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Theory and Modern Applications

Table 10 Values of equilibrium points and \(R_{0}\) of HIV and ELM models from Tables 8 and 9

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

Parameters

Disease-free

Endemic

\(R_{0}\)

HIV

\(x^{*}_{0}=w^{*}_{0}\)

\(x^{*}_{1}=w^{*}_{1}=1-\frac{\delta }{\varepsilon }\)

\(\frac{\varepsilon }{\delta }\)

Set 1

0

0.9813

53.333

Set 2

0

0.7525

4.0404

Set 3

0

0.7526

ELM

\(x^{*}_{0}=w^{*}_{0}\)

\(x^{*}_{1}=w^{*}_{1}=K (1-\frac{r}{\beta } )^{\frac{1}{\gamma }}\)

\(\frac{\beta }{r}\)

Set 1

0

2

1.333