Analytical Solution of a Spatial Sir Epidemic Model with Memory Inside a Circular Habitat with Endemic Memory using CAS

Using Computer Algebra Software (CAS) we obtained the reproduction rate of an Epidemic Propagation in a circular habitat, for two cases, in the first one the boundary has an endemic condition, in the other one it presents an infectious transference from other territories through its boundary. We transformed the initial equation into Laplace Domain, and then we solved the simplified differential equation found and then we calculated residues to achieve the solution. After a stability analysis we obtained the reproductive rate R0. The method that was used can be extended to more complex problems such as indirectly transmitted diseases with one or more intermediary hosts or effects of genetic, immunological, geographical or social heterogeneity in the human population. This application indicates that the computer algebra software for symbolic computation has a very promissory future in mathematical epidemiology.