Local stability results on a model for typhoid fever with a core group
Keywords:Subpoblaciones, Liapunov, Fiebre tifoidea
A SIRS epidemiological model with two subpopulation and vital dynamics is analized. Both subpopulations are considered constant by assuming that the birth and the death rate are equal. We analize the case where one subpopulation is a core, that is, a very infectious small group, responsible for a big fraction of the incidence. For this case a threshold is determined and the corresponding equilibrium points for the four dimensional system are shown to be locally stable by means of the classical Liapunov theorem. This system models the dynamics of typhoid fever, where the core is the group of food manipulators. Computer simulation are used to estimate the effect of vaccination on the population.
 Hethcote , H.: Qualitative analysis of conmnunicable disease models. Math. Biosc., 28, (1976), 335-356.
 Hethcote, H.: An immunization model for a heterogeneous population. Theoret. Population Biol., 14 (1978), 338-349.
 Thieme, H. R.: Global asymptotic stability in epidemic models. Equadiff, Lecture Notes in Math. 1017, Springe Verlag, Heildelberg, (1983), 608-615.
 Hethcote, H.; Thieme, H.: Stability of the Endemic Equilibrium in Epidemic Models with Subpopulatious. Math. Biosc. 75:205-227 (1985).
 González-Guzmán , J .: An epidemiological model for direct and indirect transmission of typhoid fever. Math. Biosc. 96 (1989), 33-46.
 González-Guzmán, J.; Naulin, R.: Analysis of a model of bovine brucelosis using singular perturbatiOns. Pre print.
 Beretta, E.; Cappaso, V.: Global stability results for a multigroup SIR Epidemic Model. Proc. of the Autumn Course Reseach Seminars on Mathematical Ecology. ICTP, Trieste, 1986.
 Jordan, D.W.; Smith : Nonlinear Ordinary Differential Equations, Oxford Univ. Press, 1977.
 Levine, M. ; Ferreccio, C. ; Black, R.; Tacket, C.; Germanier, R.: Progress in Vaccines Against Typhoid Fever. R. of lnfectious Diseases, Vol.11 May-June 1989.
How to Cite
Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.