I lost the file with the original conditions and I can’t find the parameters that replicate it. But I have a more generic model where each bacterium has a phage:
function Doppel!(du, u, p, t)
μ = p.μ # bacterial growth rate
κ = p.κ # bacterial carrying capacity
ω = p.ω # system wash-out rate
δ = p.δ # phagial infection rate
η = p.η # phagial lysis rate (inverse latency)
β = p.β # phagial burst size
λ = p.λ # phagial decay rate
#=
du[1] = species A sensible
du[2] = species A infected
du[3] = phage a
du[4] = species B sensible
du[5] = species B infected
du[6] = phage b
=#
N = u[1] + u[2] + u[4] + u[5] # total bacteria
ρ = 1 - N/κ # logistic term
ϡ = (δ[1]*u[1]*u[3]) # upsampi: infected bacteria A
ς = (δ[2]*u[4]*u[6]) # varsigma: infected bacteria B
du[1] = (μ[1]*u[1]*ρ) - ϡ - (ω*u[1])
du[2] = ϡ - (η[1]*u[2]) - (ω*u[2])
du[3] = (η[1]*β[1]*u[2]) - ϡ - (λ[1]*u[3]) - (ω*u[3])
du[4] = (μ[2]*u[4]*ρ) - ς - (ω*u[4])
du[5] = ς - (η[2]*u[5]) - (ω*u[5])
du[6] = (η[2]*β[2]*u[4]) - ς - (λ[2]*u[5]) - (ω*u[6])
end
# parameters
kappa = 2e7 # carrying capacity (from Weitz)
omega = 0.05 # outflow (from Weitz)
mu = [0.16, 0.31] # growth rate susceptible (pathogen)
beta = [50.0, 75.0] # burst size (from Weitz)
delta = [1e-9, 1e-9] # adsorption rate (from Weitz)
eta = [0.25, 0.75] # reciprocal of latency (from Weitz)
lambda = [0, 0] # decay rate in hours (from Weitz)
As0 = 1e6 # initial susceptible density A
Ai0 = 0 # initial infected density A
a0 = 1e5 # initial phage density a
Bs0 = 1e5 # initial susceptible density B
Bi0 = 0 # initial infected density B
b0 = 1e4 # initial phage density b
t_mx = 5e3
# implementation
u0 = [As0, Ai0, a0, Bs0, Bi0, b0]
tspan = (0.0, t_mx)
parms = ComponentArray(μ=mu, κ=kappa, ω=omega, δ=delta, η=eta, β=beta, λ=lambda)
prob = ODEProblem(Doppel!, u0, tspan, parms)
soln = solve(prob, Rosenbrock23())
# find steady state
eq = solve(prob, Rosenbrock23(), callback = TerminateSteadyState())
In this case, the carrying capacity makes quite a difference: if I use 30 000 000, I get:
eq gives the point of steady-state, as determined in a previous post.