COVID-19 Epidemic Dynamics Research Articles

Epidemiological Implications of War: Machine Learning Estimations of the Russian Invasion’s Effect on Italy’s COVID-19 Dynamics

Background: The COVID-19 pandemic has profoundly transformed the global scenario, marked by overwhelming infections, fatalities, overburdened healthcare infrastructures, economic upheavals, and significant lifestyle modifications. Concurrently, the Russian full-scale invasion of Ukraine on 24 February 2022, triggered a severe humanitarian and public health crisis, leading to healthcare disruptions, medical resource shortages, and heightened emergency care needs. Italy emerged as a significant refuge for displaced Ukrainians during this period. Aim: This research aims to discern the impact of the Russian full-scale invasion of Ukraine on the COVID-19 transmission dynamics in Italy. Materials and Methods: The study employed advanced simulation methodologies, particularly those integrating machine learning, to model the pandemic’s trajectory. The XGBoost algorithm was adopted to construct a predictive model for the COVID-19 epidemic trajectory in Italy. Results: The model demonstrated a commendable accuracy of 86.03% in forecasting new COVID-19 cases in Italy over 30 days and an impressive 96.29% accuracy in estimating fatalities. When applied to the initial 30 days following the escalation of the conflict (24 February 2022, to 25 March 2022), the model’s projections suggested that the influx of Ukrainian refugees into Italy did not significantly alter the country’s COVID-19 epidemic course. Discussion: While simulation methodologies have been pivotal in the pandemic response, their accuracy is intrinsically linked to data quality, assumptions, and modeling techniques. Enhancing these methodologies can further their applicability in future public health emergencies. The findings from the model underscore that external geopolitical events, such as the mass migration from Ukraine, did not play a determinative role in Italy’s COVID-19 epidemic dynamics during the study period. Conclusion: The research provides empirical evidence negating a substantial influence of the Ukrainian refugee influx due to the Russian full-scale invasion on the COVID-19 epidemic trajectory in Italy. The robust performance of the developed model affirms its potential value in public health analyses.

Molecular Epidemiology and Diversity of SARS-CoV-2 in Ethiopia, 2020-2022.

Ethiopia is the second most populous country in Africa and the sixth most affected by COVID-19 on the continent. Despite having experienced five infection waves, >499,000 cases, and ~7500 COVID-19-related deaths as of January 2023, there is still no detailed genomic epidemiological report on the introduction and spread of SARS-CoV-2 in Ethiopia. In this study, we reconstructed and elucidated the COVID-19 epidemic dynamics. Specifically, we investigated the introduction, local transmission, ongoing evolution, and spread of SARS-CoV-2 during the first four infection waves using 353 high-quality near-whole genomes sampled in Ethiopia. Our results show that whereas viral introductions seeded the first wave, subsequent waves were seeded by local transmission. The B.1.480 lineage emerged in the first wave and notably remained in circulation even after the emergence of the Alpha variant. The B.1.480 was outcompeted by the Delta variant. Notably, Ethiopia's lack of local sequencing capacity was further limited by sporadic, uneven, and insufficient sampling that limited the incorporation of genomic epidemiology in the epidemic public health response in Ethiopia. These results highlight Ethiopia's role in SARS-CoV-2 dissemination and the urgent need for balanced, near-real-time genomic sequencing.

The Easy-to-Use SARS-CoV-2 Assembler for Genome Sequencing: Development Study

BackgroundEarly sequencing and quick analysis of the SARS-CoV-2 genome have contributed to the understanding of the dynamics of COVID-19 epidemics and in designing countermeasures at a global level.ObjectiveAmplicon-based next-generation sequencing (NGS) methods are widely used to sequence the SARS-CoV-2 genome and to identify novel variants that are emerging in rapid succession as well as harboring multiple deletions and amino acid–changing mutations.MethodsTo facilitate the analysis of NGS sequencing data obtained from amplicon-based sequencing methods, here, we propose an easy-to-use SARS-CoV-2 genome assembler: the Easy-to-use SARS-CoV-2 Assembler (ESCA) pipeline.ResultsOur results have shown that ESCA could perform high-quality genome assembly from Ion Torrent and Illumina raw data and help the user in easily correct low-coverage regions. Moreover, ESCA includes the possibility of comparing assembled genomes of multisample runs through an easy table format.ConclusionsIn conclusion, ESCA automatically furnished a variant table output file, fundamental to rapidly recognizing variants of interest. Our pipeline could be a useful method for obtaining a complete, rapid, and accurate analysis even with minimal knowledge in bioinformatics.

Model-based assessment of COVID-19 epidemic dynamics by wastewater analysis

Continuous surveillance of COVID-19 diffusion remains crucial to control its diffusion and to anticipate infection waves. Detecting viral RNA load in wastewater samples has been suggested as an effective approach for epidemic monitoring and the development of an effective warning system. However, its quantitative link to the epidemic status and the stages of outbreak is still elusive. Modelling is thus crucial to address these challenges. In this study, we present a novel mechanistic model-based approach to reconstruct the complete epidemic dynamics from SARS-CoV-2 viral load in wastewater. Our approach integrates noisy wastewater data and daily case numbers into a dynamical epidemiological model. As demonstrated for various regions and sampling protocols, it quantifies the case numbers, provides epidemic indicators and accurately infers future epidemic trends. Following its quantitative analysis, we also provide recommendations for wastewater data standards and for their use as warning indicators against new infection waves. In situations of reduced testing capacity, our modelling approach can enhance the surveillance of wastewater for early epidemic prediction and robust and cost-effective real-time monitoring of local COVID-19 dynamics.

Analysis and modeling of COVID-19 epidemic dynamics in Saudi Arabia using SIR-PSO and machine learning approaches.

COVID-19 has become a global concern because it has extensive damage to health, social and economic systems worldwide. Consequently, there is an urgent need to develop tools to understand, analyze, monitor and control further outbreaks of the disease. The Susceptible Infected Recovered-Particle SwarmOptimization model and the feed-forward artificial neural network model were separately developed to model COVID-19 dynamics based on daily time-series data reported by the Saudi authorities from March 2, 2020 to February 21, 2021. The collected data were divided into training and validation datasets. The effectiveness of the investigated models was evaluated by using various performance metrics. The Susceptible-Infected-Recovered-Particle-Swarm-Optimization model was found to well predict the cumulative infected and recovered cases and to optimally tune the contact rate and the characteristic duration of the illness. The feed-forward artificial neural network model was found to be efficient in modeling daily new and cumulative infections, recoveries and deaths. The forecasts provided by the investigated models had high coefficient of determination values of more than 0.97 and low mean absolute percentage errors (around 7% on average). Both the Susceptible-Infected-Recovered-Particle-Swarm-Optimization and feed-forward artificial neural network models were efficient in modeling COVID-19 dynamics in Saudi Arabia. The results produced by the models can help the Saudi health authorities to analyze the virus dynamics and prepare efficient measures to control any future occurrence of the epidemic.

A Continuous Markov-Chain Model for the Simulation of COVID-19 Epidemic Dynamics.

Simple SummaryPredicting the spreading trend of the COVID-19 epidemic is one of the hot topics in the modeling field. In this study, we applied a continuous Markov-chain model to simulate the spread of the COVID-19 epidemic. The results of this study indicate that the herd immunity threshold should be significantly higher than 1 − 1/R0. Taking the immunity waning effect into consideration, the model could predict an epidemic resurgence after the herd immunity threshold. Meanwhile, this Markov-chain approach could also forecast the epidemic distribution and predict the epidemic hotspots at different times. It is implied from our model that it is significantly challenging to eradicate SARS-CoV-2 in the short term. The actual epidemic development is consistent with our prediction. In the end, this method displayed great potential as an alternative approach to traditional compartment models.To address the urgent need to accurately predict the spreading trend of the COVID-19 epidemic, a continuous Markov-chain model was, for the first time, developed in this work to predict the spread of COVID-19 infection. A probability matrix of infection was first developed in this model based upon the contact frequency of individuals within the population, the individual’s characteristics, and other factors that can effectively reflect the epidemic’s temporal and spatial variation characteristics. The Markov-chain model was then extended to incorporate both the mutation effect of COVID-19 and the decaying effect of antibodies. The developed comprehensive Markov-chain model that integrates the aforementioned factors was finally tested by real data to predict the trend of the COVID-19 epidemic. The result shows that our model can effectively avoid the prediction dilemma that may exist with traditional ordinary differential equations model, such as the susceptible–infectious–recovered (SIR) model. Meanwhile, it can forecast the epidemic distribution and predict the epidemic hotspots geographically at different times. It is also demonstrated in our result that the influence of the population’s spatial and geographic distribution in a herd infection event is needed in the model for a better prediction of the epidemic trend. At the same time, our result indicates that no simple derivative relationship exists between the threshold of herd immunity and the virus basic reproduction number R0. The threshold of herd immunity achieved through natural immunity is significantly higher than 1 − 1/R0. These not only explain the theoretical misconceptions of herd immunity thresholds in herd immunity theory but also provide a guidance for predicting the optimal vaccination coverage. In addition, our model can predict the temporal and spatial distribution of infections in different epidemic waves. It is implied from our model that it is challenging to eradicate COVID-19 in the short term for a large population size and a wide spatial distribution. It is predicted that COVID-19 is likely to coexist with humans for a long time and that it will exhibit multipoint epidemic effects at a later stage. The statistical evidence is consistent with our prediction and strongly supports our modeling results.

Model-Based Assessment of COVID-19 Epidemic Dynamics by Wastewater Analysis

Model-Based Assessment of COVID-19 Epidemic Dynamics by Wastewater Analysis

Evaluating the impacts of non-pharmaceutical interventions on the transmission dynamics of COVID-19 in Canada based on mobile network.

The COVID-19 outbreak has caused two waves and spread to more than 90% of Canada’s provinces since it was first reported more than a year ago. During the COVID-19 epidemic, Canadian provinces have implemented many Non-Pharmaceutical Interventions (NPIs). However, the spread of the COVID-19 epidemic continues due to the complex dynamics of human mobility. We develop a meta-population network model to study the transmission dynamics of COVID-19. The model takes into account the heterogeneity of mitigation strategies in different provinces of Canada, such as the timing of implementing NPIs, the human mobility in retail and recreation, grocery and pharmacy, parks, transit stations, workplaces, and residences due to work and recreation. To determine which activity is most closely related to the dynamics of COVID-19, we use the cross-correlation analysis to find that the positive correlation is the highest between the mobility data of parks and the weekly number of confirmed COVID-19 from February 15 to December 13, 2020. The average effective reproduction numbers in nine Canadian provinces are all greater than one during the time period, and NPIs have little impact on the dynamics of COVID-19 epidemics in Ontario and Saskatchewan. After November 20, 2020, the average infection probability in Alberta became the highest since the start of the COVID-19 epidemic in Canada. We also observe that human activities around residences do not contribute much to the spread of the COVID-19 epidemic. The simulation results indicate that social distancing and constricting human mobility is effective in mitigating COVID-19 transmission in Canada. Our findings can provide guidance for public health authorities in projecting the effectiveness of future NPIs.

Enhanced Sentinel Surveillance System for COVID-19 Outbreak Prediction in a Large European Dialysis Clinics Network.

Accurate predictions of COVID-19 epidemic dynamics may enable timely organizational interventions in high-risk regions. We exploited the interconnection of the Fresenius Medical Care (FMC) European dialysis clinic network to develop a sentinel surveillance system for outbreak prediction. We developed an artificial intelligence-based model considering the information related to all clinics belonging to the European Nephrocare Network. The prediction tool provides risk scores of the occurrence of a COVID-19 outbreak in each dialysis center within a 2-week forecasting horizon. The model input variables include information related to the epidemic status and trends in clinical practice patterns of the target clinic, regional epidemic metrics, and the distance-weighted risk estimates of adjacent dialysis units. On the validation dates, there were 30 (5.09%), 39 (6.52%), and 218 (36.03%) clinics with two or more patients with COVID-19 infection during the 2-week prediction window. The performance of the model was suitable in all testing windows: AUC = 0.77, 0.80, and 0.81, respectively. The occurrence of new cases in a clinic propagates distance-weighted risk estimates to proximal dialysis units. Our machine learning sentinel surveillance system may allow for a prompt risk assessment and timely response to COVID-19 surges throughout networked European clinics.

The impact of long-term non-pharmaceutical interventions on COVID-19 epidemic dynamics and control: the value and limitations of early models.

Mathematical models of epidemics are important tools for predicting epidemic dynamics and evaluating interventions. Yet, because early models are built on limited information, it is unclear how long they will accurately capture epidemic dynamics. Using a stochastic SEIR model of COVID-19 fitted to reported deaths, we estimated transmission parameters at different time points during the first wave of the epidemic (March–June, 2020) in Santa Clara County, California. Although our estimated basic reproduction number () remained stable from early April to late June (with an overall median of 3.76), our estimated effective reproduction number () varied from 0.18 to 1.02 in April before stabilizing at 0.64 on 27 May. Between 22 April and 27 May, our model accurately predicted dynamics through June; however, the model did not predict rising summer cases after shelter-in-place orders were relaxed in June, which, in early July, was reflected in cases but not yet in deaths. While models are critical for informing intervention policy early in an epidemic, their performance will be limited as epidemic dynamics evolve. This paper is one of the first to evaluate the accuracy of an early epidemiological compartment model over time to understand the value and limitations of models during unfolding epidemics.

Integrating Risk Assessment and Decision-Making Methods in Analyzing the Dynamics of COVID-19 Epidemics in Davao City, Mindanao Island, Philippines.

The COVID‐19 pandemic has become a public health crisis in the Philippines and the attention of national and local health authorities is focused on managing the fluctuating COVID‐19 cases. This study presents a method that integrates risk management tools into health care decision‐making processes to enhance the understanding and utilization of risk‐based thinking in public health decision making. The risk assessment consists of the identification of the key risk factors of the COVID‐19 contagion via bow‐tie diagrams. Second, the safety controls for each risk factor relevant to the Davao City context are taken into account and are identified as barriers in the bow‐tie. After which, the prioritization of the identified COVID‐19 risks, as well as the effectiveness of the proposed interventions, is performed using the analytic hierarchy process. Consequently, the dynamics of COVID‐19 management initiatives were explored using these priorities and a system of ordinary differential equations. Our results show that reducing the number of COVID‐19 fatalities should be the top priority of the health authorities. In turn, we predict that the COVID‐19 contagion can be controlled and eliminated in Davao city in three‐month time after prioritizing the fatalities. In order to reduce the COVID‐19 fatalities, health authorities should ensure an adequate number of COVID‐ready ICU facilities. The general public, on the other hand, should follow medical and science‐based advice and suspected and confirmed COVID‐19 patients should strictly follow isolation protocols. Overall, an informed decision‐making is necessary to avoid the unwanted consequences of an uncontrolled contagion.

Modeling the impact of racial and ethnic disparities on COVID-19 epidemic dynamics.

The impact of variable infection risk by race and ethnicity on the dynamics of SARS-CoV-2 spread is largely unknown. Here, we fit structured compartmental models to seroprevalence data from New York State and analyze how herd immunity thresholds (HITs), final sizes, and epidemic risk change across groups. A simple model where interactions occur proportionally to contact rates reduced the HIT, but more realistic models of preferential mixing within groups increased the threshold toward the value observed in homogeneous populations. Across all models, the burden of infection fell disproportionately on minority populations: in a model fit to Long Island serosurvey and census data, 81% of Hispanics or Latinos were infected when the HIT was reached compared to 34% of non-Hispanic whites. Our findings, which are meant to be illustrative and not best estimates, demonstrate how racial and ethnic disparities can impact epidemic trajectories and result in unequal distributions of SARS-CoV-2 infection. K.C.M. was supported by National Science Foundation GRFP grant DGE1745303. Y.H.G. and M.L. were funded by the Morris-Singer Foundation. M.L. was supported by SeroNet cooperative agreement U01 CA261277.

Relationship of Test Positivity Rates with COVID-19 Epidemic Dynamics.

Detection and isolation of infected people are believed to play an important role in the control of the COVID-19 pandemic. Some countries conduct large-scale screenings for testing, whereas others test mainly people with high prior probability of infection such as showing severe symptoms and/or having an epidemiological link with a known or suspected case or cluster of cases. However, what a good testing strategy is and whether the difference in testing strategy shows a meaningful, measurable impact on the COVID-19 epidemic remain unknown. Here, we showed that patterns of association between effective reproduction number (Rt) and test positivity rate can illuminate differences in testing situation among different areas, using global and local data from Japan. This association can also evaluate the adequacy of current testing systems and what information is captured in COVID-19 surveillance. The differences in testing systems alone cannot predict the results of epidemic containment efforts. Furthermore, monitoring test positivity rates and severe case proportions among the nonelderly can predict imminent case count increases. Monitoring test positivity rates in conjunction with the concurrent Rt could be useful to assess and strengthen public health management and testing systems and deepen understanding of COVID-19 epidemic dynamics.

Predictions of COVID-19 Pandemic Dynamics in Ukraine and Qatar Based on Generalized SIR Model

Background. To simulate how the number of COVID-19 cases increases versus time, various data sets and different mathematical models can be used. Since there are some differences in statistical data, the results of simulations can be different. Complex mathematical models contain many unknown parameters, the values ​​of which must be determined using a limited number of observations of the disease over time. Even long-term monitoring of the epidemic may not provide reliable estimates of the model parameters due to the constant change of testing conditions, isolation of infected, quarantine conditions, pathogen mutations, vaccinations, etc. Therefore, simpler approaches are necessary. In particular, previous simulations of the COVID-19 epidemic dynamics in Ukraine were based on smoothing of the dependence of the number of cases on time and the generalized SIR (susceptible–infected–removed) model. These approaches allowed detecting the pandemic waves and calculating adequate predictions of their duration and final sizes. In particular, eight waves of the COVID-19 pandemic in Ukraine were investigated. Objective. We aimed to detect the changes in the pandemic dynamics and present the results of SIR simu­lations based on Ukrainian national statistics and data reported by Johns Hopkins University (JHU) for Ukraine and Qatar. Methods. In this study we use the smoothing method for the dependences of the number of cases on time, the generalized SIR model for the dynamics of any epidemic wave, the exact solution of the linear differential equations, and statistical approach for the model parameter identification developed before. Results. The optimal values of the SIR model parameters were calculated and some predictions about final sizes and durations of the epidemics are presented. Corresponding SIR curves are shown and compared with the real numbers of cases. Conclusions. Unfortunately, the forecasts are not very optimistic: in Ukraine, new cases will not stop appearing until June–July 2021; in Qatar, new cases are likely to appear throughout 2021. The expected long duration of the pandemic forces us to be careful and in solidarity. Probably the presented results could be useful in order to estimate the efficiency of vaccinations.

Complex network model for COVID-19: Human behavior, pseudo-periodic solutions and multiple epidemic waves

We propose a mathematical model for the transmission dynamics of SARS-CoV-2 in a homogeneously mixing non constant population, and generalize it to a model where the parameters are given by piecewise constant functions. This allows us to model the human behavior and the impact of public health policies on the dynamics of the curve of active infected individuals during a COVID-19 epidemic outbreak. After proving the existence and global asymptotic stability of the disease-free and endemic equilibrium points of the model with constant parameters, we consider a family of Cauchy problems, with piecewise constant parameters, and prove the existence of pseudo-oscillations between a neighborhood of the disease-free equilibrium and a neighborhood of the endemic equilibrium, in a biologically feasible region. In the context of the COVID-19 pandemic, this pseudo-periodic solutions are related to the emergence of epidemic waves. Then, to capture the impact of mobility in the dynamics of COVID-19 epidemics, we propose a complex network with six distinct regions based on COVID-19 real data from Portugal. We perform numerical simulations for the complex network model, where the objective is to determine a topology that minimizes the level of active infected individuals and the existence of topologies that are likely to worsen the level of infection. We claim that this methodology is a tool with enormous potential in the current pandemic context, and can be applied in the management of outbreaks (in regional terms) but also to manage the opening/closing of borders.

Modeling the Dynamics of Coronavirus Disease Pandemic Coupled with Fear Epidemics.

A modeling approach to investigate the dynamics of COVID-19 epidemics coupled with fear is presented in this paper. The basic reproduction number R0 is computed and employed in analysing the effect of initial transmission and the conditions for disease control or eradication. Numerical simulations show that whenever there is an outbreak coupled with fear, the disease is likely to persist in the first two months, and after that, it will start to slow down as the recovery rate from fear increases. An increase in the number of recovered individuals lead to a rise in the number of susceptibles and consequently set off a second wave of infection in the third month of the epidemic.

Effect of timing of implementation of containment measures on Covid-19 epidemic. The case of the first wave in Italy.

There is evidence that adoption of non-pharmaceutical containment measures (NPMs) may have had a major impact on Covid-19 epidemic dynamics, and mitigated its effect on healthcare system. Optimal timing of implementation of these measures however is not known. In Italy, a national lockdown was decided on March 11th 2020 and ended 4th of May. At that time, cumulative incidence (CI) was different in Italian regions which ranged from <5 cases/100,000 to >11 cases/100,000 inhabitants. In this paper, we aim to evaluate how level of incidence in different regions at the time of implementation of NPMs affected CI and had an impact on the healthcare system in terms of ICU bed occupancy and mortality rates. We used regional daily new COVID-19 diagnosed cases as well number of people hospitalized in ICU and number of deaths for period February 24-May 11 from all the 19 Italian regions and two autonomous provinces. For each region we calculated: temporal daily trend of cumulative cases of Covid-19/100,000 inhabitants, daily trend of ICU bed occupancy and mortality rate at the end of period. We found that the epidemic curves show similar trends for all regions and all tend to flatten between 11-32 days. However, after 2 months, regions with lower CI at lockdown remained at substantially lower CI (<265 cases/100,000), had a peak of percentage of cases hospitalized in ICU which did not exceed 79.4% and a mortality<0.27/1,000. On the other hand, in regions with higher incidence at lockdown, CI reached 382-921 cases/100,000, the peak of percentage of cases hospitalized in ICU and mortality rate reached 270%, and 1.5/1,000, respectively. Our data suggests that level of CI at the moment of lockdown is important to control the subsequent spread of infection so NPMs should be adopted very early during the course of Covid-19 epidemic, in order to mitigate the impact on the healthcare system and to reduce related mortality.

Chopping the tail: How preventing superspreading can help to maintain COVID-19 control

Disease transmission is notoriously heterogeneous, and SARS-CoV-2 is no exception. A skewed distribution where few individuals or events are responsible for the majority of transmission can result in explosive, superspreading events, which produce rapid and volatile epidemic dynamics, especially early or late in epidemics. Anticipating and preventing superspreading events can produce large reductions in overall transmission rates. Here, we present a stochastic compartmental (SEIR) epidemiological model framework for estimating transmission parameters from multiple imperfectly observed data streams, including reported cases, deaths, and mobile phone-based mobility that incorporates individual-level heterogeneity in transmission using previous estimates for SARS-CoV-1 and SARS-CoV-2. We parameterize the model for COVID-19 epidemic dynamics by estimating a time-varying transmission rate that incorporates the impact of non-pharmaceutical intervention strategies that change over time, in five epidemiologically distinct settings—Los Angeles and Santa Clara Counties, California; Seattle (King County), Washington; Atlanta (Dekalb and Fulton Counties), Georgia; and Miami (Miami-Dade County), Florida. We find that the effective reproduction number (RE) dropped below 1 rapidly in all five locations following social distancing orders in mid-March, 2020, but that gradually increasing mobility starting around mid-April led to an RE once again above 1 in late May (Los Angeles, Miami, and Atlanta) or early June (Santa Clara County and Seattle). However, we find that increased social distancing starting in mid-July in response to epidemic resurgence once again dropped RE below 1 in all locations by August 14. We next used the fitted model to ask: how does truncating the individual-level transmission rate distribution (which removes periods of time with especially high individual transmission rates and thus models superspreading events) affect epidemic dynamics and control? We find that interventions that truncate the transmission rate distribution while partially relaxing social distancing are broadly effective, with impacts on epidemic growth on par with the strongest population-wide social distancing observed in April, 2020. Given that social distancing interventions will be needed to maintain epidemic control until a vaccine becomes widely available, “chopping off the tail” to reduce the probability of superspreading events presents a promising option to alleviate the need for extreme general social distancing.

South African COVID-19 Epidemic Dynamics Are Consistent with Widespread Cross-Immunity

The progression of the Covid-19 pandemic in South Africa, as measured by the number of deaths in excess of the seasonally-expected mortality, is inconsistent with infectivity and fatality rates estimated elsewhere in the world.A compartment model applied in prognostic and inverse mode was used to explore the combinations of key parameters that could account for the outbreak timing and magnitude of Covid-19 mortality in the Western Cape Province in South Africa, where information on reported cases and deaths are most reliable.If it is assumed that the entire population is susceptible, the total number of deaths by October 2020, after six months of propagation, is far lower than expected for fatality and infection rates in the plausible range. The unimodal infection peak, followed by a substantial decline coinciding with the relaxation of non-pharmacological interventions, suggests that herd immunity has been reached, but serological tests for exposure indicate that too few people have been infected for this to be the case. We show that the number of excess deaths, timing of the peak infection and proportion of the population infected can all be explained by assuming 30-40% pre-existing cross-immunity in the population.The dynamics of Covid-19 in South Africa cannot be explained under the assumption of a fully susceptible population. Rather than postulating, against the evidence, that the coronavirus exhibits fundamentally low infectivity or morbidity rates in South Africa, we point out that wide-spread, pre-existing cross-reactive immunity to SARS-CoV-2, could explain the observations. If this is the case, the likelihood of a large second wave is low if those infected do not rapidly lose immunity.Funding Statement: The salaries of Engelbrecht and Scholes are funded by the University of the Witwatersrand. Otherwise, no dedicated source of funding supported this research, and neither author received funding from any source to write the paper.Declaration of Interests: The authors have nothing to disclose.

The scale and dynamics of COVID-19 epidemics across Europe.

The number of COVID-19 deaths reported from European countries has varied more than 100-fold. In terms of coronavirus transmission, the relatively low death rates in some countries could be due to low intrinsic (e.g. low population density) or imposed contact rates (e.g. non-pharmaceutical interventions) among individuals, or because fewer people were exposed or susceptible to infection (e.g. smaller populations). Here, we develop a flexible empirical model (skew-logistic) to distinguish among these possibilities. We find that countries reporting fewer deaths did not generally have intrinsically lower rates of transmission and epidemic growth, and flatter epidemic curves. Rather, countries with fewer deaths locked down earlier, had shorter epidemics that peaked sooner and smaller populations. Consequently, as lockdowns were eased, we expected, and duly observed, a resurgence of COVID-19 across Europe.