On estimating the basic reproduction number in distinct stages of a contagious disease spreading

In epidemiology, the basic reproduction number R-0 is usually defined as the average number of new infections caused by a single infective individual introduced into a completely susceptible population. According to this definition. R-0 is related to the initial stage of the spreading of a contagious disease. However, from epidemiological models based on ordinary differential equations (ODE), R-0 is commonly derived from a linear stability analysis and interpreted as a bifurcation parameter: typically, when R-0 >1, the contagious disease tends to persist in the population because the endemic stationary solution is asymptotically stable: when R-0 <1, the corresponding pathogen tends to naturally disappear because the disease-free stationary solution is asymptotically stable. Here we intend to answer the following question: Do these two different approaches for calculating R-0 give the same numerical values? In other words, is the number of secondary infections caused by a unique sick individual equal to the threshold obtained from stability analysis of steady states of ODE? For finding the answer, we use a susceptibleinfective-recovered (SIR) model described in terms of ODE and also in terms of a probabilistic cellular automaton (PCA), where each individual (corresponding to a cell of the PCA lattice) is connected to others by a random network favoring local contacts. The values of R-0 obtained from both approaches are compared, showing good agreement. (C) 2012 Elsevier B.V. All rights reserved.

Phylogenetic analysis of rubella virus strains during an outbreak in Sao Paulo, 2007-2008

Rubella virus (RV) is an important human pathogen that causes rubella, an acute contagious disease. It also causes severe birth defects collectively known as congenital rubella syndrome when infection occurs during the first trimester of pregnancy. Here, we present the phylogenetic analysis of RV that circulated in Sao Paulo during the 20072008 outbreak. Samples collected from patients diagnosed with rubella were isolated in cell culture and sequenced. RV RNA was obtained from samples or RV-infected cell cultures and amplified by reverse transcriptase-polymerase chain reaction. Sequences were assigned to genotypes by phylogenetic analysis using RV reference sequences. Seventeen sequences were analyzed, and three genotypes were identified: 1a, 1G, and 2B. Genotypes 1a and 1G, which were isolated in 2007, were responsible for sporadic rubella cases in Sao Paulo. Thereafter, in late 2007, the epidemiological conditions changed, resulting in a large RV outbreak with the clear dominance of genotype 2B. The results of this study provide new approaches for monitoring the progress of elimination of rubella from Sao Paulo, Brazil. J. Med. Virol. 84:16661671, 2012. (c) 2012 Wiley Periodicals, Inc.