Analysis of The Asymptomatic SIR Model

First, we implement the asymptomatic SIR model from BioMedInformatics 2022, 2(3), 398-404; https://doi.org/10.3390/biomedinformatics2030025.

using EasyModelAnalysis
@variables t
Dₜ = Differential(t)
@variables S(t)=0.9 Iₐ(t)=0.05 Iₛ(t)=0.01 Rₐ(t)=0.2 Rₛ(t)=0.1 D(t)=0.01
@parameters α=0.6 βₐ=0.143 βₛ=0.055 ρ=0.003 μₙ=0.007 μₘ=0.011 θ=0.1 ωₛ=0.14
eqs = [Dₜ(S) ~ μₙ * S - μₘ * S - θ * α * S * Iₛ - (1 - θ) * α * S * Iₐ + ρ * (Rₐ + Rₛ)
       Dₜ(Iₐ) ~ (1 - θ) * α * S * Iₐ - βₐ * Iₐ
       Dₜ(Iₛ) ~ θ * α * S * Iₛ - βₛ * Iₛ
       Dₜ(Rₐ) ~ βₐ * Iₐ - ρ * Rₐ
       Dₜ(Rₛ) ~ (1 - ωₛ) * βₛ * Iₛ - ρ * Rₛ
       Dₜ(D) ~ ωₛ * βₛ * Iₛ]
@named asir = ODESystem(eqs)
prob = ODEProblem(asir, [], (0, 110.0))
sol = solve(prob)
plot(sol)