Vector Disease Model: Cooke [19] proposed a delayed vector disease model given b

Vector Disease Model: Cooke [19] proposed a delayed vector disease
model given b

Vector Disease Model: Cooke [19] proposed a delayed vector disease
model given by
dy
dt = by(t − τ)[1 − y(t)] − ay(t)
Modeling with Delay Differential Equations
where y(t) is the infected population, b is the contact rate and a is the
cure. The discrete time delay τ gives the incubation period before the
disease agent can infect a host. Cooke assumed that the total population
is constant and scaled so that x(t) + y(t) = 1, x(t) being the uninfected
population. He also assumed that an infected population is not subject
to death, immunity or isolation.
(i) Find the steady state solution(s) of the model.
(ii) Find the condition(s) for linear stability (if any) about the steady
state solution(s).
(iii) Obtain the numerical solution for (a) a = 5.8, b = 4.8(a>b), τ = 5
and (b) a = 38, b = 4.8(a