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Symbolic Solution of Spatial Models for Yellow Fever Urbanization Using Computer Algebra
Abstract
Spatial mathematical models about yellow fever urbanization, like a process of transport of disease from jungle and rural areas into cities and urban spaces, are analytically solved, using a special package of computer algebra. The mathematical method that was used is the Laplace transform technique jointly with the Bromwich integral and residue theorem of theory for functions of complex variables, being all the calculations implemented by computer. As results we obtain the explicit form of infected humans and mosquitoes profiles within a habitat, and the basic reproductive rate R0 whose condition for epidemics irruption is R0 > 1. It is observed that one-dimensional and partitioned habitats with endemic boundary have a R0 for yellow fever urbanization; less than the corresponding to the bi-dimensional and partitioned habitats, but the influence of such topographic aspects must be corrected with effects of social structures.
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