Timely estimation of the current value for COVID-19 reproduction factor $R$ has become a key aim of efforts to inform management strategies. $R$ is an important metric used by policy-makers in setting mitigation levels and is also important for accurate modelling of epidemic progression. This brief paper introduces a method for estimating $R$ from biased case testing data. Using testing data, rather than hospitalisation or death data, provides a much earlier metric along the symptomatic progression scale. This can be hugely important when fighting the exponential nature of an epidemic. We develop a practical estimator and apply it to Scottish case testing data to infer a current (20 May 2020) $R$ value of $0.74$ with $95\%$ confidence interval $[0.48 - 0.86]$.
As the interactions between people increases, the impending menace of COVID-19 outbreaks materialize, and there is an inclination to apply lockdowns. In this context, it is essential to have easy-to-use indicators for people to use as a reference. The basic reproduction number of confirmed positives, $R_t$, fulfill such a role. This document proposes a data-driven approach to nowcast $R_t$ based on previous observations' statistical behavior. As more information arrives, the method naturally becomes more precise about the final count of confirmed positives. Our method's strength is that it is …
The new corona virus disease -- COVID-2019 -- is rapidly spreading through the world. The availability of unbiased timely statistics of trends in disease events are a key to effective responses. But due to reporting delays, the most recently reported numbers are frequently underestimating of the total number of infections, hospitalizations and deaths creating an illusion of a downward trend. Here we describe a statistical methodology for predicting true daily quantities and their uncertainty, estimated using historical reporting delays. The methodology takes into account the observed distribut…
We analyse the temporal and regional structure in mortality rates related to COVID-19 infections. We relate the fatality date of each deceased patient to the corresponding day of registration of the infection, leading to a nowcasting model which allows us to estimate the number of present-day infections that will, at a later date, prove to be fatal. The numbers are broken down to the district level in Germany. Given that death counts generally provide more reliable information on the spread of the disease compared to infection counts, which inevitably depend on testing strategy and capacity, t…
We present a simple technique to compare the development of the Covid-19 epidemic in different regions, based only on the time series of confirmed cases. Weekly new infections, taken for every day, are interpreted as infection potential of Covid-19. We derive a robust time-varying reproduction rate for the infection potential, including asymptomatic cases, which does not depend on death rate or testing intensity. It requires few assumptions and shows a more plausible time course than official reproduction rates in several countries.
The coronavirus disease 2019 (COVID-19) has become a public health emergency of international concern affecting more than 200 countries and territories worldwide. As of September 30, 2020, it has caused a pandemic outbreak with more than 33 million confirmed infections and more than 1 million reported deaths worldwide. Several statistical, machine learning, and hybrid models have previously tried to forecast COVID-19 confirmed cases for profoundly affected countries. Due to extreme uncertainty and nonstationarity in the time series data, forecasting of COVID-19 confirmed cases has become a ver…
We discuss the generation of various reproduction ratios or numbers that are very useful to monitor an ongoing epidemic like Covid-19 and examine the effects of intervention measures. A detailed SEIR algorithm is described for their computation, with applications given to the current Covid-19 outbreaks in a number of countries (Argentina, Brazil, France, Italy, Mexico, Spain, UK and USA). The corresponding matlab script, complete and ready to use, is provided for free downloading.
A simplified method to compute $R_t$, the Effective Reproduction Number, is presented. The method relates the value of $R_t$ to the estimation of the doubling time performed with a local exponential fit. The condition $R_t = 1$ corresponds to a growth rate equal to zero or equivalently an infinite doubling time. Different assumptions on the probability distribution of the generation time are considered. A simple analytical solution is presented in case the generation time follows a gamma distribution.
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 …
Since November 6$^{\mathrm{th}}$, 2020, Italian regions have been classified according to four levels, corresponding to specific risk scenarios, for which specific restrictive measures have been foreseen. By analyzing the time evolution of the reproduction number $R_t$, we estimate how much different restrictive measures affect $R_t$, and we quantify the combined effect of the diffusion of virus variants and the beginning of the vaccination campaign upon the $R_t$ trend. We also compute the time delay between implementation of restrictive measures and the resulting effects. Three different mod…
We propose a new method to estimate the time-varying effective (or instantaneous) reproduction number of the novel coronavirus disease (COVID-19). The method is based on a discrete-time stochastic augmented compartmental model that describes the virus transmission. A two-stage estimation method, which combines the Extended Kalman Filter (EKF) to estimate the reported state variables (active and removed cases) and a low pass filter based on a rational transfer function to remove short term fluctuations of the reported cases, is used with case uncertainties that are assumed to follow a Gaussian …
This paper is an exploratory study of two epidemiological questions on a worldwide basis. How fast is the disease spreading? Are the restrictions (especially mobility restrictions) for people bring the expected effect? To answer the first question, we propose a tool for estimating the reproduction number of epidemic (the number of secondary infections $R_t$) based on the SEIR model and compare it with an non-model $R_t$ estimation. To measure the $R_t$ of COVID-19 for different countries, real-time data on coronavirus daily cases of infections, recoveries, deaths are retrieved from the Center …
Monitoring the evolution of the Covid19 pandemic constitutes a critical step in sanitary policy design. Yet, the assessment of the pandemic intensity within the pandemic period remains a challenging task because of the limited quality of data made available by public health authorities (missing data, outliers and pseudoseasonalities, notably), that calls for cumbersome and ad-hoc preprocessing (denoising) prior to estimation. Recently, the estimation of the reproduction number, a measure of the pandemic intensity, was formulated as an inverse problem, combining data-model fidelity and space-ti…
We proposed a Monte-Carlo method to estimate temporal reproduction number without complete information about symptom onsets of all cases. Province-level analysis demonstrated the huge success of Chinese control measures on COVID-19, that is, provinces' reproduction numbers quickly decrease to <1 by just one week after taking actions.
Addressed in this work is the performance of five popular algorithms, which aim at assessing the dissemination dynamics of the COVID-19 disease on the basis of the time series of new confirmed cases. The tests are based on simulated data, generated by means of a deterministic compartmental epidemiological model \cite{Matsinos2020a}, adapted herein to also include the possibility of the loss of immunity by the group of the recovered (or vaccinated) subjects. Assuming a simple temporal dependence of the effective reproduction number (the exact details are of no relevance as far as the conclusion…
We study the datafor the cumulative as well as daily number of cases in the Covid-19 outbreak in China. The cumulative data can be fit to an empirical form obtained from a Susceptible-Infected-Removed (SIR) model studied on an Euclidean network previously. Plotting the number of cases against the distance from the epicenter for both China and Italy, we find an approximate power law variation with an exponent $\sim 1.85$ showing strongly that the spatial dependence plays a key role, a factor included in the model. We report here that the SIR model on the Eucledean network can reproduce with a h…
A great issue of discussion of an infectious disease is its basic reproduction number R0, which provides an estimation of the contagiousness of the disease. When R0 > 1, the disease spread will potentially lead to an outbreak, such that of the ongoing COVID-19 pandemics. During the evolution of an outbreak, various non-pharmaceutical interventions are employed, the impact of which is frequently assessed by the reduction that they introduce to the effective reproduction number Rt; reduction below 1 is an indication of eventual dying out of the disease spread. Motivated by the fact that R0 essen…
To control the current outbreak of the Coronavirus Disease 2019, constant monitoring of the epidemic is required since, as of today, no vaccines or antiviral drugs against it are known. We provide daily updated estimates of the reproduction number over time at https://stochastik-tu-ilmenau.github.io/COVID-19/. In this document, we describe the estimator we are using which was developed in (Fraser 2007), derive its asymptotic properties, and we give details on its implementation. Furthermore, we validate the estimator on simulated data, demonstrate that estimates on real data lead to plausible …
One of the key indicators used in tracking the evolution of an infectious disease isthe reproduction number. This quantity is usually computed using the reportednumber of cases, but ignoring that many more individuals may be infected (e.g.asymptomatics). We propose a statistical procedure to quantify the impact of un-detected infectious cases on the determination of the effective reproduction number. Our approach is stochastic, data-driven and not relying on any compartmentalmodel. It is applied to the COVID-19 case in eight different countries and all Italianregions, showing that the effect o…
As the ravages caused by COVID-19 pandemic are becoming inevitable with every moment, monitoring and understanding of transmission and fatality rate has become even more paramount for containing its spread. The key purpose of this analysis is to report the real-time effective reproduction rate ($R_t$ ) and case fatality rates (CFR) of COVID-19 in South Asia region. Data for this study are extracted from JHU CSSE COVID-19 Data source up to July 31, 2020. $R_t$ is estimated using exponential growth and time-dependent methods. R0 package in R-language is employed to estimate $R_t$ by fitting the …
During the first months, the Covid-19 pandemic has required most countries to implement complex sequences of non-pharmaceutical interventions, with the aim of controlling the transmission of the virus in the population. To be able to take rapid decisions, a detailed understanding of the current situation is necessary. Estimates of time-varying, instantaneous reproduction numbers represent a way to quantify the viral transmission in real time. They are often defined through a mathematical compartmental model of the epidemic, like a stochastic SEIR model, whose parameters must be estimated from …
The ongoing pandemic of Coronavirus disease (COVID-19) emerged in Wuhan, China in the end of 2019. It has already affected more than 300,000 people, with the number of deaths nearing 13000 across the world. As it has been posing a huge threat to global public health, it is of utmost importance to identify the rate at which the disease is spreading. In this study, we propose a time series model to analyze the trend pattern of the incidence of COVID-19 outbreak. We also incorporate information on total or partial lockdown, wherever available, into the model. The model is concise in structure, an…
In the recent COVID-19 pandemic, a wide range of epidemiological modelling approaches have been used to predict the effective reproduction number, R(t), and other COVID-19 related measures such as the daily rate of exponential growth, r(t). These candidate models use different modelling approaches or differing assumptions about spatial or age mixing, and some capture genuine uncertainty in scientific understanding of disease dynamics. Combining estimates using appropriate statistical methodology from multiple candidate models is important to better understand the variation of these outcome mea…
We propose a compartmental mathematical model for the spread of the COVID-19 disease with special focus on the transmissibility of super-spreaders individuals. We compute the basic reproduction number threshold, we study the local stability of the disease free equilibrium in terms of the basic reproduction number, and we investigate the sensitivity of the model with respect to the variation of each one of its parameters. Numerical simulations show the suitability of the proposed COVID-19 model for the outbreak that occurred in Wuhan, China.
Reproduction Numbers R_0, R_t for COVID-19 Infections with Gaussian Distribution of Generation Times, and of Serial Intervals including Presymptomatic Transmission
The coronavirus pandemic has rapidly evolved into an unprecedented crisis. The susceptible-infectious-removed (SIR) model and its variants have been used for modeling the pandemic. However, time-independent parameters in the classical models may not capture the dynamic transmission and removal processes, governed by virus containment strategies taken at various phases of the epidemic. Moreover, very few models account for possible inaccuracies of the reported cases. We propose a Poisson model with time-dependent transmission and removal rates to account for possible random errors in reporting …
This is a pedagogical paper on estimating the number of people that can be infected by one infectious person during an epidemic outbreak, known as the reproduction number. Knowing the number is crucial for developing policy responses. There are generally two types of such a number, i.e., basic and effective (or instantaneous). While basic reproduction number is the average expected number of cases directly generated by one case in a population where all individuals are susceptible, effective reproduction number is the number of cases generated in the current state of a population. In this pape…
In epidemiology, the effective reproduction number $R_e$ is used to characterize the growth rate of an epidemic outbreak. In this paper, we investigate properties of $R_e$ for a modified SEIR model of COVID-19 in the city of Houston, TX USA, in which the population is divided into low-risk and high-risk subpopulations. The response of $R_e$ to two types of control measures (testing and distancing) applied to the two different subpopulations is characterized. A nonlinear cost model is used for control measures, to include the effects of diminishing returns. We propose three types of heuristic s…
We propose a new mathematical model to study the coinfection dynamics of COVID-19 and bacterial pneumonia. Our model includes two infection ways for pneumonia, corresponding to community-acquired and hospital-acquired infections. We show that the existence and local stability of equilibria depend on three different parameters, which are interpreted as the basic reproduction numbers of COVID-19, bacterial pneumonia, and bacterial population. Numerical simulations are performed to complement our theoretical analysis, and we show that both diseases can persist if the basic reproduction number of …
During epidemics, estimation of the effective reproduction number (ERN) associated with infectious disease is a challenging topic for policy development and medical resource management. There is still an open question about the dominant factors to characterize in corona virus disease 2019 (COVID-19), although recent studies based on nonlinear regression with machine learning suggested mobility. The emergence of new viral variants is common in widespread pandemics. However, understanding the potential ERN of new variants is required for policy revision, including lockdown constraints. In this s…
In May 2022, a cluster of mpox cases were detected in the UK that could not be traced to recent travel history from an endemic region. Over the coming months, the outbreak grew, with over 3000 total cases reported in the UK, and similar outbreaks occurring worldwide. These outbreaks appeared linked to sexual contact networks between gay, bisexual and other men who have sex with men. Following the COVID-19 pandemic, local health systems were strained, and therefore effective surveillance for mpox was essential for managing public health policy. However, the mpox outbreak in the UK was character…
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:…
In order to analyze the effectiveness of three successive nationwide lockdown enforced in India, we present a data-driven analysis of four key parameters, reducing the transmission rate, restraining the growth rate, flattening the epidemic curve and improving the health care system. These were quantified by the consideration of four different metrics, namely, reproduction rate, growth rate, doubling time and death to recovery ratio. The incidence data of the COVID-19 (during the period of 2nd March 2020 to 31st May 2020) outbreak in India was analyzed for the best fit to the epidemic curve, ma…
Many studies have proposed a relationship between COVID-19 transmissibility and ambient pollution levels. However, a major limitation in establishing such associations is to adequately account for complex disease dynamics, influenced by e.g. significant differences in control measures and testing policies. Another difficulty is appropriately controlling the effects of other potentially important factors, due to both their mutual correlations and a limited dataset. To overcome these difficulties, we will here use the basic reproduction number ($R_0$) that we estimate for USA states using non-li…
Timely prediction of the COVID-19 progression is not possible without a comprehensive understanding of environmental factors that may affect the infection transmissibility. Studies addressing parameters that may influence COVID-19 progression relied on either the total numbers of detected cases and similar proxies and/or a small number of analyzed factors, including analysis of regions that display a narrow range of these parameters. We here apply a novel approach, exploiting widespread growth regimes in COVID-19 detected case counts. By applying nonlinear dynamics methods to the exponential r…
The effective reproduction number is a key figure to monitor the course of the COVID-19 pandemic. In this study we consider a retrospective modelling approach for estimating the effective reproduction number based on death counts during the first year of the pandemic in Germany. The proposed Bayesian hierarchical model incorporates splines to estimate reproduction numbers flexibly over time while adjusting for varying effective infection fatality rates. The approach also provides estimates of dark figures regarding undetected infections over time. Results for Germany illustrate that estimated …
In this study, we analyze the effectiveness of measures aimed at finding and isolating infected individuals to contain epidemics like COVID-19, as the suppression induced over the effective reproduction number. We develop a mathematical model to compute the relative suppression of the effective reproduction number of an epidemic that such measures produce. This outcome is expressed as a function of a small set of parameters that describe the main features of the epidemic and summarize the effectiveness of the isolation measures. In particular, we focus on the impact when a fraction of the popu…
A mathematical model was developed describing the dynamic of the COVID-19 virus over a population considering that the infected can either be symptomatic or not. The model was calibrated using data on the confirmed cases and death from several countries like France, Philippines, Italy, Spain, United Kingdom, China, and the USA. First, we derived the basic reproduction number, $\mathcal{R}_0$, and estimated the effective reproduction $\mathcal{R}_{\rm eff}$ for each country. Second, we were interested in the merits of interventions, either by distancing or by treatment. Results revealed that to…
Since the beginning of the corona pandemic in March 2020, various parameters for describing the spread of the disease have been specified for Germany in addition to the daily infection figures (new infections and total infections), which are also used for political decisions. In addition to excess mortality and the weekly incidence, these include the doubling time $T_2$ and the reproduction number $R_t$. For the latter, various estimates can be found on the website of the Robert-Koch-Institute, see \cite{EstR:RKI}, which are calculated from the case numbers for all of Germany; local difference…
In the night of February 20, 2020, the first case of novel coronavirus disease (COVID-19) was confirmed in the Lombardy Region, Italy. In the week that followed, Lombardy experienced a very rapid increase in the number of cases. We analyzed the first 5,830 laboratory-confirmed cases to provide the first epidemiological characterization of a COVID-19 outbreak in a Western Country. Epidemiological data were collected through standardized interviews of confirmed cases and their close contacts. We collected demographic backgrounds, dates of symptom onset, clinical features, respiratory tract speci…
A dynamical epidemic model optimized using genetic algorithm and cross validation method to overcome the overfitting problem is proposed. The cross validation procedure is applied so that available data are split into a training subset used to fit the algorithm's parameters, and a smaller subset used for validation. This process is tested on the countries of Italy, Spain, Germany and South Korea before being applied to Algeria. Interestingly, our study reveals an inverse relationship between the size of the training sample and the number of generations required in the genetic algorithm. Moreov…
China adjusted the zero-COVID strategy in late 2022, triggering an unprecedented Omicron wave. We estimated the time-varying reproduction numbers of 32 provincial-level administrative divisions from December 2022 to January 2023. We found that the pooled estimate of initial reproduction numbers is 4.74 (95% CI: 4.41, 5.07).
We present a compartmental SEIAR model of epidemic spread as a generalization of the SEIR model. We believe that the asymptomatic infectious cohort is an omitted part of the understanding of the epidemic dynamics of disease COVID-19. We introduce and derive the basic reproduction number as the weighted arithmetic mean of the basic reproduction numbers of the symptomatic and asymptomatic cohorts. Since the asymptomatic subjects people are not detected, they can spread the disease much longer, and this increases the COVID-19 $R_0$ up to around 9. We show that European epidemic outbreaks in vario…
Since December 2019, A novel coronavirus (2019-nCoV) has been breaking out in China, which can cause respiratory diseases and severe pneumonia. Mathematical and empirical models relying on the epidemic situation scale for forecasting disease outbreaks have received increasing attention. Given its successful application in the evaluation of infectious diseases scale, we propose a Susceptible-Undiagnosed-Infected-Removed (SUIR) model to offer the effective prediction, prevention, and control of infectious diseases. Our model is a modified susceptible-infected-recovered (SIR) model that injects u…
In the absence of neither an effective treatment or vaccine and with an incomplete understanding of the epidemiological cycle, Govt. has implemented a nationwide lockdown to reduce COVID-19 transmission in India. To study the effect of social distancing measure, we considered a new mathematical model on COVID-19 that incorporates lockdown effect. By validating our model to the data on notified cases from five different states and overall India, we estimated several epidemiologically important parameters as well as the basic reproduction number ($R_{0}$). Combining the mechanistic mathematical …
We have proposed an SEIR compartmental mathematical model. The prime objective of this study is to analyze and forecast the pandemic in Italy for the upcoming months. The basic reproduction number has been calculated. Based on the current situation in Italy, in this paper, we will estimate the possible time for the end of the pandemic in the country. The impact of lockdown and rapid isolation on the spread of the pandemic are also discussed. Further, we have studied four of the most pandemic affected regions in Italy. Using the proposed model, a prediction has been made about the duration of p…
We analyze changes in the reproduction number, R, of COVID-19 in response to public health interventions. Our results indicate that public health measures undertaken in China reduced R from 1.5 in January to 0.4 in mid-March 2020. They also suggest, however, the limitations of isolation, quarantine, and large-scale attempts to limit travel. While the world-wide reproduction number briefly dropped below 1 as China implemented extensive public health measures, the introduction of the virus to other nations swiftly led to an increasing world-wide average value of R. In Italy, the nation hardest-h…
The spread of pandemics such as COVID-19 is strongly linked to human activities. The objective of this paper is to specify and examine early indicators of disease spread risk in cities during the initial stages of outbreak based on patterns of human activities obtained from digital trace data. In this study, the Venables distance (D_v), and the activity density (D_a) are used to quantify and evaluate human activities for 193 US counties, whose cumulative number of confirmed cases was greater than 100 as of March 31, 2020. Venables distance provides a measure of the agglomeration of the level o…
COVID-19 is a new pandemic disease that is affecting almost every country with a negative impact on social life and economic activities. The number of infected and deceased patients continues to increase globally. Mathematical models can help in developing better strategies to contain a pandemic. Considering multiple measures taken by African governments and challenging socio-economic factors, simple models cannot fit the data. We studied the dynamical evolution of COVID-19 in selected African countries. We derived a time-dependent reproduction number for each country studied to offer further …
Aims: Nonpharmaceutical interventions against the spread of SARS-CoV-2 in Germany included the cancellation of mass events (from March 8), closures of schools and child day care facilities (from March 16) as well as a "lockdown" (from March 23). This study attempts to assess the effectiveness of these interventions in terms of revealing their impact on infections over time. Methods: Dates of infections were estimated from official German case data by incorporating the incubation period and an empirical reporting delay. Exponential growth models for infections and reproduction numbers were esti…
In this article, we consider a dynamic epidemiology model for the spread of the COVID-19 infection. Starting from the classical SEIR model, the model is modified so as to better describe characteristic features of the underlying pathogen and its infectious modes. In line with the large number of secondary infections not related to contact with documented infectious individuals, the model includes a cohort of asymptomatic or oligosymptomatic infectious individuals, not accounted for in the data of new daily counts of infections. A Bayesian particle filtering algorithm is used to update dynamica…
We propose a compartmental mathematical model for the spread of the COVID-19 disease, showing its usefulness with respect to the pandemic in Portugal, from the first recorded case in the country till the end of the three states of emergency. New results include the compartmental model, described by a system of seven ordinary differential equations; proof of positivity and boundedness of solutions; investigation of equilibrium points and their stability analysis; computation of the basic reproduction number; and numerical simulations with official real data from the Portuguese health authoritie…
The infections and fatalities due to SARS-CoV-2 virus for cases specific to India have been studied using a deterministic susceptible-exposed-infected-recovered-dead (SEIRD) compartmental model. One of the most significant epidemiological parameter, namely the effective reproduction number of the infection is extracted from the daily growth rate data of reported infections and it is included in the model with a time variation. We evaluate the effect of control interventions implemented till now and estimate the case numbers for infections and deaths averted by these restrictive measures. We fu…
I employ a simple mathematical model of an epidemic process to evaluate how four basic quantities: the reproduction number (R), the numbers of sensitive (S) and infectious individuals(I), and total community size (N) affect strategies to control COVID-19. Numerical simulations show that strict suppression measures at the beginning of an epidemic can create low infectious numbers, which thereafter can be managed by mitigation measures over longer periods to flatten the epidemic curve. The stronger the suppression measure, the faster it achieves the low numbers of infections that are conducive t…
In this paper, we firstly propose SQIARD and SIARD models to investigate the transmission of COVID-19 with quarantine, infected and asymptomatic infected, and discuss the relation between the respective basic reproduction number $R_0, R_Q$ and the stability of the equilibrium points of model. Secondly, after training the related data parameters, in our numerical simulations, we respectively conduct the forecast of the data of US, South Korea, Brazil, India, Russia and Italy, and the effect of prediction of the epidemic situation in each country. Furthermore, we apply US data to compare SQIARD …
We introduce an extended SEIR infectious disease model with data assimilation for the study of the spread of COVID-19. In this framework, undetected asymptomatic and pre-symptomatic cases are taken into account, and the impact of their uncertain proportion is fully investigated. The standard SEIR model does not consider these populations, while their role in the propagation of the disease is acknowledged. An ensemble Kalman filter is implemented to assimilate reliable observations of three compartments in the model. The system tracks the evolution of the effective reproduction number and estim…
This is work in progress. We make it accessible hoping that people might find the idea useful. We propose a discrete, recursive 5-compartment model for the spread of epidemics, which we call {\em SEPIR-model}. Under mild assumptions which typically are fulfilled for the Covid-19 pandemic it can be used to reproduce the development of an epidemic from a small number of parameters closely related to the data. We demonstrate this at the development in Germany and Switzerland. It also allows model predictions assuming nearly constant reproduction numbers. Thus it might be a useful tool for sheddin…
Viral outbreaks, such as the current COVID-19 pandemic, are commonly described by compartmental models by means of ordinary differential equation (ODE) systems. The parameter values of these ODE models are typically unknown and need to be estimated based on accessible data. In order to describe realistic pandemic scenarios with strongly varying situations, these model parameters need to be assumed as time-dependent. While parameter estimation for the typical case of time-constant parameters does not pose larger issues, the determination of time-dependent parameters, e.g.~the transition rates o…
