SIAM Journal on Applied Mathematics · 1983 · 12 citations · 8 references
Veterinary MedicineInfectious DiseasesMicrobiologyBiological Systems ModelingDynamical SystemsInfectious Disease EpidemiologyBacterial InfectionsDisease DynamicsDisease SpreadInfectious Disease DynamicsNonlinear DynamicsReaction-diffusion SystemsEpidemic ModelsEpidemic Spreading ModelsExtinctionMathematical Modeling Of EpidemicsModeling Of Outbreak SpreadOutbreak PropagationPeriodic Solutions Of Differential EquationsReaction-diffusion Phenomena
In this paper we study a reaction-diffusion system consisting of two nonlinear parabolic equations which model the evolution of a class of bacterial diseases. We show that if the infection term is periodic then, for suitable values of a threshold parameter, the system admits a nontrivial periodic solution which is globally asymptotically stable. On the other hand, conditions are given for the eventual extinction of the epidemic.
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Positive Solutions of Operator Equations.
A. R. Brodsky, M. A. Krasnosel’skii, Richard E. Flaherty et al. · American Mathematical Monthly · 1967 · 2.1K citations