Modinterv COVID-19: An online platform to monitor the evolution of epidemic curves

We present the software ModInterv as an informatics tool to monitor, in an automated and user-friendly manner, the evolution and trend of COVID-19 epidemic curves, both for cases and deaths. The ModInterv software uses parametric generalized growth models, together with LOWESS regression analysis, to fit epidemic curves with multiple waves of infections for countries around the world as well as for states and cities in Brazil and the USA. The software automatically accesses publicly available COVID-19 databases maintained by the Johns Hopkins University (for countries as well as states and cities in the USA) and the Federal University of Vicosa (for states and cities in Brazil). The richness of the implemented models lies in the possibility of quantitatively and reliably detecting the distinct acceleration regimes of the disease. We describe the backend structure of software as well as its practical use. The software helps the user not only to understand the current stage of the epidemic in a chosen location but also to make short term predictions as to how the curves may evolve. The app is freely available on the internet (http://fisica.ufpr.br/modinterv), thus making a sophisticated mathematical analysis of epidemic data readily accessible to any interested user.

Situation of COVID-19 in Brazil: An analysis via growth models as implemented in the ModInterv system for monitoring the pandemic

In this work we analyze the cumulative curves of deaths attributed to COVID-19 in the 26 Brazilian States and the Federal District up until August 21, 2020. Mathematical growth models implemented by the application ModInterv COVID-19, which can be accessed via internet browser or via a mobile app, were used to investigate at which stage the epidemic is in each of the Brazilian federal units. The analysis revealed that almost all states in the Northern and Northeastern regions were already in the saturation phase, meaning that the epidemic was relatively under control, whereas in all Southern states and in most states in the Midwest the epidemic was still accelerating or showed only a slight deceleration. The Southeastern region presented a great diversity of epidemic stages, with each state being found at a different stage, ranging from acceleration to saturation. It is argued that understanding this heterogeneous geographical distribution of the epidemic is relevant for public health authorities, as it may help in devising more effective strategies against the COVID-19 pandemic in a continental country like Brazil.

Standard and anomalous second waves in the COVID-19 pandemic

We apply a generalised logistic growth model, with time dependent parameters, to describe the fatality curves of the COVID-19 disease for several countries that exhibit a second wave of infections. The model parameters vary as a function of time according to a logistic function, whose two extreme values, i.e., for early and late times, characterise the first and second waves, respectively. We show that the theoretical curves are in excellent agreement with the empirical data for all cases considered. The model also allows for predictions about the time of occurrence and relative severity of the second wave, in comparison to the first wave. It is shown furthermore that the COVID-19 second waves can be generically classified in two main types, namely, standard and anomalous second waves, according as to whether the second wave starts well after or still during the first wave, respectively. We have also observed that the standard second waves tend, in their majority, to be more severe than the corresponding first wave, whereas for anomalous second waves the opposite occurs.

Modelling the epidemic growth of preprints on COVID-19 and SARS-CoV-2

The response of the scientific community to the global health emergency caused by the COVID-19 pandemic has produced an unprecedented number of manuscripts in a short period of time, the vast majority of which have been shared in the form of preprints posted on online preprint repositories before peer review. This surge in preprint publications has in itself attracted considerable attention, although mostly in the bibliometrics literature. In the present study we apply a mathematical growth model, known as the generalized Richards model, to describe the time evolution of the cumulative number of COVID-19 related preprints. This mathematical approach allows us to infer several important aspects concerning the underlying growth dynamics, such as its current stage and its possible evolution in the near future. We also analyze the rank-frequency distribution of preprints servers, ordered by the number of COVID-19 preprints they host, and find that it follows a power law in the low rank (high frequency) region, with the high rank (low frequency) tail being better described by a q-exponential function. The Zipf-like law in the high frequency regime indicates the presence of a cumulative advantage effect, whereby servers that already have more preprints receive more submissions.

Complexity signatures in the COVID-19 epidemic: power law behaviour in the saturation regime of fatality curves

ABSTRACWe apply a versatile growth model, whose growth rate is given by a generalised beta distribution, to describe the complex behaviour of the fatality curves of the COVID-19 disease for several countries in Europe and North America. We show that the COVID-19 epidemic curves not only may present a subexponential early growth but can also exhibit a similar subexponential (power-law) behaviour in the saturation regime. We argue that the power-law exponent of the latter regime, which measures how quickly the curve approaches the plateau, is directly related to control measures, in the sense that the less strict the control, the smaller the exponent and hence the slower the diseases progresses to its end. The power-law saturation uncovered here is an important result, because it signals to policymakers and health authorities that it is important to keep control measures for as long as possible, so as to avoid a slow, power-law ending of the disease. The slower the approach to the plateau, the longer the virus lingers on in the population, and the greater not only the final death toll but also the risk of a resurgence of infections.

Modelling fatality curves of COVID-19 and the effectiveness of intervention strategies

The main objective of the present paper is twofold: first, to model the fatality curves of the COVID-19 disease, as represented by the cumulative number of deaths as a function of time; and second, to use the corresponding mathematical model to study the effectiveness of possible intervention strategies. We applied the Richards growth model (RGM) to the COVID-19 fatality curves from several countries, where we used the data from the Johns Hopkins University database up to May 8, 2020. Countries selected for analysis with the RGM were China, France, Germany, Iran, Italy, South Korea, and Spain. The RGM was shown to describe very well the fatality curves of China, which is in a late stage of the COVID-19 outbreak, as well as of the other above countries, which supposedly are in the middle or towards the end of the outbreak at the time of this writing. We also analysed the case of Brazil, which is in an initial sub-exponential growth regime, and so we used the generalised growth model which is more appropriate for such cases. An analytic formula for the efficiency of intervention strategies within the context of the RGM is derived. Our findings show that there is only a narrow window of opportunity, after the onset of the epidemic, during which effective countermeasures can be taken. We applied our intervention model to the COVID-19 fatality curve of Italy of the outbreak to illustrate the effect of several possible interventions.