Table 1:

The variable list for host cells, pathogen, IIS and AIS agents of the current HCD model

Target Cells	$\frac{d{\underset{\_}{T}}_T}{d{t}_H}=-{\underset{\_}{\beta }}_T{\underset{\_}{T}}_T\underset{\_}{V}-\underset{\_}{\varphi }\underset{\_}{F}{\underset{\_}{T}}_T+{\underset{\_}{\xi }}_R\underset{\_}{R}$
Refractory Cells	$\frac{d\underset{\_}{R}}{d{t}_H}=\underset{\_}{\varphi }\underset{\_}{F}{\underset{\_}{T}}_T-{\underset{\_}{\xi }}_R\underset{\_}{R}$
Infected Cells	$\frac{d\underset{\_}{I}}{d{t}_H}={\underset{\_}{\beta }}_T{\underset{\_}{T}}_T\underset{\_}{V}-{\underset{\_}{\kappa }}_F\underset{\_}{I}\underset{\_}{F}-{\underset{\_}{\kappa }}_E\underset{\_}{I}\underset{\_}{\gamma }{\underset{\_}{T}}_C-{\underset{\_}{\delta }}_X\underset{\_}{I}$ $\{\begin{array}{ll}{\underset{\_}{\delta }}_X={\underset{\_}{\delta }}_I\hfill & t_H<{\underset{\_}{\tau }}_A\hfill \\ {\underset{\_}{\delta }}_X={\underset{\_}{\delta }}_{l}e\underset{\_}{\sigma }\left(t_H-{\underset{\_}{\tau }}_A\right)\hfill & t_H>{\underset{\_}{\tau }}_A\hfill \end{array}$
Virus	$\frac{d\underset{\_}{V}}{d{t}_H}={\underset{\_}{\beta }}_E\underset{\_}{I}-{\underset{\_}{\delta }}_V\underset{\_}{V}-{\underset{\_}{\kappa }}_V\underset{\_}{V}\underset{\_}{A}$
Dendritic Cells	$\frac{d{\underset{\_}{D}}_M}{d{t}_H}={\underset{\_}{\beta }}_D{\underset{\_}{D}}_M\left(1-\raisebox{1ex}{${\underset{\_}{D}}_M$}\!\left/ \!\raisebox{-1ex}{${\underset{\_}{K}}_D$}\right.\right)\underset{\_}{V}-{\underset{\_}{\delta }}_D{\underset{\_}{D}}_M$
Helper T Cells	$\frac{d{\underset{\_}{T}}_H}{d{t}_H}=\left[{\underset{\_}{\pi }}_{H2}{\underset{\_}{D}}_M/\left({\underset{\_}{\pi }}_{H2}+{\underset{\_}{D}}_M\right)\right]\left(1-\raisebox{1ex}{${\underset{\_}{T}}_H$}\!\left/ \!\raisebox{-1ex}{${\underset{\_}{K}}_H$}\right.\right)-{\left[{\underset{\_}{\delta }}_{H2}{\underset{\_}{D}}_M/\left({\underset{\_}{\delta }}_{H2}+{\underset{\_}{D}}_M\right)\right]}_{{\underset{\_}{T}}_H}$
Cytotoxic T Cells	$\frac{d{\underset{\_}{T}}_C}{d{t}_H}=\left[{\underset{\_}{\pi }}_{C1}{\underset{\_}{D}}_M/\left({\underset{\_}{\pi }}_{C2}+{\underset{\_}{D}}_M\right)\right]\left(1-\raisebox{1ex}{${\underset{\_}{T}}_C$}\!\left/ \!\raisebox{-1ex}{${\underset{\_}{K}}_C$}\right.\right)-\left[{\underset{\_}{\delta }}_{C1}{\underset{\_}{D}}_M/\left({\underset{\_}{\delta }}_{C2}+{\underset{\_}{D}}_M\right)\right]{\underset{\_}{T}}_C$
B Cells	$\frac{d\underset{\_}{B}}{d{t}_H}=\frac{{\underset{\_}{\pi }}_{B1}\left[{\underset{\_}{D}}_M+\underset{\_}{h}\left(\underset{\_}{V}+{\underset{\_}{T}}_H\right)\right]}{{\underset{\_}{\pi }}_{B2}+{\underset{\_}{D}}_M+\underset{\_}{h}\left(\underset{\_}{V}+{\underset{\_}{T}}_H\right)}\left(1-\raisebox{1ex}{$\underset{\_}{B}$}\!\left/ \!\raisebox{-1ex}{${\underset{\_}{K}}_B$}\right.\right)-{\underset{\_}{\delta }}_B\underset{\_}{B}-{\underset{\_}{\pi }}_A\underset{\_}{B}$
Antibody	$\frac{d\underset{\_}{A}}{d{t}_H}={\underset{\_}{\pi }}_A\underset{\_}{B}-{\underset{\_}{\delta }}_A\underset{\_}{A}$
Interferon	$\frac{d\underset{\_}{F}}{d{t}_H}={\underset{\_}{\beta }}_F\underset{\_}{I}-{\underset{\_}{\kappa }}_A\underset{\_}{F}$