Pandemia de la COVID-19 y las Políticas de Salud Pública en el Perú: marzo-mayo 2020/COVID-19 pandemic and Public Health Policies in Peru: March-May 2020

Objetivo El trabajo tiene como objetivo analizar la dinámica del comportamiento de la COVID-19 en el Perú, estimar y evaluar el impacto de la política pública de supresión (cuarentena). Métodos El modelo epidemiológico SIR y la estimación con el método de Mínimos Cuadrados Ordinarios (MCO). Resultados Se encontró que el número básico de propagación (Ro) cayó de 6,0 a 3,2 habiéndose reducido en 54% por efecto de la estrategia de supresión, y dos meses después cayó a 1,7. Sin embargo, sigue siendo alto y evidencia que aún continúa en expansión el nivel de infectados, con los efectos sociales y económicos adversos que esta medida implica. Conclusión La COVID-19 es una enfermedad que crece exponencialmente, por lo cual, la política de salud basada en la estrategia de supresión ha permitido aplanar la curva de contagio, evitando el colapso del Sistema de Salud. Objective The objective of the study is to analyze the behavior dynamics of COVID-19 in Peru, estimate and evaluate the impact of the suppression public policy (quarantine). Methods The SIR epidemiological model and the estimation with the ordinary Least Squares (OLS) method. Results It was found that the basic number of propagation (Ro) fell from 6,0 to 3,2 having been reduced by 54% due to the suppression strategy;and two months later it falls to 1,7. However, it remains high and evidence that the level of those infected continues to expand with its adverse social and economic effects. Conclusion COVID-19 is a disease that grows exponentially, and that the health policy based on the suppression strategy has allowed to flatten the contagion curve, thus avoiding the collapse of the Health System.

A statistical moment-based spectral approach to the chance-constrained stochastic optimal control of epidemic models

This paper presents a spectral approach to the uncertainty management in epidemic models through the formulation of chance-constrained stochastic optimal control problems. Specifically, a statistical moment-based polynomial expansion is used to calculate surrogate models of the stochastic state variables of the problem that allow for the efficient computation of their main statistics as well as their marginal and joint probability density functions at each time instant, which enable the uncertainty management in the epidemic model. Moreover, the surrogate models are employed to perform the corresponding sensitivity and risk analyses. The proposed methodology provides the designers of the optimal control policies with the capability to increase the predictability of the outcomes by adding suitable chance constraints to the epidemic model and formulating a proper cost functional. The chance-constrained optimal control of a COVID-19 epidemic model is considered in order to illustrate the practical application of the proposed methodology.

Pandemic lockdown, isolation, and exit policies based on machine learning predictions.

The widespread lockdowns imposed in many countries at the beginning of the COVID-19 pandemic elevated the importance of research on pandemic management when medical solutions such as vaccines are unavailable. We present a framework that combines a standard epidemiological SEIR (susceptible-exposed-infected-removed) model with an equally standard machine learning classification model for clinical severity risk, defined as an individual's risk of needing intensive care unit (ICU) treatment if infected. Using COVID-19-related data and estimates for France as of spring 2020, we then simulate isolation and exit policies. Our simulations show that policies considering clinical risk predictions could relax isolation restrictions for millions of the lowest risk population months earlier while consistently abiding by ICU capacity restrictions. Exit policies without risk predictions, meanwhile, would considerably exceed ICU capacity or require the isolation of a substantial portion of population for over a year in order to not overwhelm the medical system. Sensitivity analyses further decompose the impact of various elements of our models on the observed effects. Our work indicates that predictive modeling based on machine learning and artificial intelligence could bring significant value to managing pandemics. Such a strategy, however, requires governments to develop policies and invest in infrastructure to operationalize personalized isolation and exit policies based on risk predictions at scale. This includes health data policies to train predictive models and apply them to all residents, as well as policies for targeted resource allocation to maintain strict isolation for high-risk individuals.

An Age of Infection Kernel, an R Formula, and Further Results for Arino–Brauer A, B Matrix Epidemic Models with Varying Populations, Waning Immunity, and Disease and Vaccination Fatalities

In this work, we first introduce a class of deterministic epidemic models with varying populations inspired by Arino et al. (2007), the parameterization of two matrices, demography, the waning of immunity, and vaccination parameters. Similar models have been focused on by Julien Arino, Fred Brauer, Odo Diekmann, and their coauthors, but mostly in the case of "closed populations” (models with varying populations have been studied in the past only in particular cases, due to the difficulty of this endeavor). Our Arino–Brauer models contain SIR–PH models of Riano (2020), which are characterized by the phase-type distribution (Formula presented.), modeling transitions in "disease/infectious compartments”. The A matrix is simply the Metzler/sub-generator matrix intervening in the linear system obtained by making all new infectious terms 0. The simplest way to define the probability row vector (Formula presented.) is to restrict it to the case where there is only one susceptible class (Formula presented.), and when matrix B (given by the part of the new infection matrix, with respect to (Formula presented.)) is of rank one, with (Formula presented.). For this case, the first result we obtained was an explicit formula (12) for the replacement number (not surprisingly, accounting for varying demography, waning immunity and vaccinations led to several nontrivial modifications of the Arino et al. (2007) formula). The analysis of (Formula presented.) Arino–Brauer models is very challenging. As obtaining further general results seems very hard, we propose studying them at three levels: (A) the exact model, where only a few results are available—see Proposition 2;and (B) a "first approximation” (FA) of our model, which is related to the usually closed population model often studied in the literature. Notably, for this approximation, an associated renewal function is obtained in (7);this is related to the previous works of Breda, Diekmann, Graaf, Pugliese, Vermiglio, Champredon, Dushoff, and Earn. (C) Finally, we propose studying a second heuristic "intermediate approximation” (IA). Perhaps our main contribution is to draw attention to the importance of (Formula presented.) Arino–Brauer models and that the FA approximation is not the only way to tackle them. As for the practical importance of our results, this is evident, once we observe that the (Formula presented.) Arino–Brauer models include a large number of epidemic models (COVID, ILI, influenza, illnesses, etc.). © 2023 by the authors.

Quarantine and Vaccination in Hierarchical Epidemic Model

The analysis of global epidemics, such as SARS, MERS, and COVID-19, suggests a hierarchical structure of the epidemic process. The pandemic wave starts locally and accelerates through human-to-human interactions, eventually spreading globally after achieving an efficient and sustained transmission. In this paper, we propose a hierarchical model for the virus spread that divides the spreading process into three levels: a city, a region, and a country. We define the virus spread at each level using a modified susceptible–exposed–infected–recovery–dead (SEIRD) model, which assumes migration between levels. Our proposed controlled hierarchical epidemic model incorporates quarantine and vaccination as complementary optimal control strategies. We analyze the balance between the cost of the active virus spread and the implementation of appropriate quarantine measures. Furthermore, we differentiate the levels of the hierarchy by their contribution to the cost of controlling the epidemic. Finally, we present a series of numerical experiments to support the theoretical results obtained. © 2023 by the authors.

Modelling presymptomatic infectiousness in COVID-19

This paper considers SEPIR, an extension of the well-known SEIR continuous simulation compartment model. Both models can be fitted to real data as they include parameters that can be estimated from the data. SEPIR deploys an additional presymptomatic infectious compartment, not modelled in SEIR but known to exist in COVID-19. This stage can also be fitted to data. We focus on how to fit SEPIR to a first wave of COVID. Both SEIR and SEPIR and the existing SEIR models assume a homogeneous mixing population with parameters fixed. Moreover, neither includes dynamically varying control strategies deployed against the virus. If either model is to represent more than just a single wave of the epidemic, then the parameters of the model would have to be time dependent. In view of this, we also show how reproduction numbers can be calculated to investigate the long-term overall outcome of an epidemic. © 2023 The Operational Research Society.

A Sir Model for Viral Growth of Coronavirus: A System Dynamics Approach

In this paper, a system dynamics model depicts the viral growth of COVID-19 at an exponential rate. The outbreak of Corona virus was started from the Feb 26, 2020 when the first case was reported in Pakistan. Local bodies and law enforcing agencies had taken initial preventive measures to restrict the COVID-19 to a particular locality but all in vain. The infected people were increasing every day rising the stocks of recoveries and deaths. Numbers of infected people were alarming and a need was felt to develop the model to calculate the existing reproduction number and transmission rate and highlight its varied values in coming days. People-oriented measures and government-based policies must be explored to fight against this deadly disease. This paper aims the development of epidemic model using the system dynamic framework on simulation software STELLA. The objective of the research is to experiment with the model to replicate the progression of the communicable disease and probe the multiple combinations of the people-based and government-based measures to reduce its spread. The containment measures are of two types;people-based measures and government-based measures and both directly affect the reproduction number and infection growth fraction for mitigating the spread of deadly coronavirus. Combined efforts of public and government can combat this pandemic. Reduced degree of reproduction number and infection growth fraction are the key metrics to judge and evaluate the effectiveness of containment measures. This research points to more holistic combination of public and government-oriented measures that play the vital role to flatten the curve and reduce its spread affecting the reproduction number. Simulation results have been traced to replicate the real-life settings against four combinations of containment measures in tabular form and graphical form. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Stability analysis of a fractional-order SEIR epidemic model with general incidence rate and time delay

In this paper, we investigate the qualitative behavior of a class of fractional SEIR epidemic models with a more general incidence rate function and time delay to incorporate latent infected individuals. We first prove positivity and boundedness of solutions of the system. The basic reproduction number (Formula presented.) of the model is computed using the method of next generation matrix, and we prove that if (Formula presented.), the healthy equilibrium is locally asymptotically stable, and when (Formula presented.), the system admits a unique endemic equilibrium which is locally asymptotically stable. Moreover, using a suitable Lyapunov function and some results about the theory of stability of differential equations of delayed fractional-order type, we give a complete study of global stability for both healthy and endemic steady states. The model is used to describe the COVID-19 outbreak in Algeria at its beginning in February 2020. A numerical scheme, based on Adams–Bashforth–Moulton method, is used to run the numerical simulations and shows that the number of new infected individuals will peak around late July 2020. Further, numerical simulations show that around 90% of the population in Algeria will be infected. Compared with the WHO data, our results are much more close to real data. Our model with fractional derivative and delay can then better fit the data of Algeria at the beginning of infection and before the lock and isolation measures. The model we propose is a generalization of several SEIR other models with fractional derivative and delay in literature. © 2023 John Wiley & Sons, Ltd.

MULTISCALE KINETIC TRANSPORT MODELS FOR THE SPREAD OF EPIDEMICS WITH UNCERTAIN DATA

Most epidemiological models are rooted in the pioneering work proposed by Ker- mack and McKendrick and are based on systems of deterministic ODEs, which describe the temporal evolution of the spread of an infectious disease assuming population and territorial homogeneity. Generally, the concept of the average behavior of a population is su cient to have a rst reliable description of an epidemic development, but the inclusion of the spatial compo-nent becomes crucial when it is necessary to consider spatially heterogeneous interventions, as in the case of the COVID-19 pandemic. Moreover, any realistic data-driven model must take into account the large uncertainty in the values reported by o cial sources such as the amount of infectious individuals. In this work, drawing inspiration from kinetic theory, recent advances on the development of stochastic multiscale kinetic transport models for the spread of epidemics under uncertain data are presented. The propagation of the infectious disease is described by the spatial movement and interactions of individuals divided into commuters moving in the ter-ritory on a wide scale and non-commuters acting only on urban scales. The resulting models are solved numerically through a suitable stochastic Asymptotic-Preserving IMEX Runge-Kutta Finite Volume Collocation Method, which ensures a consistent treatment of the system of equa-tions, without loss of accuracy when entering in the sti, di usive regime. Application studies concerning the spread of the COVID-19 pandemic in Italy assess the validity of the proposed methodology. © 2022, Scipedia S.L. All rights reserved.

A Comparative Study for Some Mathematical Models of Epidemic Diseases with Application to Strategic Management

A local performance of the SIR model on actual data is introduced. A good approximation of the SIR model parameters in Saudi Arabia during a period of 275 days (the first of April 2020 to the end of December 2020) is determined. The parameters are estimated from the recorded data and used to predict the values in the next subsequent period. The performance of the standard fourth order Runge-Kutta method is considered for the classical SIR models over different periods. A comparison of the recorded data and the predicted values during the considered period illustrated the effectiveness of the treatment. The mathematical properties and initial conditions are considered within the estimated parameter values. It is shown that lockdown and social distance attitudes effectively controlled the spread of the disease. The maximum number of daily active infected cases is 63,026, and occurs in July and this agrees with the calculated values. To make the graphs representable, we considered a fixed closed population, the effective sample during the considered period of size N = 400,000 only (represents only 1% of the overall population susceptible, this must be associated, with great thanks, to the authorities in KSA).

Effectiveness of Different Control Measures on the Spread of COVID-19

The COVID-19 pandemic has influenced most of the population worldwide. It is essential to assess the effectiveness of different control measures on the spread of the virus. In this paper, the author uses an SEIR agent-based model on the NetLogo platform to establish a simulation model and define seven types of agents: susceptible, infectious, mask-wearing, quarantined, exposed, and vaccinated. We performed an analysis of four possible scenarios: (1) doing nothing, (2) quarantine, (3) using face masks, and (4) vaccination. It is concluded that the adoption of different control measures could quickly control the epidemic situation. The use of vaccination also has a huge impact on the pressure of epidemic control. Nevertheless, If control measures are not put in place, the duration of the epidemic will be significantly prolonged. © 2022 ACM.

Leveraging Human Mobility Data for Efficient Parameter Estimation in Epidemic Models of COVID-19

Effectively predicting the evolution of COVID-19 is of great significance to contain the pandemic. Extensive previous studies proposed a great number of SIR variants, which are efficient to capture the transmission characteristics of COVID-19. However, the parameter estimation methods in previous studies are based on data from epidemiological investigations, which inevitably have caused a large delay. The popularity of digital trajectory data world-wide makes it possible to understand epidemic spreading from human mobility perspective. The major advantage of digital trajectory data lies in that the co-location level of a population is reflected at every moment, making it possible to forecast the evolution in advance. We showed that the mobility data contributed by mobile phone users could be exploited to estimate the contact probability between individuals, thus revealing the dynamic transmission of COVID-19. Specifically, we developed an estimation method to obtain human co-location levels and quantified the variations of human mobility during the epidemic. Then, we extended the infection rate with a real-time co-location level to further forecast the transmission of an epidemic, predicting the epidemic size much more accurately than conventional methods. Finally, the proposed method was applied to evaluate the quantitative effect of different non-pharmacological interventions by predicting the epidemic situations with various mobility characteristics. The empirical results and simulations corroborated our theoretical analysis, providing effective guidance to contain the pandemic. IEEE

Multiple epidemic waves as the outcome of stochastic SIR epidemics with behavioral responses: a hybrid modeling approach.

In the behavioral epidemiology (BE) of infectious diseases, little theoretical effort seems to have been devoted to understand the possible effects of individuals' behavioral responses during an epidemic outbreak in small populations. To fill this gap, here we first build general, behavior implicit, SIR epidemic models including behavioral responses and set them within the framework of nonlinear feedback control theory. Second, we provide a thorough investigation of the effects of different types of agents' behavioral responses for the dynamics of hybrid stochastic SIR outbreak models. In the proposed model, the stochastic discrete dynamics of infection spread is combined with a continuous model describing the agents' delayed behavioral response. The delay reflects the memory mechanisms with which individuals enact protective behavior based on past data on the epidemic course. This results in a stochastic hybrid system with time-varying transition probabilities. To simulate such system, we extend Gillespie's classic stochastic simulation algorithm by developing analytical formulas valid for our classes of models. The algorithm is used to simulate a number of stochastic behavioral models and to classify the effects of different types of agents' behavioral responses. In particular this work focuses on the effects of the structure of the response function and of the form of the temporal distribution of such response. Among the various results, we stress the appearance of multiple, stochastic epidemic waves triggered by the delayed behavioral response of individuals.

Spectral Method in Epidemic Time Series: Application to COVID-19 Pandemic.

BACKGROUND: The age of infection plays an important role in assessing an individual's daily level of contagiousness, quantified by the daily reproduction number. Then, we derive an autoregressive moving average model from a daily discrete-time epidemic model based on a difference equation involving the age of infection. Novelty: The article's main idea is to use a part of the spectrum associated with this difference equation to describe the data and the model. RESULTS: We present some results of the parameters' identification of the model when all the eigenvalues are known. This method was applied to Japan's third epidemic wave of COVID-19 fails to preserve the positivity of daily reproduction. This problem forced us to develop an original truncated spectral method applied to Japanese data. We start by considering ten days and extend our analysis to one month. CONCLUSION: We can identify the shape for a daily reproduction numbers curve throughout the contagion period using only a few eigenvalues to fit the data.

An implementation of a multilayer network model for the Covid-19 pandemic: A Costa Rica study.

We present a numerical implementation for a multilayer network to model the transmission of Covid-19 or other diseases with a similar transmission mechanism. The model incorporates different contact types between individuals (household, social and sporadic networks) and includes an SEIR type model for the transmission of the virus. The algorithm described in this paper includes the main ideas of the model used to give public health authorities an additional tool for the decision-making process in Costa Rica by simulating extensive possible scenarios and projections. We include two simulations: a study of the effect of restrictions on the transmission of the virus and a Costa Rica case study that was shared with the Costa Rican health authorities.

IDENTIFIABILITY OF INFECTION MODEL PARAMETERS EARLY IN AN EPIDEMIC.

It is known that the parameters in the deterministic and stochastic SEIR epidemic models are structurally identifiable. For example, from knowledge of the infected population time series I(t) during the entire epidemic, the parameters can be successfully estimated. In this article we observe that estimation will fail in practice if only infected case data during the early part of the epidemic (prepeak) is available. This fact can be explained using a well-known phenomenon called dynamical compensation. We use this concept to derive an unidentifiability manifold in the parameter space of SEIR that consists of parameters indistinguishable from I(t) early in the epidemic. Thus, identifiability depends on the extent of the system trajectory that is available for observation. Although the existence of the unidentifiability manifold obstructs the ability to exactly determine the parameters, we suggest that it may be useful for uncertainty quantification purposes. A variant of SEIR recently proposed for COVID-19 modeling is also analyzed, and an analogous unidentifiability surface is derived.

Feedback control of isolation and contact for SIQR epidemic model via strict Lyapunov function

We derive feedback control laws for isolation, contact regulation, and vaccination for infectious diseases, using a strict Lyapunov function. We use an SIQR epidemic model describing transmission, isolation via quarantine, and vaccination for diseases to which immunity is long-lasting. Assuming that mass vaccination is not available to completely eliminate the disease in a time horizon of interest, we provide feedback control laws that drive the disease to an endemic equilibrium. We prove the input-to-state stability (or ISS) robustness property on the entire state space, when the immigration perturbation is viewed as the uncertainty. We use an ISS Lyapunov function to derive the feedback control laws. A key ingredient in our analysis is that all compartment variables are present not only in the Lyapunov function, but also in a negative definite upper bound on its time derivative. We illustrate the efficacy of our method through simulations, and we discuss the usefulness of parameters in the controls. Since the control laws are feedback, their values are updated based on data acquired in real time. We also discuss the degradation caused by the delayed data acquisition occurring in practical implementations, and we derive bounds on the delays under which the ISS property is ensured when delays are present.

Model-based epidemic data reconstruction using feedback linearization

In this paper, a model-based method is proposed for the reconstruction of non-measured epidemic data of the COVID-19 pandemic in Hungary. Only the data series showing the daily number of hospitalized people are used for the reconstruction together with a nonlinear dynamical model of epidemic spread containing 8 compartments. The unknown input of the model is the infection rate, which is computed through the solution of a feedback linearization-based asymptotic output tracking problem, where the reference is the actually observed number of hospitalized people. Computations show good match with of hospitalized people. Computations show good match with previous reconstruction results, and show a roughly 3.5-4-fold underdetection of infections until the Omicron wave. © 2022 IEEE.

Numerical treatments for the optimal control of two types variable-order COVID-19 model.

In this paper, a novel variable-order COVID-19 model with modified parameters is presented. The variable-order fractional derivatives are defined in the Caputo sense. Two types of variable order Caputo definitions are presented here. The basic reproduction number of the model is derived. Properties of the proposed model are studied analytically and numerically. The suggested optimal control model is studied using two numerical methods. These methods are non-standard generalized fourth-order Runge-Kutta method and the non-standard generalized fifth-order Runge-Kutta technique. Furthermore, the stability of the proposed methods are studied. To demonstrate the methodologies' simplicity and effectiveness, numerical test examples and comparisons with real data for Egypt and Italy are shown.

Impact of spatiotemporal heterogeneity in COVID-19 disease surveillance on epidemiological parameters and case growth rates.

SARS-CoV-2 case data are primary sources for estimating epidemiological parameters and for modelling the dynamics of outbreaks. Understanding biases within case-based data sources used in epidemiological analyses is important as they can detract from the value of these rich datasets. This raises questions of how variations in surveillance can affect the estimation of epidemiological parameters such as the case growth rates. We use standardised line list data of COVID-19 from Argentina, Brazil, Mexico and Colombia to estimate delay distributions of symptom-onset-to-confirmation, -hospitalisation and -death as well as hospitalisation-to-death at high spatial resolutions and throughout time. Using these estimates, we model the biases introduced by the delay from symptom-onset-to-confirmation on national and state level case growth rates (rt) using an adaptation of the Richardson-Lucy deconvolution algorithm. We find significant heterogeneities in the estimation of delay distributions through time and space with delay difference of up to 19 days between epochs at the state level. Further, we find that by changing the spatial scale, estimates of case growth rate can vary by up to 0.13 d-1. Lastly, we find that states with a high variance and/or mean delay in symptom-onset-to-diagnosis also have the largest difference between the rt estimated from raw and deconvolved case counts at the state level. We highlight the importance of high-resolution case-based data in understanding biases in disease reporting and how these biases can be avoided by adjusting case numbers based on empirical delay distributions. Code and openly accessible data to reproduce analyses presented here are available.