The Basic Reproduction Number Obtained From Jacobian And Next Generation Matrices - A Case Study Of Dengue Transmission Modelling.

The basic reproduction number is a key parameter in mathematical modelling of transmissible diseases. From the stability analysis of the disease free equilibrium, by applying Routh-Hurwitz criteria, a threshold is obtained, which is called the basic reproduction number. However, the application of spectral radius theory on the next generation matrix provides a different expression for the basic reproduction number, that is, the square root of the previously found formula. If the spectral radius of the next generation matrix is defined as the geometric mean of partial reproduction numbers, however the product of these partial numbers is the basic reproduction number, then both methods provide the same expression. In order to show this statement, dengue transmission modelling incorporating or not the transovarian transmission is considered as a case study. Also tuberculosis transmission and sexually transmitted infection modellings are taken as further examples.

Variability Modeling Of Rainfall, Deforestation, And Incidence Of American Tegumentary Leishmaniasis In Orán, Argentina, 1985-2007.

American tegumentary leishmaniasis (ATL) is a disease transmitted to humans by the female sandflies of the genus Lutzomyia. Several factors are involved in the disease transmission cycle. In this work only rainfall and deforestation were considered to assess the variability in the incidence of ATL. In order to reach this goal, monthly recorded data of the incidence of ATL in Orán, Salta, Argentina, were used, in the period 1985-2007. The square root of the relative incidence of ATL and the corresponding variance were formulated as time series, and these data were smoothed by moving averages of 12 and 24 months, respectively. The same procedure was applied to the rainfall data. Typical months, which are April, August, and December, were found and allowed us to describe the dynamical behavior of ATL outbreaks. These results were tested at 95% confidence level. We concluded that the variability of rainfall would not be enough to justify the epidemic outbreaks of ATL in the period 1997-2000, but it consistently explains the situation observed in the years 2002 and 2004. Deforestation activities occurred in this region could explain epidemic peaks observed in both years and also during the entire time of observation except in 2005-2007.

Tree structure and richness in an Atlantic Forest fragment: distance from anthropogenic and natural edges

Approximately 7.2% of the Atlantic rainforest remains in Brazil, with only 16% of this forest remaining in the State of Rio de Janeiro, all of it distributed in fragments. This forest fragmentation can produce biotic and abiotic differences between edges and the fragment interior. In this study, we compared the structure and richness of tree communities in three habitats - an anthropogenic edge (AE), a natural edge (NE) and the fragment interior (FI) - of a fragment of Atlantic forest in the State of Rio de Janeiro, Brazil (22°50'S and 42°28'W). One thousand and seventy-six trees with a diameter at breast height > 4.8 cm, belonging to 132 morphospecies and 39 families, were sampled in a total study area of 0.75 ha. NE had the greatest basal area and the trees in this habitat had the greatest diameter:height allometric coefficient, whereas AE had a lower richness and greater variation in the height of the first tree branch. Tree density, diameter, height and the proportion of standing dead trees did not differ among the habitats. There was marked heterogeneity among replicates within each habitat. These results indicate that the forest interior and the fragment edges (natural or anthropogenic) do not differ markedly considering the studied parameters. Other factors, such as the age from the edge, type of matrix and proximity of gaps, may play a more important role in plant community structure than the proximity from edges.