|
According to the epidemic diseases history, rabies often causes a terrible threat to human being’s health. Up to the present, this disease has broken out at over 150 countries and areas, and consequently kills over fifty thousand persons each year.
In order to study the spread and development of rabies in mathematical approach, we construct three mathematical models, named SEID, under the consideration of the capacity of a logistic environment, by referring to the pathogenic factors and the pathological rabies and imitating two famous mathematical models, SI and SID, for epidemic diseases which were derived by mathematicians Kermack and Mckendrick.
Due to the lack of the analytic solutions of those nonlinear SEID models , we can discover their behavior only by finding equilibrium states, and then applying Routh table to determine the stability. Some equilibrium states are so complicated that it is hard to complete their Routh table, therefore we should apply numerical experiments to present their stabilities. Finally, we hope, in the future, those SEID models can be modified to become control models that can be used in controlling rabies.
|