A parsimonious approach for spatial transmission and heterogeneity in the COVID-19 propagation

A Stochastic Mobility-Driven Spatially Explicit SEIQRD covid-19 Model with VOCs, Seasonality, and Vaccines

In this work, we extend our previously developed compartmental SEIQRD model for sars-cov-2 in Belgium. We introduce sars-cov-2 variants of concern, vaccines, and seasonality in our model, as their addition has proven necessary for modelling sars-cov-2 transmission dynamics during the 2020-2021 covid-19 pandemic in Belgium. The model is geographically stratified into eleven spatial patches (provinces), and a telecommunication dataset provided by Belgium's biggest operator is used to incorporate interprovincial mobility. We calibrate the model using the daily number of hospitalisations in each province and serological data. We find the model adequately describes these data, but the addition of interprovincial mobility was not necessary to obtain an accurate description of the 2020-2021 sars-cov-2 pandemic in Belgium. We further demonstrate how our model can be used to help policymakers decide on the optimal timing of the release of social restrictions.We find that adding spatial heterogeneity by geographically stratifying the model results in more uncertain model projections as compared to an equivalent nation-level model, which has both communicative advantages and disadvantages. We finally discuss the impact of imposing local mobility or social contact restrictions to contain an epidemic in a given province and find that lowering social contact is a more effective strategy than lowering mobility.

Forecasting Pathogen Dynamics with Bayesian Model-Averaging: Application to Xylella fastidiosa

Forecasting invasive-pathogen dynamics is paramount to anticipate eradication and containment strategies. Such predictions can be obtained using a model grounded on partial differential equations (PDE; often exploited to model invasions) and fitted to surveillance data. This framework allows the construction of phenomenological but concise models relying on mechanistic hypotheses and real observations. However, it may lead to models with overly rigid behavior and possible data-model mismatches. Hence, to avoid drawing a forecast grounded on a single PDE-based model that would be prone to errors, we propose to apply Bayesian model averaging (BMA), which allows us to account for both parameter and model uncertainties. Thus, we propose a set of different competing PDE-based models for representing the pathogen dynamics, we use an adaptive multiple importance sampling algorithm (AMIS) to estimate parameters of each competing model from surveillance data in a mechanistic-statistical framework, we evaluate the posterior probabilities of models by comparing different approaches proposed in the literature, and we apply BMA to draw posterior distributions of parameters and a posterior forecast of the pathogen dynamics. This approach is applied to predict the extent of Xylella fastidiosa in South Corsica, France, a phytopathogenic bacterium detected in situ in Europe less than 10 years ago (Italy 2013, France 2015). Separating data into training and validation sets, we show that the BMA forecast outperforms competing forecast approaches.

Mobility and the spatial spread of sars-cov-2 in Belgium

We analyse and mutually compare time series of covid-19-related data and mobility data across Belgium's 43 arrondissements (NUTS 3). In this way, we reach three conclusions. First, we could detect a decrease in mobility during high-incidence stages of the pandemic. This is expressed as a sizeable change in the average amount of time spent outside one's home arrondissement, investigated over five distinct periods, and in more detail using an inter-arrondissement "connectivity index" (CI). Second, we analyse spatio-temporal covid-19-related hospitalisation time series, after smoothing them using a generalise additive mixed model (GAMM). We confirm that some arrondissements are ahead of others and morphologically dissimilar to others, in terms of epidemiological progression. The tools used to quantify this are time-lagged cross-correlation (TLCC) and dynamic time warping (DTW), respectively. Third, we demonstrate that an arrondissement's CI with one of the three identified first-outbreak arrondissements is correlated to a substantial local excess mortality some five to six weeks after the first outbreak. More generally, we couple results leading to the first and second conclusion, in order to demonstrate an overall correlation between CI values on the one hand, and TLCC and DTW values on the other. We conclude that there is a strong correlation between physical movement of people and viral spread in the early stage of the sars-cov-2 epidemic in Belgium, though its strength weakens as the virus spreads.

Epidemic modeling with heterogeneity and social diffusion

We propose and analyze a family of epidemiological models that extend the classic Susceptible-Infectious-Recovered/Removed (SIR)-like framework to account for dynamic heterogeneity in infection risk. The family of models takes the form of a system of reaction-diffusion equations given populations structured by heterogeneous susceptibility to infection. These models describe the evolution of population-level macroscopic quantities S, I, R as in the classical case coupled with a microscopic variable f, giving the distribution of individual behavior in terms of exposure to contagion in the population of susceptibles. The reaction terms represent the impact of sculpting the distribution of susceptibles by the infection process. The diffusion and drift terms that appear in a Fokker-Planck type equation represent the impact of behavior change both during and in the absence of an epidemic. We first study the mathematical foundations of this system of reaction-diffusion equations and prove a number of its properties. In particular, we show that the system will converge back to the unique equilibrium distribution after an epidemic outbreak. We then derive a simpler system by seeking self-similar solutions to the reaction-diffusion equations in the case of Gaussian profiles. Notably, these self-similar solutions lead to a system of ordinary differential equations including classic SIR-like compartments and a new feature: the average risk level in the remaining susceptible population. We show that the simplified system exhibits a rich dynamical structure during epidemics, including plateaus, shoulders, rebounds and oscillations. Finally, we offer perspectives and caveats on ways that this family of models can help interpret the non-canonical dynamics of emerging infectious diseases, including COVID-19.

Population density impact on COVID-19 mortality rate: A multifractal analysis using French data

The current COVID-19 pandemic caught everyone off guard and is an excellent case study to investigate the real impact of population density on emerging highly contagious infectious diseases. The relationship between the threat of COVID-19 and population density has been widely debated not only in scientific articles, but also in magazines and reports around the world. It appeared both in the columns of experts and in the speeches of politicians, yet without reaching any consensus. In this study, using COVID-19 data from France, we try to shed light on this debate. An alternative density measure, weighted by population, is used. This novel density measure clearly outperforms the commonly used density in terms of relationship with COVID-19 deaths and proved to be competitive with some of the best known predictors, including population. A multifractal analysis, characterizing different space distributions of population in France, is used to further understand the relation between density and COVID-19 mortality rate.

Population density and spreading of COVID-19 in England and Wales

We investigated daily COVID-19 cases and deaths in the 337 lower tier local authority regions in England and Wales to better understand how the disease propagated over a 15-month period. Population density scaling models revealed residual variance and skewness to be sensitive indicators of the dynamics of propagation. Lockdowns and schools reopening coincided with increased variance indicative of conditions with local impact and country scale heterogeneity. University reopening and December holidays reduced variance indicative of country scale homogenisation which reached a minimum in mid-January 2021. Homogeneous propagation was associated with better correspondence with normally distributed residuals while heterogeneous propagation was more consistent with skewed models. Skewness varied from strongly negative to strongly positive revealing an unappreciated feature of community propagation. Hot spots and super-spreading events are well understood descriptors of regional disease dynamics that would be expected to be associated with positively skewed distributions. Positively skewed behaviour was observed; however, negative skewness indicative of "cold-spots" and "super-isolation" dominated for approximately 8 months during the period of study. In contrast, death metrics showed near constant behaviour in scaling, variance, and skewness metrics over the full period with rural regions preferentially affected, an observation consistent with regional age demographics in England and Wales. Regional positions relative to density scaling laws were remarkably persistent after the first 5-9 days of the available data set. The determinants of this persistent behaviour probably precede the pandemic and remain unchanged.

The Geographical Distribution and Influencing Factors of COVID-19 in China

The study of the spatial differentiation of COVID-19 in cities and its driving mechanism is helpful to reveal the spatial distribution pattern, transmission mechanism and diffusion model, and evolution mechanism of the epidemic and can lay the foundation for constructing the spatial dynamics model of the epidemic and provide theoretical basis for the policy design, spatial planning and implementation of epidemic prevention and control and social governance. Geodetector (Origin version, Beijing, China) is a great tool for analysis of spatial differentiation and its influencing factors, and it provides decision support for differentiated policy design and its implementation in executing the city-specific policies. Using factor detection and interaction analysis of Geodetector, 15 indicators of economic, social, ecological, and environmental dimensions were integrated, and 143 cities were selected for the empirical research in China. The research shows that, first of all, risks of both infection and death show positive spatial autocorrelation, but the geographical distribution of local spatial autocorrelation differs significantly between the two. Secondly, the inequalities in urban economic, social, and residential environments interact with COVID-19 spatial heterogeneity, with stronger explanatory power especially when multidimensional inequalities are superimposed. Thirdly, the spatial distribution and spread of COVID-19 are highly spatially heterogeneous and correlated due to the complex influence of multiple factors, with factors such as Area of Urban Construction Land, GDP, Industrial Smoke and Dust Emission, and Expenditure having the strongest influence, the factors such as Area of Green, Number of Hospital Beds and Parks, and Industrial NOx Emissions having unignorable influence, while the factors such as Number of Free Parks and Industrial Enterprises, Per-GDP, and Population Density play an indirect role mainly by means of interaction. Fourthly, the factor interaction effect from the infected person's perspective mainly shows a nonlinear enhancement effect, that is, the joint influence of the two factors is greater than the sum of their direct influences; but from the perspective of the dead, it mainly shows a two-factor enhancement effect, that is, the joint influence of the two factors is greater than the maximum of their direct influences but less than their sum. Fifthly, some suggestions are put forward from the perspectives of building a healthy, resilient, safe, and smart city, providing valuable reference and decision basis for city governments to carry out differentiated policy design.

Spatial Patterns of the Spread of COVID-19 in Singapore and the Influencing Factors

Exploring the spatial patterns of COVID-19 transmission and its key determinants could provide a deeper understanding of the evolution of the COVID-19 pandemic. The goal of this study is to investigate the spatial patterns of COVID-19 transmission in different periods in Singapore, as well as their relationship with demographic and built-environment factors. Based on reported cases from 23 January to 30 September 2020, we divided the research time into six phases and used spatial autocorrelation analysis, the ordinary least squares (OLS) model, the multiscale geographically weighted regression (MGWR) model, and dominance analysis to explore the spatial patterns and influencing factors in each phase. The results showed that the spatial patterns of COVID-19 cases differed across time, and imported cases presented a random pattern, whereas local cases presented a clustered pattern. Among the selected variables, the supermarket density, elderly population density, hotel density, business land proportion, and park density may be particular fitting indicators explaining the different phases of pandemic development in Singapore. Furthermore, the associations between determinants and COVID-19 transmission changed dynamically over time. This study provides policymakers with valuable information for developing targeted interventions for certain areas and periods.

Heterogeneity of the COVID-19 Pandemic in the United States of America: A Geo-Epidemiological Perspective

The spread of the COVID-19 pandemic has shown great heterogeneity between regions of countries, e. g., in the United States of America (USA). With the growing of the worldwide COVID-19 pandemic, there is a need to better highlight the variability in the trajectory of this disease in different worldwide geographic areas. Indeed, the epidemic trends across areas can display completely different evolution at a given time. Geo-epidemiological analyses using data, that are publicly available, could be a major topic to help governments and public administrations to implement health policies. Geo-epidemiological analyses could provide a basis for the implementation of relevant public health policies. With the COVID-19 pandemic, geo-epidemiological analyses can be readily utilized by policy interventions and USA public health authorities to highlight geographic areas of particular concern and enhance the allocation of resources.

A new logistic growth model applied to COVID-19 fatality data

BACKGROUND

Recent work showed that the temporal growth of the novel coronavirus disease (COVID-19) follows a sub-exponential power-law scaling whenever effective control interventions are in place. Taking this into consideration, we present a new phenomenological logistic model that is well-suited for such power-law epidemic growth.

METHODS

We empirically develop the logistic growth model using simple scaling arguments, known boundary conditions and a comparison with available data from four countries, Belgium, China, Denmark and Germany, where (arguably) effective containment measures were put in place during the first wave of the pandemic. A non-linear least-squares minimization algorithm is used to map the parameter space and make optimal predictions.

RESULTS

Unlike other logistic growth models, our presented model is shown to consistently make accurate predictions of peak heights, peak locations and cumulative saturation values for incomplete epidemic growth curves. We further show that the power-law growth model also works reasonably well when containment and lock down strategies are not as stringent as they were during the first wave of infections in 2020. On the basis of this agreement, the model was used to forecast COVID-19 fatalities for the third wave in South Africa, which was in progress during the time of this work.

CONCLUSION

We anticipate that our presented model will be useful for a similar forecasting of COVID-19 induced infections/deaths in other regions as well as other cases of infectious disease outbreaks, particularly when power-law scaling is observed.

Estimation of Daily Reproduction Numbers during the COVID-19 Outbreak

(1) Background: The estimation of daily reproduction numbers throughout the contagiousness period is rarely considered, and only their sum R0 is calculated to quantify the contagiousness level of an infectious disease. (2) Methods: We provide the equation of the discrete dynamics of the epidemic’s growth and obtain an estimation of the daily reproduction numbers by using a deconvolution technique on a series of new COVID-19 cases. (3) Results: We provide both simulation results and estimations for several countries and waves of the COVID-19 outbreak. (4) Discussion: We discuss the role of noise on the stability of the epidemic’s dynamics. (5) Conclusions: We consider the possibility of improving the estimation of the distribution of daily reproduction numbers during the contagiousness period by taking into account the heterogeneity due to several host age classes.

Multi-population analysis of the Cuban SARS-CoV-2 epidemic transmission before and during the vaccination process

In this work, several mathematical models for the spread of viruses and diseases are presented. In particular, the work focuses on the coronavirus disease 2019 (COVID-19) pandemic. A multi-population model is presented for the study of the interaction of various populations and the contagion of the virus between them. A second model on vaccination is presented, which allows analyzing the behavior of the disease taking into account the effectiveness of the vaccine and the speed of COVID-19 after the vaccination process. Finally, both models are applied to analyze the epidemic in Cuba. For this study, the official data reported by the Cuban Ministry of Health from March 2020 to August 2021 is used.

Plateaus, rebounds and the effects of individual behaviours in epidemics

Plateaus and rebounds of various epidemiological indicators are widely reported in Covid-19 pandemics studies but have not been explained so far. Here, we address this problem and explain the appearance of these patterns. We start with an empirical study of an original dataset obtained from highly precise measurements of SARS-CoV-2 concentration in wastewater over nine months in several treatment plants around the Thau lagoon in France. Among various features, we observe that the concentration displays plateaus at different dates in various locations but at the same level. In order to understand these facts, we introduce a new mathematical model that takes into account the heterogeneity and the natural variability of individual behaviours. Our model shows that the distribution of risky behaviours appears as the key ingredient for understanding the observed temporal patterns of epidemics.

The Spatiotemporal Interaction Effect of COVID-19 Transmission in the United States

(1) Background: Human mobility between geographic units is an important way in which COVID-19 is spread across regions. Due to the pressure of epidemic control and economic recovery, states in the United States have adopted different policies for mobility limitations. Assessing the impact of these policies on the spatiotemporal interaction of COVID-19 transmission among counties in each state is critical to formulating epidemic policies. (2) Methods: We utilized Moran’s I index and K-means clustering to investigate the time-varying spatial autocorrelation effect of 49 states (excluding the District of Colombia) with daily new cases at the county level from 22 January 2020 to 20 August 2020. Based on the dynamic spatial lag model (SLM) and the SIR model with unreported infection rate (SIRu), the integrated SLM-SIRu model was constructed to estimate the inter-county spatiotemporal interaction coefficient of daily new cases in each state, which was further explored by Pearson correlation test and stepwise OLS regression with socioeconomic factors. (3) Results: The K-means clustering divided the time-varying spatial autocorrelation curves of the 49 states into four types: continuous increasing, fluctuating increasing, weak positive, and weak negative. The Pearson correlation analysis showed that the spatiotemporal interaction coefficients in each state estimated by SLM-SIRu were significantly positively correlated with the variables of median age, population density, and proportions of international immigrants and highly educated population, but negatively correlated with the birth rate. Further stepwise OLS regression retained only three positive correlated variables: poverty rate, population density, and highly educated population proportion. (4) Conclusions: This result suggests that various state policies in the U.S. have imposed different impacts on COVID-19 transmission among counties. All states should provide more protection and support for the low-income population; high-density populated states need to strengthen regional mobility restrictions; and the highly educated population should reduce unnecessary regional movement and strengthen self-protection.

Modelling COVID-19 contagion: risk assessment and targeted mitigation policies

We use a spatial epidemic model with demographic and geographical heterogeneity to study the regional dynamics of COVID-19 across 133 regions in England. Our model emphasizes the role of variability of regional outcomes and heterogeneity across age groups and geographical locations, and provides a framework for assessing the impact of policies targeted towards subpopulations or regions. We define a concept of efficiency for comparative analysis of epidemic control policies and show targeted mitigation policies based on local monitoring to be more efficient than country-level or non-targeted measures. In particular, our results emphasize the importance of shielding vulnerable subpopulations and show that targeted policies based on local monitoring can considerably lower fatality forecasts and, in many cases, prevent the emergence of second waves which may occur under centralized policies.