Mathematical Analysis of a Malaria Model with Partial Immunity to Reinfection

Figure 2

Backward bifurcation regions for the model (4) in the 𝜎-𝛽_ℎ parameter space corresponding to 𝜎=0.5 and various ranges of 𝛽_ℎ. Parameter values used are: Λ_ℎ=30,Λ_𝑣=24,𝛿_ℎ=0.2,𝛾_ℎ=0.0005,𝜇_ℎ=0.00004,𝑏=0.4,𝜇_𝑣=0.0.015,  𝛽_𝑣=0.09. In (a) 𝜇_𝑣=0.05,ℜ₀=0.0014046 (backward bifurcation region for 𝛽_ℎ is 𝛽_ℎ∈[0.1038,0.35556]), (b) 𝜇_𝑣=0.1,ℜ₀=0.00035113 (backward bifurcation region for 𝛽_ℎ is 𝛽_ℎ∈[0.2077,0.71083]), and (c) 𝜇_𝑣=0.2,ℜ₀=0.0000087788 (backward bifurcation region for 𝛽_ℎ is 𝛽_ℎ∈[0.4153,1.9468]). With the above set of parameter values, 𝑎₁>0,𝑏₁>0, and ℜ₀<1.

(a)

(b)

(c)