The SEIR model with nonlinear incidence rates in epidemiology is studied. Global stability of the endemic equilibrium is proved using a general criterion for the orbital stability of periodic orbits associated with higher-dimensional nonlinear autonomous systems as well as the theory of competitive systems of differential equations.
The study of fuzzy differential systems is initiated and sufficient conditions, in terms of Lyapunov-like functions, are provided for the new concept of stability which unifies Lyapunov and orbital stabilities as well as includes new notions in between.
Host community composition and biodiversity can limit and regulate tick abundance which can have profound impacts on the incidence and severity of tick-borne diseases. Our understanding of the relationship between host community composition and tick abundance is still very limited. Here, we present a novel mathematical model of a stage-structured tick… (More)
Nonlinear Dynamics and Systems Theory represent a new direction of investigation during the last two decades. The primary goal of the Theory of Systems is to develop unified methods of mathematical modelling of processes and phenomena, in nature and society, so that to establish the conditions of their dynamics and to control them, if necessary. This aim… (More)