I have a system of ordinary differential equations (ODEs) that model the interaction between a bacterium and phage:
dN/dt = μN(1-(N+I)/κ) -φNP -ωN dI/dt = φNP -ηI -ωI dP/dt = βηI -φNP -ωP
I am looking for the values of P that bring N to zero in a stable term. As is, the addition of P to the system reduces N, but then N and P go into oscillation and then they reach an equilibrium where N >> 0.
I understand this might be a problem for Boundary Value Problem but how do I set the system?
I understand BVP requires a function to work upon, which probably is the dN/dt I indicated, hence:
function fun!(du, u, p, t) μ, κ, φ, ω = p #= du = susceptible =# du = ((μ * u) * (1 - ((u+u)/κ))) - (φ * u * u) - (ω * u) end
(do I need to include dI/dt?) This is derived from the system of ODEs I set for the model:
function modelFun!(du, u, p, t) # base infection model with logistic term μ, κ, φ, ω, η, β = p #= du = susceptible du = infected du = phages =# du = ((μ * u) * (1 - ((u+u)/κ))) - (φ * u * u) - (ω * u) du = (φ * u * u) - (η * u) - (ω * u) du = (β * η * u) - (φ * u * u) - (ω * u) end
I then need an implicit function bc, but what would that be?
How is the setting of this kind of problem?
The parameters I used are:
κ = 2.2 ⋅ 10^7 μ = 0.47 φ = 10^-9 β = 50 η = 1.0 ω = 0.05 N0 = 1.0*10^7 P0 = 2*10^8