Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 3 Values of ρ and η in linearized delay equations at equilibrium points

From: Andronov–Hopf and Neimark–Sacker bifurcations in time-delay differential equations and difference equations with applications to models for diseases and animal populations

Version	HIV: \(R_{0} =\frac{\varepsilon }{\delta }\)				ELM: Λ = β − r, \(R_{0} = \frac{\beta }{r}\)
	Disease-free		Endemic		Disease-free		Endemic
	ρ	η	ρ	η	ρ	η	ρ	η
1: dnn	ε	δ	2δ − ε	δ	β	r	r − γΛ	r
2: ndn	−δ	−ε	−ε	−δ	−r	−β	−r − γΛ	−r
3: nnd	ε − δ	0	0	ε − δ	β − r	0	0	γΛ
4: ddn	0	δ − ε	−ε + δ	0	0	r − β	−γΛ	0
5: dnd	ε	δ	δ	ε	β	r	r	r + γΛ
6: ndd	−δ	−ε	−δ	ε − 2δ	−r	−β	−r	−r + γΛ
7: ddd	0	δ − ε	0	ε − δ	0	r − β	0	γΛ

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