The linear stability and basic reproduction numbers for autonomous FDEs
Copyright policy )The linear stability and basic reproduction numbers for autonomous FDEs
In this paper, we first prove the stability equivalence between a linear autonomous and cooperative functional differential equation (FDE) and its associated autonomous and cooperative system without time delay. Then we present the theory of basic reproduction number $\mathcal{R}_0$ for general autonomous FDEs. As an illustrative example, we also establish the threshold dynamics for a time-delayed population model of black-legged ticks in terms of $\mathcal{R}_0$.
autonomous FDEs, Dynamical Systems (math.DS), Monotone flows as dynamical systems, Stability problems for infinite-dimensional dissipative dynamical systems, exponential growth bound, Population dynamics (general), threshold dynamics, basic reproduction number, Linear functional-differential equations, FOS: Mathematics, Mathematics - Dynamical Systems, 34K06, 34K30, 37C65, 37L15, 92D25, Functional-differential equations in abstract spaces, linear stability
autonomous FDEs, Dynamical Systems (math.DS), Monotone flows as dynamical systems, Stability problems for infinite-dimensional dissipative dynamical systems, exponential growth bound, Population dynamics (general), threshold dynamics, basic reproduction number, Linear functional-differential equations, FOS: Mathematics, Mathematics - Dynamical Systems, 34K06, 34K30, 37C65, 37L15, 92D25, Functional-differential equations in abstract spaces, linear stability
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