Algorithm 1: The forward-backward finite difference numerical scheme.

Step 1: for $j=-M,\dots ,0,$ do:      $X_j=X_0$, $Y_j=Y_0$, $D_j=D_0$, $V_j=V_0$, $Z_j=Z_0$, ${\eta }_1^j=0$, ${\eta }_2^j=0$. end for for $j=N,\dots ,N+M$, do:      ${\lambda }_1^j=0,{\lambda }_2^j=0,{\lambda }_3^j=0,{\lambda }_4^j=0,{\lambda }_5^j=0,{\lambda }_6^j=0.$ end for Step 2: for $j=0,\dots ,N-1,$ do:      $X_{j+1}=X_j+h[s-\mu X_j-k(1-{\eta }_1^j)V_j{X}_j],$      $Y_{j+1}=Y_j+h[k{e}^{-\lambda \tau }(1-{\eta }_1^j)X_{j-M}{V}_{j-M}-\delta Y_j-p{Y}_j{Z}_j],$      $D_{j+1}=D_j+h[(1-{\eta }_2^i)a{Y}_j-\delta D_j-\beta D_j],$      $V_{j+1}=V_j+h[\beta D_j-u{V}_j-q{V}_j{W}_j],$      $W_{j+1}=W_j+h[g{V}_j{W}_j-h{W}_j],$      $Z_{j+1}=Z_j+h[c{Y}_j{Z}_j-b{Z}_j],$      ${\lambda }_1^{N-j-1}={\lambda }_1^{N-j}-h[1+{\lambda }_1^{N-j}(\mu +k(1-{\eta }_1^j)V_{j+1})]$                 $+{\chi }_{[0,t_f-\tau ]}(t_{N-j}){\lambda }_2^{N-j+M}k({\eta }_1^{j+M}-1)e^{-\lambda \tau }{V}_{j+1}],$      ${\lambda }_2^{N-j-1}={\lambda }_2^{N-j}-h[{\lambda }_2^{N-j}(\delta +p{Z}_{j+1})-{\lambda }_3^{N-j}a(1-{\eta }_2^j)-{\lambda }_6^{N-j}c{Z}_{j+1}],$      ${\lambda }_3^{N-j-1}={\lambda }_3^{N-j}-h[{\lambda }_3^{N-j}(\delta +\beta )-{\lambda }_4^{N-j}\beta ],$      ${\lambda }_4^{N-j-1}={\lambda }_4^{N-j}-h[{\lambda }_1^{N-j}k(1-{\eta }_1^j)X_{j+1}+{\lambda }_4^{N-j}(u+q{W}_{j+1})$                 $+{\chi }_{[0,t_f-\tau ]}(t_{N-j}){\lambda }_2^{N-j+M}k({\eta }_1^{j+M}-1)e^{-\lambda \tau }{X}_{j+1}],$      ${\lambda }_5^{N-j-1}={\lambda }_5^{N-j}-h[1+{\lambda }_2^{N-j}q{V}_{j+1}+{\lambda }_5^{N-j}(h-g{V}_{j+1})],$      ${\lambda }_6^{N-j-1}={\lambda }_6^{N-j}-h[1+{\lambda }_2^{N-j}p{Y}_{j+1}+{\lambda }_6^{N-j}(b-c{Y}_{j+1})],$      $R_1^{j+1}=(1/A_1)(k{\lambda }_2^{N-j-1}{e}^{-\lambda \tau }{V}_{j-M+1}{X}_{j-M+1}-k{\lambda }_1^{N-j-1}{V}_{j+1}{X}_{j+1})$      $R_2^{j+1}=(1/A_2){\lambda }_3^{N-j-1}a{Y}_{j+1},$      ${\eta }_1^{j+1}=min(1,max(R_1^{j+1},0)),$      ${\eta }_2^{j+1}=min(1,max(R_2^{j+1},0)),$ end for Step 3: for $j=1,\dots ,N,$ write   $X^{*}(t_j)=X_j,Y^{*}(t_j)=Y_j,D^{*}(t_j)=D_j,V^{*}(t_j)=V_j,W^{*}(t_j)=W_j$,  $Z^{*}(t_j)=Z_j,{\eta }_1^{*}(t_j)={\eta }_1^j,{\eta }_2^{*}(t_j)={\eta }_2^j.$ end for