Mathematical models to characterize early epidemic growth: A review

Deterministic epidemic models overestimate the basic reproduction number of observed outbreaks

The basic reproduction number, R0, is a well-known quantifier of epidemic spread. However, a class of existing methods for estimating R0 from incidence data early in the epidemic can lead to an over-estimation of this quantity. In particular, when fitting deterministic models to estimate the rate of spread, we do not account for the stochastic nature of epidemics and that, given the same system, some outbreaks may lead to epidemics and some may not. Typically, an observed epidemic that we wish to control is a major outbreak. This amounts to implicit selection for major outbreaks which leads to the over-estimation problem. We formally characterised the split between major and minor outbreaks by using Otsu's method which provides us with a working definition. We show that by conditioning a 'deterministic' model on major outbreaks, we can more reliably estimate the basic reproduction number from an observed epidemic trajectory.

Emergence failure of early epidemics: A mathematical modeling approach

Epidemic or pathogen emergence is the phenomenon by which a poorly transmissible pathogen finds its evolutionary pathway to become a mutant that can cause an epidemic. Many mathematical models of pathogen emergence rely on branching processes. Here, we discuss pathogen emergence using Markov chains, for a more tractable analysis, generalizing previous work by Kendall and Bartlett about disease invasion. We discuss the probability of emergence failure for early epidemics, when the number of infected individuals is small and the number of the susceptible individuals is virtually unlimited. Our formalism addresses both directly transmitted and vector-borne diseases, in the cases where the original pathogen is 1) one step-mutation away from the epidemic strain, and 2) undergoing a long chain of neutral mutations that do not change the epidemiology. We obtain analytic results for the probabilities of emergence failure and two features transcending the transmission mechanism. First, the reproduction number of the original pathogen is determinant for the probability of pathogen emergence, more important than the mutation rate or the transmissibility of the emerged pathogen. Second, the probability of mutation within infected individuals must be sufficiently high for the pathogen undergoing neutral mutations to start an epidemic, the mutation threshold depending again on the basic reproduction number of the original pathogen. Finally, we discuss the parameterization of models of pathogen emergence, using SARS-CoV1 as an example of zoonotic emergence and HIV as an example for the emergence of drug resistance. We also discuss assumptions of our models and implications for epidemiology.

A novel simulation-based analysis of a stochastic HIV model with the time delay using high order spectral collocation technique

The economic impact of Human Immunodeficiency Virus (HIV) goes beyond individual levels and it has a significant influence on communities and nations worldwide. Studying the transmission patterns in HIV dynamics is crucial for understanding the tracking behavior and informing policymakers about the possible control of this viral infection. Various approaches have been adopted to explore how the virus interacts with the immune system. Models involving differential equations with delays have become prevalent across various scientific and technical domains over the past few decades. In this study, we present a novel mathematical model comprising a system of delay differential equations to describe the dynamics of intramural HIV infection. The model characterizes three distinct cell sub-populations and the HIV virus. By incorporating time delay between the viral entry into target cells and the subsequent production of new virions, our model provides a comprehensive understanding of the infection process. Our study focuses on investigating the stability of two crucial equilibrium states the infection-free and endemic equilibriums. To analyze the infection-free equilibrium, we utilize the LaSalle invariance principle. Further, we prove that if reproduction is less than unity, the disease free equilibrium is locally and globally asymptotically stable. To ensure numerical accuracy and preservation of essential properties from the continuous mathematical model, we use a spectral scheme having a higher-order accuracy. This scheme effectively captures the underlying dynamics and enables efficient numerical simulations.

Transmission matrices used in epidemiologic modelling

Mixing matrices are included in infectious disease models to reflect transmission opportunities between population strata. These matrices were originally constructed on the basis of theoretical considerations and most of the early work in this area originates from research on sexually transferred diseases in the 80s, in response to AIDS. Later work in the 90s populated these matrices on the basis of survey data gathered to capture transmission risks for respiratory diseases. We provide an overview of developments in the construction of matrices for capturing transmission opportunities in populations. Such transmission matrices are useful for epidemiologic modelling to capture within and between stratum transmission and can be informed from theoretical mixing assumptions, informed by empirical evidence gathered through investigation as well as generated on the basis of data. Links to summary measures and threshold conditions are also provided.

What Influence Could the Acceptance of Visitors Cause on the Epidemic Dynamics of a Reinfectious Disease?: A Mathematical Model

The globalization in business and tourism becomes crucial more and more for the economical sustainability of local communities. In the presence of an epidemic outbreak, there must be such a decision on the policy by the host community as whether to accept visitors or not, the number of acceptable visitors, or the condition for acceptable visitors. Making use of an SIRI type of mathematical model, we consider the influence of visitors on the spread of a reinfectious disease in a community, especially assuming that a certain proportion of accepted visitors are immune. The reinfectivity of disease here means that the immunity gained by either vaccination or recovery is imperfect. With the mathematical results obtained by our analysis on the model for such an epidemic dynamics of resident and visitor populations, we find that the acceptance of visitors could have a significant influence on the disease's endemicity in the community, either suppressive or supportive.

Assessing the Impact of Non-Pharmaceutical Interventions on Consumer Mobility Patterns and COVID-19 Transmission in the US

The initial outbreak of COVID-19 during late December 2019 and the subsequent global pandemic markedly changed consumer mobility patterns worldwide, largely in response to government-ordered non-pharmaceutical interventions (NPIs). In this study, we investigate these changes as they relate to the initial spread of COVID-19 within two states-Massachusetts and Michigan. Specifically, we use linear and generalized linear mixed-effects models to quantify the relationship between four NPIs and individuals' point-of-sale (POS) credit card transactions, as well as the relationship between subsequent changes in POS transactions and county-level COVID-19 case growth rates. Our analysis reveals a significant negative association between NPIs and daily POS transactions, particularly a dose-response relationship, in which stringent workplace closures, stay-at-home requirements, and gathering restrictions were all associated with decreased POS transactions. We also uncover a significant positive association between 12-day lagged changes in POS transactions compared to pre-pandemic baselines and county-level COVID-19 case growth rates. Overall, our study supports previous findings that early NPIs reduced human mobility and COVID-19 transmission in the US, providing policymakers with quantitative evidence concerning the effectiveness of NPIs.

An agent-based model with antibody dynamics information in COVID-19 epidemic simulation

Accurate prediction of the temporal and spatial characteristics of COVID-19 infection is of paramount importance for effective epidemic prevention and control. In order to accomplish this objective, we incorporated individual antibody dynamics into an agent-based model and devised a methodology that encompasses the dynamic behaviors of each individual, thereby explicitly capturing the count and spatial distribution of infected individuals with varying symptoms at distinct time points. Our model also permits the evaluation of diverse prevention and control measures. Based on our findings, the widespread employment of nucleic acid testing and the implementation of quarantine measures for positive cases and their close contacts in China have yielded remarkable outcomes in curtailing a less transmissible yet more virulent strain; however, they may prove inadequate against highly transmissible and less virulent variants. Additionally, our model excels in its ability to trace back to the initial infected case (patient zero) through early epidemic patterns. Ultimately, our model extends the frontiers of traditional epidemiological simulation methodologies and offers an alternative approach to epidemic modeling.

Data-driven estimation of the instantaneous reproduction number and growth rates for the 2022 monkeypox outbreak in Europe

OBJECTIVE

To estimate the instantaneous reproduction number Rt and the epidemic growth rates for the 2022 monkeypox outbreaks in the European region.

METHODS

We gathered daily laboratory-confirmed monkeypox cases in the most affected European countries from the beginning of the outbreak to September 23, 2022. A data-driven estimation of the instantaneous reproduction number is obtained using a novel filtering type Bayesian inference. A phenomenological growth model coupled with a Bayesian sequential approach to update forecasts over time is used to obtain time-dependent growth rates in several countries.

RESULTS

The instantaneous reproduction number Rt for the laboratory-confirmed monkeypox cases in Spain, France, Germany, the UK, the Netherlands, Portugal, and Italy. At the early phase of the outbreak, our estimation for Rt, which can be used as a proxy for the basic reproduction number R0, was 2.06 (95% CI 1.63 - 2.54) for Spain, 2.62 (95% CI 2.23 - 3.17) for France, 2.81 (95% CI 2.51 - 3.09) for Germany, 1.82 (95% CI 1.52 - 2.18) for the UK, 2.84 (95% CI 2.07 - 3.91) for the Netherlands, 1.13 (95% CI 0.99 - 1.32) for Portugal, 3.06 (95% CI 2.48 - 3.62) for Italy. Cumulative cases for these countries present subexponential rather than exponential growth dynamics.

CONCLUSIONS

Our findings suggest that the current monkeypox outbreaks present limited transmission chains of human-to-human secondary infection so the possibility of a huge pandemic is very low. Confirmed monkeypox cases are decreasing significantly in the European region, the decline might be attributed to public health interventions and behavioral changes in the population due to increased risk perception. Nevertheless, further strategies toward elimination are essential to avoid the subsequent evolution of the monkeypox virus that can result in new outbreaks.

Mathematical modeling for Delta and Omicron variant of SARS-CoV-2 transmission dynamics in Greece

A compartmental, epidemiological, mathematical model was developed in order to analyze the transmission dynamics of Delta and Omicron variant, of SARS-CoV-2, in Greece. The model was parameterized twice during the 4th and 5th wave of the pandemic. The 4th wave refers to the period during which the Delta variant was dominant (approximately July to December of 2021) and the 5th wave to the period during which the Omicron variant was dominant (approximately January to May of 2022), in accordance with the official data from the National Public Health Organization (NPHO). Fitting methods were applied to evaluate important parameters in connection with the transmission of the variants, as well as the social behavior of population during these periods of interest. Mathematical models revealed higher numbers of contagiousness and cases of asymptomatic disease during the Omicron variant period, but a decreased rate of hospitalization compared to the Delta period. Also, parameters related to the behavior of the population in Greece were also assessed. More specifically, the use of protective masks and the abidance of social distancing measures. Simulations revealed that over 5,000 deaths could have been avoided, if mask usage and social distancing were 20% more efficient, during the short period of the Delta and Omicron outbreak. Furthermore, the spread of the variants was assessed using viral load data. The data were recorded from PCR tests at 417 Army Equity Fund Hospital (NIMTS), in Athens and the Ct values from 746 patients with COVID-19 were processed, to explain transmission phenomena and disease severity in patients. The period when the Delta variant prevailed in the country, the average Ct value was calculated as 25.19 (range: 12.32-39.29), whereas during the period when the Omicron variant prevailed, the average Ct value was calculated as 28 (range: 14.41-39.36). In conclusion, our experimental study showed that the higher viral load, which is related to the Delta variant, may interpret the severity of the disease. However, no correlation was confirmed regarding contagiousness phenomena. The results of the model, Ct analysis and official data from NPHO are consistent.

Impact of school operating scenarios on COVID-19 transmission under vaccination in the U.S.: an agent-based simulation model

At the height of the COVID-19 pandemic, K-12 schools struggled to safely operate under the fast-changing pandemic situation. However, little is known about the impact of different school operating scenarios considering the ongoing efforts of vaccination. In this study, we deployed an agent-based simulation model to mimic disease transmission in a mid-sized community consisting of 10,000 households. A total of eight school operating scenarios were simulated, in decreasing order of restrictiveness regarding COVID-19 mitigation measures. When masks were worn at school, work, and community environments, increasing in-person education from 50% to 100% would result in only 1% increase in cumulative infections. When there were no masks nor contact tracing while schools were 100% in person, the cumulative infection increased by 86% compared to the scenario when both masking and contact tracing were in place. In the sensitivity analysis for vaccination efficacy, we found that higher vaccination efficacy was essential in reducing overall infections. Our findings showed that full in-person education was safe, especially when contact tracing, masking, and widespread vaccination were in place. If no masking nor contact tracing was practiced, the transmission would rose dramatically but eventually slow down due to herd immunity.

An algebraic formula, deep learning and a novel SEIR-type model for the COVID-19 pandemic

The most extensively used mathematical models in epidemiology are the susceptible-exposed-infectious-recovered (SEIR) type models with constant coefficients. For the first wave of the COVID-19 epidemic, such models predict that at large times equilibrium is reached exponentially. However, epidemiological data from Europe suggest that this approach is algebraic. Indeed, accurate long-term predictions have been obtained via a forecasting model only if it uses an algebraic as opposed to the standard exponential formula. In this work, by allowing those parameters of the SEIR model that reflect behavioural aspects (e.g. spatial distancing) to vary nonlinearly with the extent of the epidemic, we construct a model which exhibits asymptoticly algebraic behaviour. Interestingly, the emerging power law is consistent with the typical dynamics observed in various social settings. In addition, using reliable epidemiological data, we solve in a numerically robust way the inverse problem of determining all model parameters characterizing our novel model. Finally, using deep learning, we demonstrate that the algebraic forecasting model used earlier is optimal.

The use of networks in spatial and temporal computational models for outbreak spread in epidemiology: A systematic review

OBJECTIVES

To examine recent literature in order to present a comprehensive overview of the current trends as regards the computational models used to represent the propagation of an infectious outbreak in a population, paying particular attention to those that represent network-based transmission.

METHODS

a systematic review was conducted following the PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) guidelines. Papers published in English between 2010 and September 2021 were sought in the ACM Digital Library, IEEE Xplore, PubMed and Scopus databases.

RESULTS

Upon considering their titles and abstracts, 832 papers were obtained, of which 192 were selected for a full content-body check. Of these, 112 studies were eventually deemed suitable for quantitative and qualitative analysis. Emphasis was placed on the spatial and temporal scales studied, the use of networks or graphs, and the granularity of the data used to evaluate the models. The models principally used to represent the spreading of outbreaks have been stochastic (55.36%), while the type of networks most frequently used are relationship networks (32.14%). The most common spatial dimension used is a region (19.64%) and the most used unit of time is a day (28.57%). Synthetic data as opposed to an external source were used in 51.79% of the papers. With regard to the granularity of the data sources, aggregated data such as censuses or transportation surveys are the most common.

CONCLUSION

We identified a growing interest in the use of networks to represent disease transmission. We detected that research is focused on only certain combinations of the computational model, type of network (in both the expressive and the structural sense) and spatial scale, while the search for other interesting combinations has been left for the future.

Inferring ASF transmission in domestic pigs and wild boars using a paired model iterative approach

The rapid spread of African swine fever (ASF) in recent years has once again raised awareness of the need to improve our preparedness in preventing and managing outbreaks, for which modelling-based forecasts can play an important role. This is even more important in the case of a disease such as ASF, involving several types of hosts, characterised by a high case-fatality rate and for which there is currently no treatment or vaccine. Within the framework of the ASF challenge, we proposed a modelling approach based on a stochastic mechanistic model and an inference procedure to estimate key transmission parameters from provided data (incomplete and noisy) and generate forecasts for unobserved time horizons. The model is partly data driven and composed of two modules, corresponding to epidemic and demographic dynamics in domestic pig and wild boar (WB) populations, interconnected through the networks of animal trade and/or spatial proximity. The inference consists in an iterative procedure, alternating between the two models and based on a criterion optimisation. Estimates of transmission and detection parameters appeared to be of similar magnitude for each of the three periods of the challenge, except for the transmission rates in WB population through contact with infectious individuals and carcasses, higher during the first period. The predicted number of infected domestic pig farms was in overall agreement with the data. The proportion of positive tested WB was overestimated, but with a trend close to that observed in the data. Comparison of the spatial simulated and observed distributions of detected cases also showed an overestimation of the spread of the pathogen within WB metapopulation. Beyond the quantitative results and the inherent difficulties of real-time forecasting, we built a modelling framework that is flexible enough to accommodate changes in transmission processes and control measures that may occur during an epidemic emergency.

On regime changes of COVID-19 outbreak

The COVID-19 pandemic has had a very serious impact on societies and caused large-scale economic changes and death toll worldwide. The first cases were detected in China, but soon the virus spread quickly worldwide and the intensity of newly reported infections grew high during this initial period almost everywhere. Later, despite all imposed measures, the intensity shifted abruptly multiple times during the two-year period between 2020 and 2022 causing waves of too high infection rates in almost every part of the world. To target this problem, we assume the data heterogeneity as multiple consecutive regime changes. The research study includes the development of a model based on automatic regime change detection and their combination with the linear birth-death process for long-run data fits. The results are empirically verified on data for 38 countries and US states for the period from February 2020 to April 2022. Finally, the initial phase (conditions) properties of infection development are studied.

Mobility decisions, economic dynamics and epidemic

We propose a model, which nests a susceptible-infected-recovered-deceased (SIRD) epidemic model into a dynamic macroeconomic equilibrium framework with agents' mobility. The latter affect both their income and their probability of infecting and being infected. Strategic complementarities among individual mobility choices drive the evolution of aggregate economic activity, while infection externalities caused by individual mobility affect disease diffusion. The continuum of rational forward-looking agents coordinates on the Nash equilibrium of a discrete time, finite-state, infinite-horizon Mean Field Game. We prove the existence of an equilibrium and provide a recursive construction method for the search of an equilibrium(a), which also guides our numerical investigations. We calibrate the model by using Italian experience on COVID-19 epidemic and we discuss policy implications.

Comparing Short-Term Univariate and Multivariate Time-Series Forecasting Models in Infectious Disease Outbreak

Predicting infectious disease outbreak impacts on population, healthcare resources and economics and has received a special academic focus during coronavirus (COVID-19) pandemic. Focus on human disease outbreak prediction techniques in current literature, Marques et al. (Predictive models for decision support in the COVID-19 crisis. Springer, Switzerland, 2021) state that there are four main methods to address forecasting problem: compartmental models, classic statistical models, space-state models and machine learning models. We adopt their framework to compare our research with previous works. Besides being divided by methods, forecasting problems can also be divided by the number of variables that are considered to make predictions. Considering this number of variables, forecasting problems can be classified as univariate, causal and multivariate models. Multivariate approaches have been applied in less than 10% of research found. This research is the first attempt to evaluate, over real time-series data of 3 different countries with univariate and multivariate methods to provide a short-term prediction. In literature we found no research with that scope and aim. A comparison of univariate and multivariate methods has been conducted and we concluded that besides the strong potential of multivariate methods, in our research univariate models presented best results in almost all regions' predictions.

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.

Strain-stream model of epidemic spread in application to COVID-19

ABSTRACT

The recently developed model of the epidemic spread of two virus strains in a closed population is generalized to the situation typical for the couple of strains delta and omicron, when there is a high probability of omicron infection soon enough after recovering from delta infection. This model can be considered as a kind of combination of SIR and SIS models for the case of competition of two strains of the same virus with different contagiousness in a population. The obtained equations and results can be directly implemented for practical calculations of the replacement of strains of the SARS-CoV-2 virus. A comparison between the estimated replacement time and the corresponding statistics shows reasonable agreement.

Spatial proliferation of African swine fever virus in South Korea

The African swine fever virus (ASFV) was first detected in South Korea on a pig farm in September 2019. Despite active preventive measures to control the spread of ASFV, outbreaks on pig farms and in wild boar have been increasing. In this study, we investigated the spatial contamination area using the minimum convex polygon (MCP) approach, and growth rate using a logistic diffusion model. On the basis of the ASFV outbreak locations recorded from September 17^th, 2019, to May 20^th, 2022, the MCP area for the second week was 618.41 km² and expanded to 37959.67 km² in the final week. The maximum asymptote of the logistic function was considered as the land area of South Korea, and we estimated logistic growth rates of 0.022 km² per week and 0.094 km² per month. Administrative bodies should implement preventive and quarantine measures for infectious diseases. The results of this study will be a reference for epidemiologists, ecologists, and policy makers and contribute to the establishment of appropriate quarantine measures for disease control and management.

Spatial Methods for Inferring Extremes in Dengue Outbreak Risk in Singapore

Dengue is a major vector-borne disease worldwide. Here, we examined the spatial distribution of extreme weekly dengue outbreak risk in Singapore from 2007 to 2020. We divided Singapore into equal-sized hexagons with a circumradius of 165 m and obtained the weekly number of dengue cases and the surface characteristics of each hexagon. We accounted for spatial heterogeneity using max-stable processes. The 5-, 10-, 20-, and 30-year return levels, or the weekly dengue case counts expected to be exceeded once every 5, 10, 20, and 30 years, respectively, were determined for each hexagon conditional on their surface characteristics remaining constant over time. The return levels were higher in the country's east, with the maximum weekly dengue cases per hexagon expected to exceed 51 at least once in 30 years in many areas. The surface characteristics with the largest impact on outbreak risk were the age of public apartments and the percentage of impervious surfaces, where a 3-year and 10% increase in each characteristic resulted in a 3.8% and 3.3% increase in risk, respectively. Vector control efforts should be prioritized in older residential estates and places with large contiguous masses of built-up environments. Our findings indicate the likely scale of outbreaks in the long term.

ModInterv: An automated online software for modeling epidemics

The COVID-19 pandemic has proven the importance of mathematical tools to understand the evolution of epidemic outbreaks and provide reliable information to the general public and health authorities. In this perspective, we have developed ModInterv, an online software that applies growth models to monitor the evolution of the COVID-19 epidemic in locations chosen by the user among countries worldwide or states and cities in the USA or Brazil. This paper describes the software capabilities and its use both in recent research works and by technical committees assisting government authorities. Possible applications to other epidemics are also briefly discussed.

The stochastic world of emerging viruses

The acquisition of new hosts is a fundamental mechanism by which parasitic organisms expand their host range and perpetuate themselves on an evolutionary scale. Among pathogens, viruses, due to their speed of evolution, are particularly efficient in producing new emergence events. However, even though these phenomena are particularly important to the human species and therefore specifically studied, the processes of virus emergence in a new host species are very complex and difficult to comprehend in their entirety. In order to provide a structured framework for understanding emergence in a species (including humans), a comprehensive qualitative model is an indispensable cornerstone. This model explicitly describes all the stages necessary for a virus circulating in the wild to come to the crossing of the epidemic threshold. We have therefore developed a complete descriptive model explaining all the steps necessary for a virus circulating in host populations to emerge in a new species. This description of the parameters presiding over the emergence of a new virus allows us to understand their nature and importance in the emergence process.

Optimal lockdowns

This paper provides a framework for understanding optimal lockdowns and makes three contributions. First, it theoretically analyzes lockdown policies and argues that policy makers systematically enact too strict lockdowns because their incentives are misaligned with achieving desired ends and they cannot adapt to changing circumstances. Second, it provides a benchmark to determine how strongly policy makers in different locations should respond to COVID-19. Finally, it provides a framework for understanding how, when, and why lockdown policy is expected to change.

Cattle transport network predicts endemic and epidemic foot-and-mouth disease risk on farms in Turkey

The structure of contact networks affects the likelihood of disease spread at the population scale and the risk of infection at any given node. Though this has been well characterized for both theoretical and empirical networks for the spread of epidemics on completely susceptible networks, the long-term impact of network structure on risk of infection with an endemic pathogen, where nodes can be infected more than once, has been less well characterized. Here, we analyze detailed records of the transportation of cattle among farms in Turkey to characterize the global and local attributes of the directed—weighted shipments network between 2007-2012. We then study the correlations between network properties and the likelihood of infection with, or exposure to, foot-and-mouth disease (FMD) over the same time period using recorded outbreaks. The shipments network shows a complex combination of features (local and global) that have not been previously reported in other networks of shipments; i.e. small-worldness, scale-freeness, modular structure, among others. We find that nodes that were either infected or at high risk of infection with FMD (within one link from an infected farm) had disproportionately higher degree, were more central (eigenvector centrality and coreness), and were more likely to be net recipients of shipments compared to those that were always more than 2 links away from an infected farm. High in-degree (i.e. many shipments received) was the best univariate predictor of infection. Low in-coreness (i.e. peripheral nodes) was the best univariate predictor of nodes always more than 2 links away from an infected farm. These results are robust across the three different serotypes of FMD observed in Turkey and during periods of low-endemic prevalence and high-prevalence outbreaks.

Contact network epidemiology has been extensively used in the context of infectious diseases, primarily focusing on epidemic diseases. In this paper we use detailed recorded data about cattle exchange between farms in Turkey from 2007 to 2012, to build, analyze and characterize the directed-weighted complex network of shipments of cattle. Additionally, using outbreaks data about recorded cases of foot-and-mouth disease (FMD) in Turkey, we assess the correlation between the “farm’s” position in the network (importance) and the risk of being infected with FMD, which has been endemic in Turkey for a long time. We find some network measures that are more likely to identify high-risk and low-risk farms (in-degree and in-coreness, respectively) when proposing strategies for surveillance or containment of an infectious disease.

Effects of human mobility and behavior on disease transmission in a COVID-19 mathematical model

Human interactions and perceptions about health risk are essential to understand the evolution over the course of a pandemic. We present a Susceptible-Exposed-Asymptomatic-Infectious-Recovered-Susceptible mathematical model with quarantine and social-distance-dependent transmission rates, to study COVID-19 dynamics. Human activities are split across different location settings: home, work, school, and elsewhere. Individuals move from home to the other locations at rates dependent on their epidemiological conditions and maintain a social distancing behavior, which varies with their location. We perform simulations and analyze how distinct social behaviors and restrictive measures affect the dynamic of the disease within a population. The model proposed in this study revealed that the main focus on the transmission of COVID-19 is attributed to the “home” location setting, which is understood as family gatherings including relatives and close friends. Limiting encounters at work, school and other locations will only be effective if COVID-19 restrictions occur simultaneously at all those locations and/or contact tracing or social distancing measures are effectively and strictly implemented, especially at the home setting.

Generic approach for mathematical model of multi-strain pandemics

Multi-strain pandemics have emerged as a major concern. We introduce a new model for assessing the connection between multi-strain pandemics and mortality rate, basic reproduction number, and maximum infected individuals. The proposed model provides a general mathematical approach for representing multi-strain pandemics, generalizing for an arbitrary number of strains. We show that the proposed model fits well with epidemiological historical world health data over a long time period. From a theoretical point of view, we show that the increasing number of strains increases logarithmically the maximum number of infected individuals and the mean mortality rate. Moreover, the mean basic reproduction number is statistically identical to the single, most aggressive pandemic strain for multi-strain pandemics.

An Easy-to-Use Public Health-Driven Method (the Generalized Logistic Differential Equation Model) Accurately Simulated COVID-19 Epidemic in Wuhan and Correctly Determined the Early Warning Time

Introduction

Modeling on infectious diseases is significant to facilitate public health policymaking. There are two main mathematical methods that can be used for the simulation of the epidemic and prediction of optimal early warning timing: the logistic differential equation (LDE) model and the more complex generalized logistic differential equation (GLDE) model. This study aimed to compare and analyze these two models.

Methods

We collected data on (coronavirus disease 2019) COVID-19 and four other infectious diseases and classified the data into four categories: different transmission routes, different epidemic intensities, different time scales, and different regions, using R2 to compare and analyze the goodness-of-fit of LDE and GLDE models.

Results

Both models fitted the epidemic curves well, and all results were statistically significant. The R2 test value of COVID-19 was 0.924 (p < 0.001) fitted by the GLDE model and 0.916 (p < 0.001) fitted by the LDE model. The R2 test value varied between 0.793 and 0.966 fitted by the GLDE model and varied between 0.594 and 0.922 fitted by the LDE model for diseases with different transmission routes. The R2 test values varied between 0.853 and 0.939 fitted by the GLDE model and varied from 0.687 to 0.769 fitted by the LDE model for diseases with different prevalence intensities. The R2 test value varied between 0.706 and 0.917 fitted by the GLDE model and varied between 0.410 and 0.898 fitted by the LDE model for diseases with different time scales. The GLDE model also performed better with nation-level data with the R2 test values between 0.897 and 0.970 vs. 0.731 and 0.953 that fitted by the LDE model. Both models could characterize the patterns of the epidemics well and calculate the acceleration weeks.

Conclusion

The GLDE model provides more accurate goodness-of-fit to the data than the LDE model. The GLDE model is able to handle asymmetric data by introducing shape parameters that allow it to fit data with various distributions. The LDE model provides an earlier epidemic acceleration week than the GLDE model. We conclude that the GLDE model is more advantageous in asymmetric infectious disease data simulation.

An investigation of spatial-temporal patterns and predictions of the coronavirus 2019 pandemic in Colombia, 2020-2021

Colombia announced the first case of severe acute respiratory syndrome coronavirus 2 on March 6, 2020. Since then, the country has reported a total of 5,002,387 cases and 127,258 deaths as of October 31, 2021. The aggressive transmission dynamics of SARS-CoV-2 motivate an investigation of COVID-19 at the national and regional levels in Colombia. We utilize the case incidence and mortality data to estimate the transmission potential and generate short-term forecasts of the COVID-19 pandemic to inform the public health policies using previously validated mathematical models. The analysis is augmented by the examination of geographic heterogeneity of COVID-19 at the departmental level along with the investigation of mobility and social media trends. Overall, the national and regional reproduction numbers show sustained disease transmission during the early phase of the pandemic, exhibiting sub-exponential growth dynamics. Whereas the most recent estimates of reproduction number indicate disease containment, with Rt<1.0 as of October 31, 2021. On the forecasting front, the sub-epidemic model performs best at capturing the 30-day ahead COVID-19 trajectory compared to the Richards and generalized logistic growth model. Nevertheless, the spatial variability in the incidence rate patterns across different departments can be grouped into four distinct clusters. As the case incidence surged in July 2020, an increase in mobility patterns was also observed. On the contrary, a spike in the number of tweets indicating the stay-at-home orders was observed in November 2020 when the case incidence had already plateaued, indicating the pandemic fatigue in the country.

In search of peak human athletic potential: A mathematical investigation

This paper applies existing and new approaches to study trends in the performance of elite athletes over time. We study both track and field scores of men and women athletes on a yearly basis from 2001 to 2019, revealing several trends and findings. First, we perform a detailed regression study to reveal the existence of an "Olympic effect," where average performance improves during Olympic years. Next, we study the rate of change in athlete performance and fail to reject the notion that athlete scores are leveling off, at least among the top 100 annual scores. Third, we examine the relationship in performance trends among men and women's categories of the same event, revealing striking similarity, together with some anomalous events. Finally, we analyze the geographic composition of the world's top athletes, attempting to understand how the diversity by country and continent varies over time across events. We challenge a widely held conception of athletics that certain events are more geographically dominated than others. Our methods and findings could be applied more generally to identify evolutionary dynamics in group performance and highlight spatiotemporal trends in group composition.

A Survey on Mathematical, Machine Learning and Deep Learning Models for COVID-19 Transmission and Diagnosis

COVID-19 is a life threatening disease which has a enormous global impact. As the cause of the disease is a novel coronavirus whose gene information is unknown, drugs and vaccines are yet to be found. For the present situation, disease spread analysis and prediction with the help of mathematical and data driven model will be of great help to initiate prevention and control action, namely lockdown and qurantine. There are various mathematical and machine-learning models proposed for analyzing the spread and prediction. Each model has its own limitations and advantages for a particluar scenario. This article reviews the state-of-the art mathematical models for COVID-19, including compartment models, statistical models and machine learning models to provide more insight, so that an appropriate model can be well adopted for the disease spread analysis. Furthermore, accurate diagnose of COVID-19 is another essential process to identify the infected person and control further spreading. As the spreading is fast, there is a need for quick auotomated diagnosis mechanism to handle large population. Deep-learning and machine-learning based diagnostic mechanism will be more appropriate for this purpose. In this aspect, a comprehensive review on the deep learning models for the diagnosis of the disease is also provided in this article.

An interpretation of COVID-19 in Tokyo using a combination of SIR models

A year and a half has passed since the outbreak of the COVID-19 pandemic. Mathematical models to predict infection are expected and many studies have been conducted. In this study, a new interpretation was created that could reproduce the daily positive cases in Tokyo using only a simple SIR model. In addition, the data on the ratio of transfer to delta variants could also be simulated. It is anticipated that this interpretation will be a basis for the development of forecasting methods.

Estimating a continuously varying offset between multivariate time series with application to COVID-19 in the United States

This paper introduces new methods to track the offset between two multivariate time series on a continuous basis. We then apply this framework to COVID-19 counts on a state-by-state basis in the United States to determine the progression from cases to deaths as a function of time. Across multiple approaches, we reveal an "up-down-up" pattern in the estimated offset between reported cases and deaths as the pandemic progresses. This analysis could be used to predict imminent increased load on a healthcare system and aid the allocation of additional resources in advance.

Modeling Early Phases of COVID-19 Pandemic in Northern Italy and Its Implication for Outbreak Diffusion

The COVID-19 pandemic has sparked an intense debate about the hidden factors underlying the dynamics of the outbreak. Several computational models have been proposed to inform effective social and healthcare strategies. Crucially, the predictive validity of these models often depends upon incorporating behavioral and social responses to infection. Among these tools, the analytic framework known as “dynamic causal modeling” (DCM) has been applied to the COVID-19 pandemic, shedding new light on the factors underlying the dynamics of the outbreak. We have applied DCM to data from northern Italian regions, the first areas in Europe to contend with the outbreak, and analyzed the predictive validity of the model and also its suitability in highlighting the hidden factors governing the pandemic diffusion. By taking into account data from the beginning of the pandemic, the model could faithfully predict the dynamics of outbreak diffusion varying from region to region. The DCM appears to be a reliable tool to investigate the mechanisms governing the spread of the SARS-CoV-2 to identify the containment and control strategies that could efficiently be used to counteract further waves of infection.

Collective Reactions to Epidemic Threat: Attachment and Cultural Orientations Predict Early COVID-19 Infection and Mortality Rates and Trajectories

Hypotheses on culture-level attachment and individualism/collectivism relationships with COVID-19 infection and death rates during a period at the beginning of the epidemic were tested in data from 53 countries and 50 U.S. states. Results from multilevel growth curve analyses showed group-average anxious attachment predicted a lower initial number of cases and deaths cross-culturally and in the United States, while avoidant attachment predicted a higher initial number of COVID-19 infections in the United States and a higher initial number of deaths in both studies. Yet, during this period, culture-level anxious attachment was associated with a higher growth rate of infections and deaths, while a lower growth rate of infections and deaths was observed in countries and U.S. states with higher individualism and avoidance. The research provides new insights into attachment and culture relationships and points to different mechanisms that may explain initial and growth rate trajectories at the beginning of the epidemic.

The epidemic volatility index, a novel early warning tool for identifying new waves in an epidemic

Early warning tools are crucial for the timely application of intervention strategies and the mitigation of the adverse health, social and economic effects associated with outbreaks of epidemic potential such as COVID-19. This paper introduces, the Epidemic Volatility Index (EVI), a new, conceptually simple, early warning tool for oncoming epidemic waves. EVI is based on the volatility of newly reported cases per unit of time, ideally per day, and issues an early warning when the volatility change rate exceeds a threshold. Data on the daily confirmed cases of COVID-19 are used to demonstrate the use of EVI. Results from the COVID-19 epidemic in Italy and New York State are presented here, based on the number of confirmed cases of COVID-19, from January 22, 2020, until April 13, 2021. Live daily updated predictions for all world countries and each of the United States of America are publicly available online. For Italy, the overall sensitivity for EVI was 0.82 (95% Confidence Intervals: 0.75; 0.89) and the specificity was 0.91 (0.88; 0.94). For New York, the corresponding values were 0.55 (0.47; 0.64) and 0.88 (0.84; 0.91). Consecutive issuance of early warnings is a strong indicator of main epidemic waves in any country or state. EVI’s application to data from the current COVID-19 pandemic revealed a consistent and stable performance in terms of detecting new waves. The application of EVI to other epidemics and syndromic surveillance tasks in combination with existing early warning systems will enhance our ability to act swiftly and thereby enhance containment of outbreaks.

Mobility Choices and Strategic Interactions in a Two-Group Macroeconomic-Epidemiological Model

We analyze the implications of strategic interactions between two heterogeneous groups (i.e., young and old, men and women) in a macroeconomic-epidemiological framework. The interactions between groups determine the overall prevalence of a communicable disease, which in turn affects the level of economic activity. Individuals may lower their disease exposure by reducing their mobility, but since changing mobility patterns is costly, each group has an incentive to free ride negatively affecting the chances of disease containment at the aggregate level. By focusing on an early epidemic setting, we explicitly characterize the cooperative and noncooperative equilibria, determining how the inefficiency induced by noncooperation (i.e., failure to internalize epidemic externalities) depends both on economic and epidemiological parameters. We show that long-run eradication may be possible even in the absence of coordination, but coordination leads to a faster reduction in the number of infectives in finite time. Moreover, the inefficiency induced by noncooperation increases (decreases) with the factors increasing (decreasing) the pace of the disease spread.

Biomodeling for Controlling the Spread of Coronavirus 2019

Wuhan has informed an outbreak of a typical lungs infection created by the 2019 novel coronavirus (2019-nCoV) in December 2019. Infections have been consigned to other cities, along with internationally which aggressing to trigger a global epidemic. In the past four years, coronavirus infections have become the most dangerous infections since of the event of some fresh deaths caused by corona infections in Saudi Arabia. Coronavirus infections may be planted in and spread out of Saudi Arabia by inbound and outbound Umrah visitors and non-Umrah visitors. The impact of fundamental reproductive number and zoonotic strength of infectivity on susceptible, exposed and infected peoples rate was assessed using Runge–Kutta–Felhberg strategy with shooting method. In this investigation, the vulnerable people's rate is significantly climbing in the brief interval of period owing to overwhelming and mean inactive period. Our examination shows the transmissibility of coronavirus is more grounded as contrasted and the Asia continent countries respiratory confusion. Middle East Respiratory Syndrome coronavirus is already spread in creature and human pools in Ethiopia. The Severe Acute Respiratory Syndrome coronavirus-2 growth in the Saudi Arabia may have a solemn crash on genetic assortment, interspecies circulation of these infections mostly with the reference to the alteration and recombination expectation of coronaviruses. Researches of the molecular mechanisms and genetics of this infection are provided in the component can act an important part of this project to follow tactics to prevent subsequent coronavirus outbreak.

A multi-scale agent-based model of infectious disease transmission to assess the impact of vaccination and non-pharmaceutical interventions: The COVID-19 case

Mathematical and computational models are useful tools for virtual policy experiments on infectious disease control. Most models fail to provide flexible and rapid simulation of various epidemic scenarios for policy assessment. This paper establishes a multi-scale agent-based model to investigate the infectious disease propagation between cities and within a city using the knowledge from person-to-person transmission. In the model, the contact and infection of individuals at the micro scale where an agent represents a person provide insights for the interactions of agents at the meso scale where an agent refers to hundreds of individuals. Four cities with frequent population movements in China are taken as an example and actual data on traffic patterns and demographic parameters are adopted. The scenarios for dynamic propagation of infectious disease with no external measures are compared versus the scenarios with vaccination and non-pharmaceutical interventions. The model predicts that the peak of infections will decline by 67.37% with 80% vaccination rate, compared to a drop of 89.56% when isolation and quarantine measures are also in place. The results highlight the importance of controlling the source of infection by isolation and quarantine throughout the epidemic. We also study the effect when cities implement inconsistent public health interventions, which is common in practical situations. Based on our results, the model can be applied to COVID-19 and other infectious diseases according to the various needs of government agencies.

A runtime alterable epidemic model with genetic drift, waning immunity and vaccinations

We present methods for building a Java Runtime-Alterable-Model Platform (RAMP) of complex dynamical systems. We illustrate our methods by building a multivariant SEIR (epidemic) RAMP. Underlying our RAMP is an individual-based model that includes adaptive contact rates, pathogen genetic drift, waning and cross-immunity. Besides allowing parameter values, process descriptions and scriptable runtime drivers to be easily modified during simulations, our RAMP can used within R-Studio and other computational platforms. Process descriptions that can be runtime altered within our SEIR RAMP include pathogen variant-dependent host shedding, environmental persistence, host transmission and within-host pathogen mutation and replication. They also include adaptive social distancing and adaptive application of vaccination rates and variant-valency of vaccines. We present simulation results using parameter values and process descriptions relevant to the current COVID-19 pandemic. Our results suggest that if waning immunity outpaces vaccination rates, then vaccination rollouts may fail to contain the most transmissible variants, particularly if vaccine valencies are not adapted to deal with escape mutations. Our SEIR RAMP is designed for easy use by others. More generally, our RAMP concept facilitates construction of highly flexible complex systems models of all types, which can then be easily shared as stand-alone application programs.

A comparative study of SIR Model, Linear Regression, Logistic Function and ARIMA Model for forecasting COVID-19 cases

Starting February 2020, COVID-19 was confirmed in 11,946 people worldwide, with a mortality rate of almost 2%. A significant number of epidemic diseases consisting of human Coronavirus display patterns. In this study, with the benefit of data analytic, we develop regression models and a Susceptible-Infected-Recovered (SIR) model for the contagion to compare the performance of models to predict the number of cases. First, we implement a good understanding of data and perform Exploratory Data Analysis (EDA). Then, we derive parameters of the model from the available data corresponding to the top 4 regions based on the history of infections and the most infected people as of the end of August 2020. Then models are compared, and we recommend further research.

A model for social spreading of Covid-19: Cases of Mexico, Finland and Iceland

The shocking severity of the Covid-19 pandemic has woken up an unprecedented interest and accelerated effort of the scientific community to model and forecast epidemic spreading to find ways to control it regionally and between regions. Here we present a model that in addition to describing the dynamics of epidemic spreading with the traditional compartmental approach takes into account the social behaviour of the population distributed over a geographical region. The region to be modelled is defined as a two-dimensional grid of cells, in which each cell is weighted with the population density. In each cell a compartmental SEIRS system of delay difference equations is used to simulate the local dynamics of the disease. The infections between cells are modelled by a network of connections, which could be terrestrial, between neighbouring cells, or long range, between cities by air, road or train traffic. In addition, since people make trips without apparent reason, noise is considered to account for them to carry contagion between two randomly chosen distant cells. Hence, there is a clear separation of the parameters related to the biological characteristics of the disease from the ones that represent the spatial spread of infections due to social behaviour. We demonstrate that these parameters provide sufficient information to trace the evolution of the pandemic in different situations. In order to show the predictive power of this kind of approach we have chosen three, in a number of ways different countries, Mexico, Finland and Iceland, in which the pandemics have followed different dynamic paths. Furthermore we find that our model seems quite capable of reproducing the path of the pandemic for months with few initial data. Unlike similar models, our model shows the emergence of multiple waves in the case when the disease becomes endemic.

COVID-PA Bulletin: reports on artificial intelligence-based forecasting in coping with COVID-19 pandemic in the state of Pará, Brazil

OBJECTIVE

To report the university extension research result entitled 'The COVID-PA Bulletin', which presented forecasts on the behavior of the pandemic in the state of Pará, Brazil.

METHODS

The artificial intelligence technique also known as 'artificial neural networks' was used to generate 13 bulletins with short-term forecasts based on historical data from the State Department of Public Health information system.

RESULTS

After eight months of predictions, the technique generated reliable results, with an average accuracy of 97% (observed for147 days) for confirmed cases, 96% (observed for 161 days) for deaths and 86% (observed for 72 days) for Intensive Care Unit bed occupancy.

CONCLUSION

These bulletins have become a useful decision-making tool for public managers, assisting in the reallocation of hospital resources and optimization of COVID-19 control strategies in various regions of the state of Pará.

COVID-19 related interdisciplinary methods: Preventing errors and detecting research opportunities

More than 130,000 peer-reviewed studies have been published within one year after COVID-19 emerged in many countries. This large and rapidly growing field may overwhelm the synthesizing abilities of both researchers and policy-makers. To provide a sinopsis, prevent errors, and detect cognitive gaps that may require interdisciplinary research methods, the literature on COVID-19 is summarized, twice. The overall purpose of this study is to generate a dialogue meant to explain the genesis of and/or find remedies for omissions and contradictions. The first review starts in Biology and ends in Policy. Policy is chosen as a destination because it is the setting where cognitive integration must occur. The second review follows the opposite path: it begins with stated policies on COVID-19 and then their assumptions and disciplinary relationships are identified. The purpose of this interdisciplinary method on methods is to yield a relational and explanatory view of the field -one strategy likely to be incomplete but usable when large bodies of literature need to be rapidly summarized. These reviews identify nine inter-related problems, research needs, or omissions, namely: (1) nation-wide, geo-referenced, epidemiological data collection systems (open to and monitored by the public); (2) metrics meant to detect non-symptomatic cases -e.g., test positivity-; (3) cost-benefit oriented methods, which should demonstrate they detect silent viral spreaders even with limited testing; (4) new personalized tests that inform on biological functions and disease correlates, such as cell-mediated immunity, co-morbidities, and immuno-suppression; (5) factors that influence vaccine effectiveness; (6) economic predictions that consider the long-term consequences likely to follow epidemics that growth exponentially; (7) the errors induced by self-limiting and/or implausible paradigms, such as binary and reductionist approaches; (8) new governance models that emphasize problem-solving skills, social participation, and the use of scientific knowledge; and (9) new educational programs that utilize visual aids and audience-specific communication strategies. The analysis indicates that, to optimally address these problems, disciplinary and social integration is needed. By asking what is/are the potential cause(s) and consequence(s) of each issue, this methodology generates visualizations that reveal possible relationships as well as omissions and contradictions. While inherently limited in scope and likely to become obsolete, these shortcomings are avoided when this 'method on methods' is frequently practiced. Open-ended, inter-/trans-disciplinary perspectives and broad social participation may help researchers and citizens to construct, de-construct, and re-construct COVID-19 related research.

Modelling infectious diseases with herd immunity in a randomly mixed population

The conventional susceptible-infectious-recovered (SIR) model tends to magnify the transmission dynamics of infectious diseases, and thus the estimated total infections and immunized population may be higher than the threshold required for infection control and eradication. The study developed a new SIR framework that allows the transmission rate of infectious diseases to decline along with the reduced risk of contact infection to overcome the limitations of the conventional SIR model. Two new SIR models were formulated to mimic the declining transmission rate of infectious diseases at different stages of transmission. Model A utilized the declining transmission rate along with the reduced risk of contact infection following infection, while Model B incorporated the declining transmission rate following recovery. Both new models and the conventional SIR model were then used to simulate an infectious disease with a basic reproduction number (r₀) of 3.0 and a herd immunity threshold (HIT) of 0.667 with and without vaccination. Outcomes of simulations were assessed at the time when the total immunized population reached the level predicted by the HIT, and at the end of simulations. Further, all three models were used to simulate the transmission dynamics of seasonal influenza in the United States and disease burdens were projected and compared with estimates from the Centers for Disease Control and Prevention. For the simulated infectious disease, in the initial phase of the outbreak, all three models performed expectedly when the sizes of infectious and recovered populations were relatively small. As the infectious population increased, the conventional SIR model appeared to overestimate the infections even when the HIT was achieved in all scenarios with and without vaccination. For the same scenario, Model A appeared to attain the level predicted by the HIT and in comparison, Model B projected the infectious disease to be controlled at the level predicted by the HIT only at high vaccination rates. For infectious diseases with high r₀, and at low vaccination rates, the level at which the infectious disease was controlled cannot be accurately predicted by the current theorem. Transmission dynamics of infectious diseases with herd immunity can be accurately modelled by allowing the transmission rate of infectious diseases to decline along with the reduction of contact infection risk after recovery or vaccination. Model B provides a credible framework for modelling infectious diseases with herd immunity in a randomly mixed population.

Change sign detection with differential MDL change statistics and its applications to COVID-19 pandemic analysis

We are concerned with the issue of detecting changes and their signs from a data stream. For example, when given time series of COVID-19 cases in a region, we may raise early warning signals of an epidemic by detecting signs of changes in the data. We propose a novel methodology to address this issue. The key idea is to employ a new information-theoretic notion, which we call the differential minimum description length change statistics (D-MDL), for measuring the scores of change sign. We first give a fundamental theory for D-MDL. We then demonstrate its effectiveness using synthetic datasets. We apply it to detecting early warning signals of the COVID-19 epidemic using time series of the cases for individual countries. We empirically demonstrate that D-MDL is able to raise early warning signals of events such as significant increase/decrease of cases. Remarkably, for about [Formula: see text] of the events of significant increase of cases in studied countries, our method can detect warning signals as early as nearly six days on average before the events, buying considerably long time for making responses. We further relate the warning signals to the dynamics of the basic reproduction number R0 and the timing of social distancing. The results show that our method is a promising approach to the epidemic analysis from a data science viewpoint.

A farewell to R: time-series models for tracking and forecasting epidemics

The time-dependent reproduction number, R_t, is a key metric used by epidemiologists to assess the current state of an outbreak of an infectious disease. This quantity is usually estimated using time-series observations on new infections combined with assumptions about the distribution of the serial interval of transmissions. Bayesian methods are often used with the new cases data smoothed using a simple, but to some extent arbitrary, moving average. This paper describes a new class of time-series models, estimated by classical statistical methods, for tracking and forecasting the growth rate of new cases and deaths. Very few assumptions are needed and those that are made can be tested. Estimates of R_t, together with their standard deviations, are obtained as a by-product.

Rational evaluation of various epidemic models based on the COVID-19 data of China

In this paper, based on the Akaike information criterion, root mean square error and robustness coefficient, a rational evaluation of various epidemic models/methods, including seven empirical functions, four statistical inference methods and five dynamical models, on their forecasting abilities is carried out. With respect to the outbreak data of COVID-19 epidemics in China, we find that before the inflection point, all models fail to make a reliable prediction. The Logistic function consistently underestimates the final epidemic size, while the Gompertz’s function makes an overestimation in all cases. Towards statistical inference methods, the methods of sequential Bayesian and time-dependent reproduction number are more accurate at the late stage of an epidemic. And the transition-like behavior of exponential growth method from underestimation to overestimation with respect to the inflection point might be useful for constructing a more reliable forecast. Compared to ODE-based SIR, SEIR and SEIR-AHQ models, the SEIR-QD and SEIR-PO models generally show a better performance on studying the COVID-19 epidemics, whose success we believe could be attributed to a proper trade-off between model complexity and fitting accuracy. Our findings not only are crucial for the forecast of COVID-19 epidemics, but also may apply to other infectious diseases.

A spatial epidemic model with a moving boundary

We present a new mathematical model to investigate the spatial spread of an infectious disease. The model consists of a nonlinear PDE system with an unknown velocity field, defined on an epidemic domain that changes with time. The moving boundary of the domain represents the wavefront of the epidemic. We conduct an equilibrium analysis to the simplified models represented by ODE systems. We also perform a numerical study on the original PDE system for a range of scenarios, including one under a realistic epidemic setting.

An Ecological Study Assessing the Relationship between Public Health Policies and Severity of the COVID-19 Pandemic

Reliance on government-led policies have heightened during the COVID-19 pandemic. Further research on the policies associated with outcomes other than mortality rates remains warranted. We aimed to determine associations between government public health policies on the severity of the COVID-19 pandemic. This ecological study including countries reporting ≥25 daily COVID-related deaths until end May 2020, utilised public data on policy indicators described by the Blavatnik school of Government. Associations between policy indicators and severity of the pandemic (mean mortality rate, time to peak, peak deaths per 100,000, cumulative deaths after peak per 100,000 and ratio of mean slope of the descending curve to mean slope of the ascending curve) were measured using Spearman rank-order tests. Analyses were stratified for age, income and region. Among 22 countries, containment policies such as school closures appeared effective in younger populations (rs = -0.620, p = 0.042) and debt/contract relief in older populations (rs = -0.743, p = 0.009) when assessing peak deaths per 100,000. In European countries, containment policies were generally associated with good outcomes. In non-European countries, school closures were associated with mostly good outcomes (rs = -0.757, p = 0.049 for mean mortality rate). In high-income countries, health system policies were generally effective, contrasting to low-income countries. Containment policies may be effective in younger populations or in high-income or European countries. Health system policies have been most effective in high-income countries.

An Ecological Study Assessing the Relationship between Public Health Policies and Severity of the COVID-19 Pandemic

Reliance on government-led policies have heightened during the COVID-19 pandemic. Further research on the policies associated with outcomes other than mortality rates remains warranted. We aimed to determine associations between government public health policies on the severity of the COVID-19 pandemic. This ecological study including countries reporting ≥25 daily COVID-related deaths until end May 2020, utilised public data on policy indicators described by the Blavatnik school of Government. Associations between policy indicators and severity of the pandemic (mean mortality rate, time to peak, peak deaths per 100,000, cumulative deaths after peak per 100,000 and ratio of mean slope of the descending curve to mean slope of the ascending curve) were measured using Spearman rank-order tests. Analyses were stratified for age, income and region. Among 22 countries, containment policies such as school closures appeared effective in younger populations (r_s = -0.620, p = 0.042) and debt/contract relief in older populations (r_s = -0.743, p = 0.009) when assessing peak deaths per 100,000. In European countries, containment policies were generally associated with good outcomes. In non-European countries, school closures were associated with mostly good outcomes (r_s = -0.757, p = 0.049 for mean mortality rate). In high-income countries, health system policies were generally effective, contrasting to low-income countries. Containment policies may be effective in younger populations or in high-income or European countries. Health system policies have been most effective in high-income countries.