The severe acute respiratory syndrome COVID-19 has been in the center of the ongoing global health crisis in 2020. The high prevalence of mild cases facilitates sub-notification outside hospital environments and the number of those who are or have been infected remains largely unknown, leading to poor estimates of the crude mortality rate of the disease. Here we use a simple model to describe the number of accumulated deaths caused by COVID-19. The close connection between the proposed model and an approximate solution of the SIR model provides a system of equations whose solutions are robust estimates of epidemiological parameters. We find that the crude mortality varies between $10^{-4}$ and $10^{-3}$ depending on the severity of the outbreak which is lower than previous estimates obtained from laboratory confirmed patients. We also estimate quantities of practical interest such as the basic reproduction number and the expected number of deaths in the asymptotic limit with and without social distancing measures and lockdowns, which allow us to measure the efficiency of these interventions.
The death toll for Covid-19 may be reduced by dividing the population into two classes, the vulnerable and the fit, with different lockdown regimes. Instead of one reproduction number there now are four parameters. These make it possible to quantify the effect of the social distancing measures. There is a simple stochastic model for epidemics in a two type population. Apart from the size of the population of the vulnerable and the fit, and the initial number of infected in the two classes, only the four reproduction parameters are needed to run the two type Reed-Frost model. The program is sim…
Multiple epidemiological models have been proposed to predict the spread of Ebola in West Africa. These models include consideration of counter-measures meant to slow and, eventually, stop the spread of the disease. Here, we examine one component of Ebola dynamics that is of growing concern -- the transmission of Ebola from the dead to the living. We do so by applying the toolkit of mathematical epidemiology to analyze the consequences of post-death transmission. We show that underlying disease parameters cannot be inferred with confidence from early-stage incidence data (that is, they are not…
We shall apply a generalized SEIR model to study the outbreak of COVID-19 in Brazil. In particular, we would like to explain the projections of the increase in the level of infection over a long period of time, overlapping large local outbreaks in the most populous states in the country. A time-dependent dynamic SEIR model inspired in a model previously used during the outbreak in China was used to analyses the time trajectories of infected, recovered, and deaths. The model has parameters that vary with time and are fitted considering a nonlinear least-squares method. The simulations starting …
In this paper, we introduce a modified epidemic model on regular and scale-free networks respectively. We consider the birth rate $δ$, cure rate $γ$, infection rate $λ$, $α$ from the infectious disease, and death rate $β$ from other factors. Through mean-field analysis, we find that on regular network there is an epidemic threshold $λ_{c}$ dependent on the parameters $δ$, $γ$, $α$, and $β$; while for power law degree distribution network epidemic threshold is absent in the thermodynamic limit. The result is the same as that of the standard SIS model. This reminds us the structure of the networ…
In a given country, the cumulative death toll of the first wave of the COVID-19 epidemic follows a sigmoid curve as a function of time. In most cases, the curve is well described by the Gompertz function, which is characterized by two essential parameters, the initial growth rate and the decay rate as the first epidemic wave subsides. These parameters are determined by socioeconomic factors and the countermeasures to halt the epidemic. The Gompertz model implies that the total death toll depends exponentially, and hence very sensitively, on the ratio between these rates. The remarkably differe…
We are interested in describing the infected size of the SIS Epidemic model using Birth-Death Markov process. The Susceptible-Infected-Susceptible (SIS) model is defined within a population of constant size $M$; the size is kept constant by replacing each death with a newborn healthy individual. The life span of each individual in the population is modelled by an exponential distribution with parameter $α$; and the disease spreads within the population is modelled by a Poisson process with a rate $λ_{I}$. $λ_{I}=βI(1-\frac{I}{M}) $ is similar to the instantaneous rate in the logistic populatio…
In this paper, the exact analytical solution of the Susceptible-Infected-Recovered (SIR) epidemic model is obtained in a parametric form. By using the exact solution we investigate some explicit models corresponding to fixed values of the parameters, and show that the numerical solution reproduces exactly the analytical solution. We also show that the generalization of the SIR model, including births and deaths, described by a nonlinear system of differential equations, can be reduced to an Abel type equation. The reduction of the complex SIR model with vital dynamics to an Abel type equation …
We develop an agent-based model to assess the cumulative number of deaths during hypothetical Covid-19-like epidemics for various non-pharmaceutical intervention strategies. We consider local and non-local modes of disease transmission. The first simulates transmission through social contacts in the vicinity of the place of residence while the second through social contacts in public places: schools, hospitals, airports, etc., where many people meet, who live in remote geographic locations. Epidemic spreading is modeled as a discrete-time stochastic process on random geometric networks. We use…
Many countries are managing COVID-19 epidemic by switching between lighter and heavier restrictions. While an open-close and a close-open cycle have comparable socio-economic costs, the former leads to a much heavier burden in terms of deaths and pressure on the healthcare system. An empirical demonstration of the toll ensuing from procrastination was recently observed in Israel, where both cycles were enforced from late August to mid-December 2020, yielding some 1,600 deaths with open-close compared to 440 with close-open.
Within the context of SEIR models, we consider a lockdown that is both imposed and lifted at an early stage of an epidemic. We show that, in these models, although such a lockdown may delay deaths, it eventually does not avert a significant number of fatalities. Therefore, in these models, the efficacy of a lockdown cannot be gauged by simply comparing figures for the deaths at the end of the lockdown with the projected figure for deaths by the same date without the lockdown. We provide a simple but robust heuristic argument to explain why this conclusion should generalize to more elaborate co…
The SARS-CoV-2 pandemic has necessitated mitigation efforts around the world. We use only reported deaths in the two weeks after the first death to determine infection parameters, in order to make predictions of hidden variables such as the time dependence of the number of infections. Early deaths are sporadic and discrete so the use of network models of epidemic spread is imperative, with the network itself a crucial random variable. Location-specific population age distributions and population densities must be taken into account when attempting to fit these events with parametrized models. …
We are currently living in a state of uncertainty due to the pandemic caused by the Sars-CoV-2 virus. There are several factors involved in the epidemic spreading such as the individual characteristics of each city/country. The true shape of the epidemic dynamics is a large, complex system such as most of the social systems. In this context, Complex networks are a great candidate to analyze these systems due to their ability to tackle structural and dynamical properties. Therefore this study presents a new approach to model the COVID-19 epidemic using a multi-layer complex network, where nodes…
Background: Following the outbreak of the coronavirus epidemic in early 2020, municipalities, regional governments and policymakers worldwide had to plan their Non-Pharmaceutical Interventions (NPIs) amidst a scenario of great uncertainty. At this early stage of an epidemic, where no vaccine or medical treatment is in sight, algorithmic prediction can become a powerful tool to inform local policymaking. However, when we replicated one prominent epidemiological model to inform health authorities in a region in the south of Brazil, we found that this model relied too heavily on manually predeter…
We assess the impact of COVID-19 response measures implemented in Germany and Switzerland on cumulative COVID-19-related hospitalization and death rates. Our analysis exploits the fact that the epidemic was more advanced in some regions than in others when certain lockdown measures came into force, based on measuring health outcomes relative to the region-specific start of the epidemic and comparing outcomes across regions with earlier and later start dates. When estimating the effect of the relative timing of measures, we control for regional characteristics and initial epidemic trends by lin…
The reconstruction of phylogenetic trees based on viral genetic sequence data sequentially sampled from an epidemic provides estimates of the past transmission dynamics, by fitting epidemiological models to these trees. To our knowledge, none of the epidemiological models currently used in phylogenetics can account for recovery rates and sampling rates dependent on the time elapsed since transmission. Here we introduce an epidemiological model where infectives leave the epidemic, either by recovery or sampling, after some random time which may follow an arbitrary distribution. We derive an exp…
Objective: To conduct an early estimation of the Basic Reproduction Number (BRN) induced by government interference, and to project resulting day to day number of in-patients, ICU-patients and cumulative number of deaths in a Danish setting. Method: We used the Kermack and McKendrick model with varying basic reproduction number to estimate number infected and age stratified percentages to estimate number of in-patients, ICU-patients and cumulative number of deaths. Changes in basic reproduction number was estimated based on current in-patient numbers. Results: The basic reproductive number in …
The Covid-19 pandemic has made clear the need to improve modern multivariate time-series forecasting models. Current state of the art predictions of future daily deaths and, especially, hospital resource usage have confidence intervals that are unacceptably wide. Policy makers and hospitals require accurate forecasts to make informed decisions on passing legislation and allocating resources. We used US county-level data on daily deaths and population statistics to forecast future deaths. We extended the SIR epidemiological model to a novel model we call the PECAIQR model. It adds several new v…
Coronavirus disease (COVID-2019) is a severe ongoing novel pandemic that is spreading quickly across the world. Italy, that is widely considered one of the main epicenters of the pandemic, has registered the highest COVID-2019 death rates and death toll in the world, to the present day. In this article I estimate an autoregressive integrated moving average (ARIMA) model to forecast the epidemic trend over the period after April 4, 2020, by using the Italian epidemiological data at national and regional level. The data refer to the number of daily confirmed cases officially registered by the It…
The data analysis on deaths in the Lombardy Region and of both the provinces of Bergamo and Brescia shows a twofold aspect on the trend of the epidemic: - all the data show a bias linked to the event of March 10th (day for which the Lombardy region data is partial) and the subsequent change in the way in which positive cases and deaths are calculated; - following the containment measures of the Prime Minister's Decree of March 11th, the spread of the epidemic, although still exponential in nature, has a reduced multiplication coefficient. Our analysis concludes that the situation is not yet co…
In a previous article [1] we have described the temporal evolution of the Sars- Cov-2 in Italy in the time window February 24-April 1. As we can see in [1] a generalized logistic equation captures both the peaks of the total infected and the deaths. In this article our goal is to study the missing peak, i.e. the currently infected one (or total currently positive). After the April 7 the large increase in the number of swabs meant that the logistical behavior of the infected curve no longer worked. So we decided to generalize the model, introducing new parameters. Moreover, we adopt a similar a…
The goal of this work is to analyse the effects of control policies for the coronavirus (COVID-19) epidemic in Brazil. This is done by considering an age-structured SEIR model with a quarantine class and two types of controls. The first one studies the sensitivity with regard to the parameters of the basic reproductive number R0 which is calculated by the next generation method. The second one evaluates different quarantine strategies by comparing their relative total number of deaths.
In this paper, we propose a two-group SIR epidemic model to simulate the outcome of stay-at-home policy and wearing face masks during the first COVID-19 epidemic wave in the United States. Based on our proposed model, we further use the optimal control approach (with the objective of minimizing total deaths) to find the optimal dynamical distribution of face masks between the healthcare workers and the general public. It is not surprising that all the face masks should be solely reserved for the healthcare workers if the supply is short. However, when the supply is indeed sufficient, our numer…
The temporal growth in the number of deaths in the COVID-19 epidemic is subexponential. Here we show that a piecewise quadratic law provides an excellent fit during the thirty days after the first three fatalities on January 20 and later since the end of March 2020. There is also a brief intermediate period of exponential growth. During the second quadratic growth phase, the characteristic time of the growth is about eight times shorter than in the beginning, which can be understood as the occurrence of separate hotspots. Quadratic behavior can be motivated by peripheral growth when further sp…
The evolution of RNA viruses such as HIV, Hepatitis C and Influenza virus occurs so rapidly that the viruses' genomes contain information on past ecological dynamics. Hence, we develop a phylodynamic method that enables the joint estimation of epidemiological parameters and phylogenetic history. Based on a compartmental susceptible-infected-removed (SIR) model, this method provides separate information on incidence and prevalence of infections. Detailed information on the interaction of host population dynamics and evolutionary history can inform decisions on how to contain or entirely avoid d…
A new epidemic model for Covid-19 has been constructed and simulated for eight US states. The coefficients for this model, based on seven coupled differential equations, are carefully evaluated against recorded data on cases and deaths. These projections reveal that Covid-19 will become endemic, spreading for more than two years. If stay-at-home orders are relaxed, most states may experience a secondary peak in 2021. The number of Covid-19 deaths could have been significantly lower in most states that opened up, if lockdowns had been maintained. Additionally, our model predicts that decreasing…
We propose an SEIR-type meta-population model to simulate and monitor the Covid-19 epidemic evolution. The basic model consists of seven compartments, namely susceptible (S), exposed (E), three infective classes, recovered (R), and deceased (D). We define these compartments for n age and gender groups in m different spatial locations. So, the resulting model has, for each age group, gender, and place, all epidemiological classes. The mixing between them is accomplished by means of time-dependent infection rate matrices. The model is calibrated with the curve of daily new infections in New York…
We present Coronavirus disease 2019 (COVID-19) statistics in China dataset: daily statistics of the COVID-19 outbreak in China at the city/county level. For each city/country, we include the six most important numbers for epidemic research: daily new infections, accumulated infections, daily new recoveries, accumulated recoveries, daily new deaths, and accumulated deaths. We cross validate the dataset and the estimate error rate is about 0.04%. We then give several examples to show how to trace the spreading in particular cities or provinces, and also contrast the development of COVID-19 in al…
In this paper we develop a predictive model for the spread of COVID-19 infection at a provincial (i.e. EU NUTS-3) level in Italy by using official data from the Italian Ministry of Health integrated with data extracted from daily official press conferences of regional authorities and from local newspaper websites. This integration is mainly concerned with COVID-19 cause specific death data which are not available at NUTS-3 level from open official data data channels. An adjusted time-dependent SIRD model is used to predict the behavior of the epidemic, specifically the number of susceptible, i…
Background: Northern Italy was one of the most impacted areas by COVID. It is now widely assumed that the virus was silently spreading for at least 2 weeks before the first patient was identified. During this silent phase, and in the following weeks when the hospital system was overburdened, data collection was not performed in an accurate enough way to estimate an epidemic curve. With the aim of assessing both the dynamics of the introduction of the virus and the effectiveness of containment measures introduced, we try to reconstruct the epidemic curve using all cause mortality data. Methods:…
The ongoing COVID-19 pandemic is being responded with various methods, applying vaccines, experimental treatment options, total lockdowns or partial curfews. Weekend curfews is one of the methods to reduce the amount of infected persons and this method is practically applied in some countries such as Turkey. In this study, the effect of weekend curfews on reducing the spread of a contagious disease, such as COVID-19, is modeled using a Monte Carlo algorithm with a hybrid lattice model. In the simulation setup, a fictional country with three towns and 26,610 citizens were used as a model. Resul…
We consider extinction times for a class of birth-death processes commonly found in applications, where there is a control parameter which determines whether the population quickly becomes extinct, or rather persists for a long time. We give an exact expression for the discrete case and its asymptotic expansion for large values of the population. We have results below the threshold, at the threshold, and above the threshold (where there is a quasi-stationary state and the extinction time is very long.) We show that the Fokker-Planck approximation is valid only quite near the threshold. We comp…
At the time of writing, the ongoing COVID-19 pandemic, caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), had already resulted in more than thirty-two million cases infected and more than one million deaths worldwide. Given the fact that the pandemic is still threatening health and safety, it is in the urgency to understand the COVID-19 contagion process and know how it might be controlled. With this motivation in mind, in this paper, we consider a version of a stochastic discrete-time Susceptible-Infected-Recovered-Death~(SIRD)-based epidemiological model with two uncerta…
We developed a model and a software package for stochastic simulations of transmission of COVID-19 and other similar infectious diseases, that takes into account contact network structures and geographical distribution of population density, detailed up to a level of location of individuals. Our analysis framework includes a surrogate model optimization process for quick fitting of the model's parameters to the observed epidemic curves for cases, hospitalizations and deaths. This set of instruments (the model, the simulation code, and the optimizer) is a useful tool for policymakers and epidem…
In December 2019, a novel coronavirus was found in a seafood wholesale market in Wuhan, China. WHO officially named this coronavirus as COVID-19. Since the first patient was hospitalized on December 12, 2019, China has reported a total of 78,824 confirmed CONID-19 cases and 2,788 deaths as of February 28, 2020. Wuhan's cumulative confirmed cases and deaths accounted for 61.1% and 76.5% of the whole China mainland , making it the priority center for epidemic prevention and control. Meanwhile, 51 countries and regions outside China have reported 4,879 confirmed cases and 79 deaths as of February…
Since the first outbreak of the COVID-19 epidemic at the end of 2019, data has been made available on the number of infections, deaths and recoveries for all countries of the World, and that data can be used for statistical analysis. The primary interest of this paper is how well the logistic equation can predict the outcome of COVID-19 epidemic in any regions of the World assuming that the methodology of the testing process, namely the data collection method and social behavior is not changing over the course of time. Besides the social relevance, this study has two scientific purposes: we in…
This study develops a framework for quantification of the impact of changes in population mobility due to social distancing on the COVID-19 infection growth rate. Using the Susceptible-Infected-Recovered (SIR) epidemiological model we establish that under some mild assumptions the growth rate of COVID-19 deaths is a time-delayed approximation of the growth rate of COVID-19 infections. We then hypothesize that the growth rate of COVID-19 infections is a function of population mobility, which leads to a statistical model that predicts the growth rate of COVID-19 deaths as a delayed function of p…
In the absence of other tools, monitoring the effects of protective measures, including social distancing and forecasting the outcome of outbreaks is of immense interest. Real-time data is noisy and very often hampered by systematic errors in reporting. Detailed epidemic models may contain a large number of empirical parameters, which cannot be determined with sufficient accuracy. In this paper, we show that the cumulative number of deaths can be regarded as a master variable, and the parameters of the epidemic such as the basic reproduction number, the size of the susceptible population, and …
Why are the epidemic patterns of COVID-19 so different among different cities or countries which are similar in their populations, medical infrastructures, and people's behavior? Why are forecasts or predictions made by so-called experts often grossly wrong, concerning the numbers of people who get infected or die? The purpose of this study is to better understand the stochastic nature of an epidemic disease, and answer the above questions. Much of the work on infectious diseases has been based on "SIR deterministic models," (Kermack and McKendrick:1927.) We will explore stochastic models that…
The Ebola epidemic in West Africa is the largest ever recorded, with over 27,000 cases and 11,000 deaths as of June 2015. The public health response was challenged by difficulties with disease surveillance, which impacted subsequent analysis and decision-making regarding optimal interventions. We developed a stage-structured model of Ebola virus disease (EVD). A key feature of the model is that it includes a generalized correction term accounting for factors such as the fraction of cases reported and fraction of the population at risk (e.g. due to contact patterns, interventions, spatiotempora…
Pathogen introduction in plant communities can cause serious impact and biodiversity losses that may take long time to manage and restore. Effective control of epidemic spreading in the wild is a problem of paramount importance, because of its implications in conservation and potential economic losses. Understanding the mechanisms that hinder pathogen's propagation is, therefore, crucial. Usual modelization approaches in epidemic spreading are based in compartmentalized models, without keeping track of pathogen's concentrations during spreading. In this contribution we present and fully analyz…
We study the reported data from the COVID-19 pandemic outbreak in January - May 2020 in 119 countries. We observe that the time series of active cases in individual countries (the difference of the total number of confirmed infections and the sum of the total number of reported deaths and recovered cases) display a strong agreement with polynomial growth and at a later epidemic stage also with a combined polynomial growth with exponential decay. Our results are also formulated in terms of compartment type mathematical models of epidemics. Within these models the universal scaling characterizin…
Several epidemiological models have been proposed to study the evolution of COVID-19 pandemic. In this paper, we propose an extension of the SUIHTER model, first introduced in [Parolini et al, Proc R. Soc. A., 2021] to analyse the COVID-19 spreading in Italy, which accounts for the vaccination campaign and the presence of new variants when they become dominant. In particular, the specific features of the variants (e.g. their increased transmission rate) and vaccines (e.g. their efficacy to prevent transmission, hospitalization and death) are modeled, based on clinical evidence. The new model i…
We measure the effect of different public health regulations to the spread of COVID-19, based on a SEIRA model -- a SEIR model including asymptomatic transmissions. The cumulative confirmed cases and death show nonlinear positive relationship with the value of asymptomatic rate. Based on this model, we analyze the inhibit effects to COVID-19 of three types of public health policies, i.e. isolation of laboratory confirmed cases, general personal protection and quarantine (lock-down). The simulations conclude that the isolation display limited effects to the asymptomatic viral carriers. The gene…
An epidemic disease caused by a new coronavirus has spread in Northern Italy with a strong contagion rate. We implement an SEIR model to compute the infected population and number of casualties of this epidemic. The example may ideally regard the situation in the Italian Region of Lombardy, where the epidemic started on February 25. We calibrate the model with the number of dead individuals to date (May 5, 2020) and constraint the parameters on the basis of values reported in the literature. The peak occurs at day 37 (March 31) approximately, when there is a rapid decrease, with a reproduction…
In this note we analyze the temporal dynamics of the coronavirus disease 2019 outbreak in China, Italy and France in the time window $22/01-09/03/2020$. A first analysis of simple day-lag maps points to some universality in the epidemic spreading, suggesting that simple mean-field models can be meaningfully used to gather a quantitative picture of the epidemic spreading, and notably the height and time of the peak of confirmed infected individuals. The analysis of the same data within a simple susceptible-(confirmed) infected-recovered-deaths model indicates that the kinetic parameter that des…
For practical reasons, many forecasts of case, hospitalization and death counts in the context of the current COVID-19 pandemic are issued in the form of central predictive intervals at various levels. This is also the case for the forecasts collected in the COVID-19 Forecast Hub (https://covid19forecasthub.org/). Forecast evaluation metrics like the logarithmic score, which has been applied in several infectious disease forecasting challenges, are then not available as they require full predictive distributions. This article provides an overview of how established methods for the evaluation o…
Objective: To make an estimate of the excess deaths caused by COVID-19 in the non-violent mortality of Peru, controlling for the effect of quarantine. Methods: Analysis of longitudinal data from the departments of Peru using official public information from the National Death Information System and the Ministry of Health of Peru. The analysis is performed between January 1, 2018 and June 23, 2020 (100 days of quarantine). The daily death rate per million inhabitants has been used. The days in which the departments were quarantined with a limit number of accumulated cases of COVID-19 were used …
We present modeling of the COVID-19 epidemic in Illinois, USA, capturing the implementation of a Stay-at-Home order and scenarios for its eventual release. We use a non-Markovian age-of-infection model that is capable of handling long and variable time delays without changing its model topology. Bayesian estimation of model parameters is carried out using Markov Chain Monte Carlo (MCMC) methods. This framework allows us to treat all available input information, including both the previously published parameters of the epidemic and available local data, in a uniform manner. To accurately model …
In this paper a Bayesian SEIR model is studied to estimate the proportion of the population infected with SARS-CoV-2, the virus responsible for COVID-19. To capture heterogeneity in the population and the effect of interventions to reduce the rate of epidemic spread, the model uses a time-varying contact rate, whose logarithm has a Gaussian process prior. A Poisson point process is used to model the occurrence of deaths due to COVID-19 and the model is calibrated using data of daily death counts in combination with a snapshot of the the proportion of individuals with an active infection, perfo…
Forecasting the effect of COVID-19 is essential to design policies that may prepare us to handle the pandemic. Many methods have already been proposed, particularly, to forecast reported cases and deaths at country-level and state-level. Many of these methods are based on traditional epidemiological model which rely on simulations or Bayesian inference to simultaneously learn many parameters at a time. This makes them prone to over-fitting and slow execution. We propose an extension to our model SIkJ$α$ to forecast deaths and show that it can consider the effect of many complexities of the epi…
The Penna model is a strategy to simulate the genetic dynamics of age-structured populations, in which the individuals genomes are represented by bit-strings. It provides a simple metaphor for the evolutionary process in terms of the mutation accumulation theory. In its original version, an individual dies due to inherited diseases when its current number of accumulated mutations, n, reaches a threshold value, T. Since the number of accumulated diseases increases with age, the probability to die is zero for very young ages (n < T) and equals 1 for the old ones (n >= T). Here, instead of using …
The risk of dying increases exponentially with age, in humans as well as in many other species. This increase is often attributed to the "accumulation of damage" known to occur in many biological structures and systems. The aim of this paper is to describe a generic model of damage accumulation and death in which mortality increases exponentially with age. The damage-accumulation process is modeled by a stochastic process know as a queue, and risk of dying is a function of the accumulated damage, i.e. length of the queue. The model has four parameters and the main characteristics of the model …
We propose an SEIARD mathematical model to investigate the current outbreak of coronavirus disease (COVID-19) in Mexico. We conduct a detailed analysis of this model and demonstrate its application using publicly reported data. We calculate the basic reproduction number ($R_0$) via the next-generation matrix method, and we estimate the per day infection, death and recovery rates. We calibrate the parameters of the SEIARD model to the reported data by minimizing the sum of squared errors and attempt to forecast the evolution of the outbreak until June 2020. Our results estimate that the peak of…
The novel coronavirus disease (COVID-19) is known as the causative virus of outbreak pneumonia initially recognized in the mainland of China, late December 2019. COVID-19 reaches out to many countries in the world, and the number of daily cases continues to increase rapidly. In order to simulate, track, and forecast the trend of the virus spread, several mathematical and statistical models have been developed. Susceptible-Exposed-Infected-Quarantined-Recovered-Death-Insusceptible (SEIQRDP) model is one of the most promising dynamic systems that has been proposed for estimating the transmissibi…
Faced with the 2020 SARS-CoV2 epidemic, public health officials have been seeking models that could be used to predict not only the number of new cases but also the levels of hospitalisation, critical care and deaths. In this paper we present a stochastic compartmental model capable of real-time monitoring and forecasting of the pandemic incorporating multiple streams of real-world data, reported cases, testing intensity, deaths, hospitalisations and critical care occupancy. Model parameters are estimated via a Bayesian particle filtering technique. The model successfully tracks the key variab…
Since the beginning of the epidemic, daily reports of CoViD-19 cases, hospitalizations, and deaths from around the world have been publicly available. This paper describes methods to characterize broad features of the spread of the disease, with relatively long periods of constant transmission rates, using a new population modeling framework based on discrete-time difference equations. Comparative parameters are chosen for their weak dependence on model assumptions. Approaches for their point and interval estimation, accounting for additional sources of variance in the case data, are presented…
In this paper we establish a relation between the spread of infectious diseases and the dynamics of so called M/G/1 queues with processor sharing. The in epidemiology well known relation between the spread of epidemics and branching processes and the in queueing theory well known relation between M/G/1 queues and birth death processes will be combined to provide a framework in which results from queueing theory can be used in epidemiology and vice versa. In particular, we consider the number of infectious individuals in a standard SIR epidemic model at the moment of the first detection of the …
