Stability Analysis of a Vector-Borne Disease with Variable Human Population

Table 1

Asymptotic behavior with threshold criteria.

𝑅0	𝑅1	𝑅2	𝑁ℎ	(𝑠ℎ,𝑖ℎ,𝑟ℎ,𝑖𝑣)→	(𝑆ℎ,𝐼ℎ,𝑅ℎ)→
≤1	=1, 𝛿ℎ=0	≤1	𝑁ℎ=𝑁ℎ0	(1,0,0,0)	(𝑁ℎ0,0,0)
>1	=1, 𝛿ℎ=0	=1	𝑁ℎ=𝑁ℎ0	(𝑠^∗ℎ,𝑖^∗ℎ,𝑟^∗ℎ,𝑖^∗𝑣)	𝑁ℎ0(𝑠^∗ℎ,𝑖^∗ℎ,𝑟^∗ℎ)
≤1	<1	<1	𝑁ℎ→0	(1,0,0,0)	(0,0,0)
>1	<1	<1	𝑁ℎ→0	(𝑠^∗ℎ,𝑖^∗ℎ,𝑟^∗ℎ,𝑖^∗𝑣)	(0,0,0)
≤1	>1	<1	𝑁ℎ→∞	(1,0,0,0)	(∞,0,0)
≤1	>1	>1	𝑁ℎ→∞	(1,0,0,0)	(∞,∞,∞)
<1	=1	<1	𝑁ℎ→𝑁^∗ℎ	(1,0,0,0)	(𝑁^∗ℎ,0,0)
>1	>1	>1	𝑁ℎ→∞	(𝑠^∗ℎ,𝑖^∗ℎ,𝑟^∗ℎ,𝑖^∗𝑣)	(∞,∞,∞)
>1	=1	=1	𝑁ℎ→𝑁^∗ℎ	(𝑠^∗ℎ,𝑖^∗ℎ,𝑟^∗ℎ,𝑖^∗𝑣)	(𝑠^∗ℎ,𝑖^∗ℎ,𝑟^∗ℎ)