Algorithm 1 Determining the numerical solution of SEIUR model

at all time $t\in \{1,2,\dots ,n\}$

Input:

The initial value of variables: $S\left[0\right]$, $E\left[0\right]$, $I\left[0\right]$, $U\left[0\right]$ and $R\left[0\right]$;

The optimal parameters: $\beta$, $\gamma$, $f$ and $\sigma$;

Total population of the United States: $N$;

The number of iterations or days: $n$;

Output

$S\left[t\right]$, $E\left[t\right]$, $I\left[t\right]$, $U\left[t\right]$ and $R\left[t\right]$ at all time $t\in \{1,2,\dots ,n\}$

Procedure

For$i$ in $1$ to $n$

$S\left[i\right]=S[i-1]-\frac{\beta S[i-1]\left(I[i-1]\right)}{N}$

$E\left[i\right]=E[i-1]+\frac{\beta S[i-1]\left(I[i-1]\right)}{N}-\sigma E[i-1]$

$I\left[i\right]=I[i-1]+\sigma fE[i-1]-\gamma I[i-1]$

$U\left[i\right]=U[i-1]+\sigma (1-f)E[i-1]-\gamma U[i-1]$

$R\left[i\right]=R[i-1]+\gamma (I[i-1]+U[i-1])$

Return$S\left[i\right]$, $E\left[i\right]$, $I\left[i\right]$, $U\left[i\right]$ and $R\left[i\right]$