A Schistosomiasis Model with Praziquantel Resistance

Table 1

Existence and stability of equilibria. The sign “∃  !” means the existence and uniqueness. LAS means locally asymptotically stable, and GAS means globally asymptotically stable.

	𝜌=0		𝜌≠0
	Existence	Stability	Existence	Stability
𝐸0	∃  !	If 𝑅0<1, LAS; If 𝑅0≤1, GAS	∃  !	If 𝑅0<1, LAS; If 𝑅0≤1, GAS
𝐸0𝑖	If 𝑅0𝑖>1, ∃  !	If 𝑅0𝑖>1 and 𝑅0𝑖>𝑅0𝑟, LAS; If 𝑅0𝑖>1≥𝑅0𝑟, GAS	Not exist	/
𝐸0𝑟	If 𝑅0𝑟>1, ∃  !	If 𝑅0𝑟>1 and 𝑅0𝑟>𝑅0𝑖, LAS; If 𝑅0𝑟>1≥𝑅0𝑖, GAS	If 𝑅0𝑟>1, ∃  !	If 𝑅0𝑟>1 and 𝑅0𝑟>𝑅0𝑖, LAS; If 𝑅0𝑟>1≥𝑅0𝑖, GAS
𝐸𝑐	If 𝑅0𝑖=𝑅0𝑟>1,; a line	/	If 𝑅0𝑖>1 and 𝑅0𝑖>𝑅0𝑟, ∃  !	If 𝑅0𝑖>1 and 𝑘≤min𝑚2/𝑚1,𝑚4/𝑚3, LAS