Table 3.

Formulas for endemic sensitivity coefficients in Eq. (37).

Par	$\xi$	$\psi$	$\omega$
$\beta$	$\mu {\alpha }_L$	$\mu {\alpha }_L$	0
$\nu$	$-\nu {\alpha }_S$	$-\nu {\alpha }_N$	0
${\epsilon }_E$	$\mu \beta {\epsilon }_E{\alpha }_E$	$\mu \beta {\epsilon }_E{\alpha }_E$	0
${\epsilon }_Q$	$\mu \beta {\epsilon }_Q{\alpha }_Q$	$\mu \beta {\epsilon }_Q{\alpha }_Q$	0
${\epsilon }_J$	$\mu \beta {\epsilon }_J{\alpha }_J$	$\mu \beta {\epsilon }_J{\alpha }_J$	0
${\gamma }_1$	${\gamma }_1{\alpha }_E(-D_S$	${\gamma }_1{\alpha }_E(-\frac{D_S{d}_2{k}_2}{D_J{D}_Q}.$	${\gamma }_1{\alpha }_E$
	$+\frac{\mu \beta }{D_Q}({\epsilon }_Q+\frac{{\epsilon }_J{k}_2}{D_J}))$	$+\frac{\mu \beta }{D_Q}({\epsilon }_Q+\frac{{\epsilon }_J{k}_2}{D_J}))$
${\gamma }_2$	$\frac{{\gamma }_2}{k_1}(-D_E{D}_S+\frac{\mu \beta {\epsilon }_J{k}_1}{D_J}$	$\frac{{\gamma }_2}{k_1}(-\frac{D_S{d}_2}{D_J}(k_1+\frac{{\gamma }_1{k}_2}{D_Q})+\frac{\mu \beta {\epsilon }_J{k}_1}{D_J}$	$\frac{D_E{\gamma }_2}{k_1}$
	$+\mu \beta ({\epsilon }_E+\frac{{\epsilon }_Q{\gamma }_1}{D_Q}+\frac{{\epsilon }_J{\gamma }_1{k}_2}{D_J{D}_Q}))$	$+\mu \beta ({\epsilon }_E+\frac{{\epsilon }_Q{\gamma }_1}{D_Q}+\frac{{\epsilon }_J{\gamma }_1{k}_2}{D_J{D}_Q}))$
${\sigma }_1$	$\frac{{\sigma }_1}{k_1}(-D_E{D}_S$	$\frac{{\sigma }_1}{k_1}(-\frac{D_S{d}_2{\gamma }_1{k}_2}{D_J{D}_Q}$	$\frac{{\sigma }_1{D}_E}{k_1}$
	$+\mu \beta ({\epsilon }_E+\frac{{\epsilon }_Q{\gamma }_1}{D_Q}+\frac{{\epsilon }_J{\gamma }_1{k}_2}{D_J{D}_Q}))$	$+\mu \beta ({\epsilon }_E+\frac{{\epsilon }_Q{\gamma }_1}{D_Q}+\frac{{\epsilon }_J{\gamma }_1{k}_2}{D_J{D}_Q}))$
${\sigma }_2$	$-\frac{{\sigma }_2\mu \beta {\epsilon }_J{\alpha }_J}{D_J}$	$\frac{{\sigma }_2{\alpha }_J}{D_J}(D_S{d}_2-\mu \beta {\epsilon }_J)$	0
$k_1$	$-{\alpha }_E(D_S(k_1-D_E)$	$-{\alpha }_E(-\frac{D_S{d}_2{\gamma }_1{k}_2}{D_J{D}_Q}$	$(k_1-D_E){\alpha }_E$
	$+\mu \beta ({\epsilon }_E+\frac{{\epsilon }_Q{\gamma }_1}{D_Q}+\frac{{\epsilon }_J{\gamma }_1{k}_2}{D_J{D}_Q}))$	$+\mu \beta ({\epsilon }_E+\frac{{\epsilon }_Q{\gamma }_1}{D_Q}+\frac{{\epsilon }_J{\gamma }_1{k}_2}{D_J{D}_Q}))$
$k_2$	$\frac{\mu \beta k_2{\alpha }_Q}{D_J{D}_Q}({\epsilon }_J(D_Q-k_2)$	$\frac{k_2{\alpha }_Q}{D_J{D}_Q}(-\mu \beta {\epsilon }_Q{D}_J$	$0$
	$-{\epsilon }_Q{D}_J)$	$+(\mu \beta {\epsilon }_J-D_S{d}_2)(D_Q-k_2))$
$d_1$	$\frac{d_1}{k_1}(-D_E{D}_S$	$\frac{d_1}{k_1}(-D_S(k_1+\frac{d_2{\gamma }_1{k}_2}{D_J{D}_Q})$	$\frac{d_1{D}_E}{k_1}$
	$+\mu \beta ({\epsilon }_E+\frac{{\epsilon }_Q{\gamma }_1}{D_Q}+\frac{{\epsilon }_J{\gamma }_1{k}_2}{D_J{D}_Q}))$	$+\mu \beta ({\epsilon }_E+\frac{{\epsilon }_Q{\gamma }_1}{D_Q}+\frac{{\epsilon }_J{\gamma }_1{k}_2}{D_J{D}_Q}))$
$d_2$	$-\frac{d_2\mu \beta {\epsilon }_J{\alpha }_J}{D_J}$	$-\frac{d_2{\alpha }_J}{D_J}(\mu \beta {\epsilon }_J+D_S(D_J-d_2))$	0