The Dynamics of the Epidemic Process with the Antibiotic-Resistant Variant of the Pathogen Agent

Resumo

The parasite–host system is considered with two different variants of a pathogen agent with complete cross protection, where one of the variants may transform into another with a certain probability. This system corresponds to the epidemic process initiated by the antibiotic-resistant variant of the pathogen agent. The behavior of solutions is studied. It is proved that the main case has a unique nontrivial steady-state solution that is a global attractor. The speed of the exponential approach of small deviations to the steady-state solution is obtained.