, non-pharmaceutical interventions such as social distancing, home quarantine and far-reaching shutdown of public life are the only available strategies to prevent the spread of epidemics. Based on an extended SEIR (susceptible-exposed-infectious-recovered) model and continuous-time optimal control theory, we compute the optimal non-pharmaceutical intervention strategy for the case that a vaccine is never found and complete containment (eradication of the epidemic) is impossible. In this case, the optimal control must meet competing requirements: First, the minimization of disease-related deaths, and, second, the establishment of a sufficient degree of natural immunity at the end of the measures, in order to exclude a second wave. Moreover, the socio-economic costs of the intervention shall be kept at a minimum. The numerically computed optimal control strategy is a single-intervention scenario that goes beyond heuristically motivated interventions and simple “flattening of the curve”. Careful analysis of the computed control strategy reveals, however, that the obtained solution is in fact a tightrope walk close to the stability boundary of the system, where socio-economic costs and the risk of a new outbreak must be constantly balanced against one another. The model system is calibrated to reproduce the initial exponential growth phase of the COVID-19 pandemic in Germany.
75 citations
TL;DR: A model for the COVID-19 epidemic where the population is partitioned into classes corresponding to ages (that remain constant during the epidemic) is proposed, to take into account the infection age of the infected population.
Abstract: We propose a model for the COVID-19 epidemic where the population is partitioned into classes corresponding to ages (that remain constant during the epidemic). The main feature is to take into account the infection age of the infected population. This allows to better simulate the infection propagation that crucially depend on the infection age. We discuss how to estimate the coefficients from data available in the future, and introduce a confinement variable as control. The cost function is a compromise between a confinement term, the hospitalization peak and the death toll. Our numerical experiments allow to evaluate the interest of confinement varying with age classes.
24 citations
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
Posted Content•
TL;DR: In this article, the authors provide insights on how much testing and social distancing is required to control COVID-19 and develop a compartmental model that accounts for key aspects of the disease: 1) incubation time, 2) age-dependent symptom severity, and 3) testing and hospitalization delays.
Abstract: In this paper, we provide insights on how much testing and social distancing is required to control COVID-19. To this end, we develop a compartmental model that accounts for key aspects of the disease: 1) incubation time, 2) age-dependent symptom severity, and 3) testing and hospitalization delays; the model's parameters are chosen based on medical evidence, and, for concreteness, adapted to the German situation. Then, optimal mass-testing and age-dependent social-distancing policies are determined by solving optimal control problems both in open loop and within a model predictive control framework. We aim to minimize testing and/or social distancing until herd immunity sets in under a constraint on the number of available intensive care units. We find that an early and short lockdown is inevitable but can be slowly relaxed over the following months.
12 citations
TL;DR: In this paper, the authors proposed the Delta Time Spent in Public Places (ΔTSPP) as a measure to quantify daily changes in mobility for each US county from 2019-2020.
Abstract: With the onset of COVID-19 and the resulting shelter in place guidelines combined with remote working practices, human mobility in 2020 has been dramatically impacted. Existing studies typically examine whether mobility in specific localities increases or decreases at specific points in time and relate these changes to certain pandemic and policy events. However, a more comprehensive analysis of mobility change over time is needed. In this paper, we study mobility change in the US through a five-step process using mobility footprint data. (Step 1) Propose the Delta Time Spent in Public Places (ΔTSPP) as a measure to quantify daily changes in mobility for each US county from 2019-2020. (Step 2) Conduct Principal Component Analysis (PCA) to reduce the ΔTSPP time series of each county to lower-dimensional latent components of change in mobility. (Step 3) Conduct clustering analysis to find counties that exhibit similar latent components. (Step 4) Investigate local and global spatial autocorrelation for each component. (Step 5) Conduct correlation analysis to investigate how various population characteristics and behavior correlate with mobility patterns. Results show that by describing each county as a linear combination of the three latent components, we can explain 59% of the variation in mobility trends across all US counties. Specifically, change in mobility in 2020 for US counties can be explained as a combination of three latent components: 1) long-term reduction in mobility, 2) no change in mobility, and 3) short-term reduction in mobility. Furthermore, we find that US counties that are geographically close are more likely to exhibit a similar change in mobility. Finally, we observe significant correlations between the three latent components of mobility change and various population characteristics, including political leaning, population, COVID-19 cases and deaths, and unemployment. We find that our analysis provides a comprehensive understanding of mobility change in response to the COVID-19 pandemic.
9 citations
References
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TL;DR: Wang et al. as discussed by the authors used univariable and multivariable logistic regression methods to explore the risk factors associated with in-hospital death, including older age, high SOFA score and d-dimer greater than 1 μg/mL.
20,189 citations
TL;DR: There is evidence that human-to-human transmission has occurred among close contacts since the middle of December 2019 and considerable efforts to reduce transmission will be required to control outbreaks if similar dynamics apply elsewhere.
Abstract: Background The initial cases of novel coronavirus (2019-nCoV)–infected pneumonia (NCIP) occurred in Wuhan, Hubei Province, China, in December 2019 and January 2020. We analyzed data on the...
13,101 citations
TL;DR: In this article, the authors considered the problem of finding a causal factor which appears to be adequate to account for the magnitude of the frequent epidemics of disease which visit almost every population.
Abstract: (1) One of the most striking features in the study of epidemics is the difficulty of finding a causal factor which appears to be adequate to account for the magnitude of the frequent epidemics of disease which visit almost every population. It was with a view to obtaining more insight regarding the effects of the various factors which govern the spread of contagious epidemics that the present investigation was undertaken. Reference may here be made to the work of Ross and Hudson (1915-17) in which the same problem is attacked. The problem is here carried to a further stage, and it is considered from a point of view which is in one sense more general. The problem may be summarised as follows: One (or more) infected person is introduced into a community of individuals, more or less susceptible to the disease in question. The disease spreads from the affected to the unaffected by contact infection. Each infected person runs through the course of his sickness, and finally is removed from the number of those who are sick, by recovery or by death. The chances of recovery or death vary from day to day during the course of his illness. The chances that the affected may convey infection to the unaffected are likewise dependent upon the stage of the sickness. As the epidemic spreads, the number of unaffected members of the community becomes reduced. Since the course of an epidemic is short compared with the life of an individual, the population may be considered as remaining constant, except in as far as it is modified by deaths due to the epidemic disease itself. In the course of time the epidemic may come to an end. One of the most important probems in epidemiology is to ascertain whether this termination occurs only when no susceptible individuals are left, or whether the interplay of the various factors of infectivity, recovery and mortality, may result in termination, whilst many susceptible individuals are still present in the unaffected population. It is difficult to treat this problem in its most general aspect. In the present communication discussion will be limited to the case in which all members of the community are initially equally susceptible to the disease, and it will be further assumed that complete immunity is conferred by a single infection.
8,238 citations
Book•
11 Jul 1991
TL;DR: This book discusses the biology of host-microparasite associations, dynamics of acquired immunity heterogeneity within the human community indirectly transmitted helminths, and the ecology and genetics of hosts and parasites.
Abstract: Part 1 Microparasites: biology of host-microparasite associations the basic model - statics static aspects of eradication and control the basic model - dynamics dynamic aspects of eradication and control beyond the basic model - empirical evidence of inhomogeneous mixing age-related transmission rates genetic heterogeneity social heterogeneity and sexually transmitted diseases spatial and other kinds of heterogeneity endemic infections in developing countries indirectly transmitted microparasites. Part 2 Macroparasites: biology of host-macroparasite associations the basic model - statics the basic model - dynamics acquired immunity heterogeneity within the human community indirectly transmitted helminths experimental epidemiology parasites, genetic variability, and drug resistance the ecology and genetics of host-parasite associations.
7,675 citations
TL;DR: Threshold theorems involving the basic reproduction number, the contact number, and the replacement number $R$ are reviewed for classic SIR epidemic and endemic models and results with new expressions for $R_{0}$ are obtained for MSEIR and SEIR endemic models with either continuous age or age groups.
Abstract: Many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases. Threshold theorems involving the basic reproduction number $R_{0}$, the contact number $\sigma$, and the replacement number $R$ are reviewed for the classic SIR epidemic and endemic models. Similar results with new expressions for $R_{0}$ are obtained for MSEIR and SEIR endemic models with either continuous age or age groups. Values of $R_{0}$ and $\sigma$ are estimated for various diseases including measles in Niger and pertussis in the United States. Previous models with age structure, heterogeneity, and spatial structure are surveyed.
5,915 citations