RESUMO
The SIR (susceptible-infectious-recovered) model is a well known method for predicting the number of people (or animals) in a population who become infected by and then recover from a disease. Modifications can include categories such people who have been exposed to the disease but are not yet infectious or those who die from the disease. However, the model has nearly always been applied to the entire population of a country or state but there is considerable observational evidence that diseases can spread at different rates in densely populated urban regions and sparsely populated rural areas. This work presents a new approach that applies a SIR type model to a country or state that has been divided into a number of geographical regions, and uses different infection rates in each region which depend on the population density in that region. Further, the model contains a simple matrix based method for simulating the movement of people between different regions. The model is applied to the spread of disease in the United Kingdom and the state of Rio Grande do Sul in Brazil.
Assuntos
Modelos Teóricos , Animais , Brasil/epidemiologia , Humanos , Densidade Demográfica , Reino UnidoRESUMO
The direct effects Of soil phosphorus on sport germination and hyphal growth of the arbuscular mycorrhizal fungi (AM), Glomus etunicatum Beck &Beck &Gerd., E3 and Scutellospora heterogama (Nicol &Gerd) Walker &Sanders, were investigated by means of two soil-agar plate experiments. In the first experiment, the percentage spore germination and hyphal length of G. etunicatum, measured at ten different P levels and three periods of incubation, were affected by the P status of the soil. The best correslation with P level in the soil occurred at 7 d of incubation for spore germination and at 14 d far hyphal growth and hyphal growth increment. Spore germination was stimulated when 12.5 µ PO g-1 was applied to the soil and decreased with further soil P increments. Hyphal growth decreased significantly with soil P amendments above 37.5 µg P g-1 In the second experiment including three different P levels and the three AM endophytes, soil P affected spore germination and hyphal growth, and both decreased at the high phosphate treatment for G. etunicatum and S. heterogama. The K3 spare germination was similar to the other two species, but the hyphal growth was poorer. S. heterogama was more sensitive to P fertilization than the Glomus spp. and for the three species the hyphal production was not proportional to spore size.