Ross-Macdonald Malaria

SD ✦ 112

Two-host vector model: humans X infected, mosquitoes Y infected. dX/dt = abY(1−X) − rX; dY/dt = acX(1−Y) − μY. Threshold: R₀ = ma²bc/(rμ). Below 1 the disease dies; above, it settles to endemic prevalence.

a biting rate 0.30

m mosq/human 5.0

b H→M trans. 0.50

c M→H trans. 0.50

r human recov 0.05

μ mosq death 0.10

t (days)0.0

X infected H—

Y infected M—

R₀—

X* endemic—

X humansY mosquitoes