Table 1.

Classification of the disease free and endemic blocks for the network described in Fig. 1

$R_1$	$R_2$	$R_3$	$R_4$	Disease free blocks	Endemic blocks	Globally stable equilibrium
$\le$1	$\le$1	$\le$1	$\le$1	$1,2,3,4$	No such block	$(\mathbf{0},\mathbf{0},\mathbf{0},\mathbf{0})$
$\le$1	$\le$1	$\le$1	$>$1	$1,2,3$	$4$	$(\mathbf{0},\mathbf{0},\mathbf{0},{\mathbf{I}}_4^{+})$
$\le$1	$\le$1	$>$1	Any	$1,2$	$3,4$	$(\mathbf{0},\mathbf{0},{\mathbf{I}}_3^{+},{\mathbf{I}}_4^{+})$
$\le$1	$>$1	Any	Any	$1$	$2,3,4$	$(\mathbf{0},{\mathbf{I}}_2^{+},{\mathbf{I}}_3^{+},{\mathbf{I}}_4^{+})$
$>$1	$\le$1	Any	Any	$2$	$1,3,4$	$({\mathbf{I}}_1^{+},\mathbf{0},{\mathbf{I}}_3^{+},{\mathbf{I}}_4^{+})$
$>$1	$>$1	Any	Any	No such block	$1,2,3,4$	$({\mathbf{I}}_1^{+},{\mathbf{I}}_2^{+},{\mathbf{I}}_3^{+},{\mathbf{I}}_4^{+})$