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Theory and Modern Applications

Table 2 Discrete time-delay equations for HIV and ELM

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

1: dnn

\(w_{n+1} = w_{n}-\delta h_{m}\tau w_{n-m} +\varepsilon h_{m} \tau w_{n}(1-w_{n})\)

2: ndn

\(w_{n+1} = w_{n}-\delta h_{m}\tau w_{n} +\varepsilon h_{m} \tau w_{n-m}(1-w_{n}) \)

3: nnd

\(w_{n+1} = w_{n}-\delta h_{m}\tau w_{n} +\varepsilon h_{m} \tau w_{n}(1-w_{n-m})\)

4: ddn

\(w_{n+1} = w_{n}-\delta h_{m}\tau w_{n-m} +\varepsilon h_{m} \tau w_{n-m}(1-w_{n})\)

5: dnd

\(w_{n+1} = w_{n}-\delta h_{m}\tau w_{n-m} +\varepsilon h_{m} \tau w_{n}(1-w_{n-m}) \)

6: ndd

\(w_{n+1} = w_{n}-\delta h_{m}\tau w_{n} +\varepsilon h_{m} \tau w_{n-m}(1-w_{n-m})\)

7: ddd

\(w_{n+1} = w_{n}-\delta h_{m}\tau w_{n-m} +\varepsilon h_{m} \tau w_{n-m}(1-w_{n-m}) \)

Version

ELM

1: dnn

\(w_{n+1} = w_{n}-r h_{m}\tau w_{n-m} +\beta h_{m} \tau w_{n}[1-(w_{n}/K)^{\gamma }]\)

2: ndn

\(w_{n+1} = w_{n}-r h_{m}\tau w_{n} +\beta h_{m} \tau w_{n-m}[1-(w_{n}/K)^{\gamma }]\)

3: nnd

\(w_{n+1} = w_{n}-r h_{m}\tau w_{n} +\beta h_{m} \tau w_{n}[1-(w_{n-m}/K)^{\gamma }]\)

4: ddn

\(w_{n+1} = w_{n}-r h_{m}\tau w_{n-m} +\beta h_{m} \tau w_{n-m}[1-(w_{n}/K)^{\gamma }]\)

5: dnd

\(w_{n+1} = w_{n}-r h_{m}\tau w_{n-m} +\beta h_{m} \tau w_{n}[1-(w_{n-m}/K)^{\gamma }]\)

6: ndd

\(w_{n+1} = w_{n}-r h_{m}\tau w_{n} +\beta h_{m} \tau w_{n-m}[1-(w_{n-m}/K)^{\gamma }] \)

7: ddd

\(w_{n+1} = w_{n}-r h_{m}\tau w_{n-m} +\beta h_{m} \tau w_{n-m}[1-(w_{n-m}/K)^{\gamma }]\)