Estimating the effective reproduction number for heterogeneous models using incidence data

Spatial analysis of Dengue through the reproduction numbers relating to socioeconomic features: Case studies on two Brazilian urban centers

The study of the propagation of infectious diseases in urban centers finds a close connection with their population's social characteristics and behavior. This work performs a spatial analysis of dengue cases in urban centers based on the basic reproduction numbers, R0, and incidence by planning areas (PAs), as well as their correlations with the Human Development Index (HDI) and the number of trips. We analyzed dengue epidemics in 2002 at two Brazilian urban centers, Belo Horizonte (BH) and Rio de Janeiro (RJ), using PAs as spatial units. Our results reveal heterogeneous spatial scenarios for both cities, with very weak correlations between R0 and both the number of trips and the HDI; in BH, the values of R0 show a less spatial heterogeneous pattern than in RJ. For BH, there are moderate correlations between incidence and both the number of trips and the HDI; meanwhile, they weakly correlate for RJ. Finally, the absence of strong correlations between the considered measures indicates that the transmission process should be treated considering the city as a whole.

A semi-empirical risk panel to monitor epidemics: multi-faceted tool to assist healthcare and public health professionals

Introduction

Bronchiolitis, mostly caused by Respiratory Syncytial Virus (RSV), and influenza among other respiratory infections, lead to seasonal saturation at healthcare centers in temperate areas. There is no gold standard to characterize the stages of epidemics, nor the risk of respiratory infections growing. We aimed to define a set of indicators to assess the risk level of respiratory viral epidemics, based on both incidence and their short-term dynamics, and considering epidemical thresholds.

Methods

We used publicly available data on daily cases of influenza for the whole population and bronchiolitis in children <2 years from the Information System for Infection Surveillance in Catalonia (SIVIC). We included a Moving Epidemic Method (MEM) variation to define epidemic threshold and levels. We pre-processed the data with two different nowcasting approaches and performed a 7-day moving average. Weekly incidences (cases per 105 population) were computed and the 5-day growth rate was defined to create the effective potential growth (EPG) indicator. We performed a correlation analysis to define the forecasting ability of this index.

Results

Our adaptation of the MEM method allowed us to define epidemic weekly incidence levels and epidemic thresholds for bronchiolitis and influenza. EPG was able to anticipate daily 7-day cumulative incidence by 4-5 (bronchiolitis) or 6-7 (influenza) days.

Discussion

We developed a semi-empirical risk panel incorporating the EPG index, which effectively anticipates surpassing epidemic thresholds for bronchiolitis and influenza. This panel could serve as a robust surveillance tool, applicable to respiratory infectious diseases characterized by seasonal epidemics, easy to handle for individuals lacking a mathematical background.

Novel Approach for Identification of Basic and Effective Reproduction Numbers Illustrated with COVID-19

This paper presents a novel numerical technique for the identification of effective and basic reproduction numbers, Re and R0, for long-term epidemics, using an inverse problem approach. The method is based on the direct integration of the SIR (Susceptible-Infectious-Removed) system of ordinary differential equations and the least-squares method. Simulations were conducted using official COVID-19 data for the United States and Canada, and for the states of Georgia, Texas, and Louisiana, for a period of two years and ten months. The results demonstrate the applicability of the method in simulating the dynamics of the epidemic and reveal an interesting relationship between the number of currently infectious individuals and the effective reproduction number, which is a useful tool for predicting the epidemic dynamics. For all conducted experiments, the results show that the local maximum (and minimum) values of the time-dependent effective reproduction number occur approximately three weeks before the local maximum (and minimum) values of the number of currently infectious individuals. This work provides a novel and efficient approach for the identification of time-dependent epidemics parameters.

Estimating the effective reproduction number for heterogeneous models using incidence data

The effective reproduction number, R ( t ) , plays a key role in the study of infectious diseases, indicating the current average number of new infections caused by an infected individual in an epidemic process. Estimation methods for the time evolution of R ( t ) , using incidence data, rely on the generation interval distribution, g(τ), which is usually obtained from empirical data or theoretical studies using simple epidemic models. However, for systems that present heterogeneity, either on the host population or in the expression of the disease, there is a lack of data and of a suitable general methodology to obtain g(τ). In this work, we use mathematical models to bridge this gap. We present a general methodology for obtaining explicit expressions of the reproduction numbers and the generation interval distributions, within and between model sub-compartments provided by an arbitrary compartmental model. Additionally, we present the appropriate expressions to evaluate those reproduction numbers using incidence data. To highlight the relevance of such methodology, we apply it to the spread of COVID-19 in municipalities of the state of Rio de Janeiro, Brazil. Using two meta-population models, we estimate the reproduction numbers and the contributions of each municipality in the generation of cases in all others.