Bifurcation Analysis in Models for Vector-Borne Diseases with Logistic Growth

Table 1

The birth and incidence rates for different vector-borne disease models.

Disease	Literature	Birth		Incidence rate
		𝑆ℎ	𝑆𝑣	Host	Vector
	[3]	𝜆ℎ𝑁ℎ	𝜆𝑣𝑁𝑣	𝛽ℎ𝐼𝑣𝑆ℎ𝑁ℎ	𝛽𝑣𝐼ℎ𝑆𝑣𝑁ℎ
Malaria	[5, 6]	Λℎ+𝜆ℎ𝑁ℎ	𝜆𝑣𝑁𝑣	𝛽ℎ𝐼𝑣𝑆ℎ𝜎𝑣𝑁𝑣+𝜎ℎ𝑁ℎ	𝛽𝑣𝐼ℎ𝑆𝑣𝜎𝑣𝑁𝑣+𝜎ℎ𝑁ℎ
	[7]	(1−𝜙)Λℎ	𝜆𝑣𝑁𝑣	𝛽ℎ𝐼𝑣𝑆ℎ𝑁ℎ	𝛽𝑣𝐼ℎ𝑆𝑣𝑁ℎ
	[8]	𝜆ℎ𝑁ℎ	Λℎ	𝛽ℎ𝐼𝑣𝑆ℎ𝑁ℎ+𝑚	𝛽𝑣𝐼ℎ𝑆𝑣𝑁ℎ+𝑚
Dengue fever	[9]	𝜆ℎ𝑁ℎ	𝜆𝑣𝑁𝑣	𝛽ℎ𝐼𝑣𝑆ℎ𝑁𝑣	𝛽𝑣𝐼ℎ𝑆𝑣𝑁ℎ
	[10]	𝜆ℎ𝑁ℎ	𝜆𝑣𝑁𝑣	𝛽ℎ𝐼𝑣𝑆ℎ𝑁ℎ+𝑚	𝛽𝑣𝐼ℎ𝑆𝑣𝑁ℎ+𝑚
	[13]			𝛽1𝐼𝑣𝑆ℎ𝑁ℎ	𝛽𝑣𝐼ℎ𝑆𝑣𝑁ℎ
WNV	[14]	Λℎ	Λ𝑣	𝛽ℎ𝐼𝑣𝑆ℎ𝑁ℎ	𝛽𝑣𝐼ℎ𝑆𝑣𝑁ℎ
	[15, 18]	Λℎ	𝜆𝑣𝑁𝑣	𝛽ℎ𝐼𝑣𝑆ℎ𝑁ℎ	𝛽𝑣𝐼ℎ𝑆𝑣𝑁ℎ