Library

Epidemic_Params

Struct that contains the parameters related with the epidemic parameters and compartmental evolution.

Fields

All the parameters contained in this structure are probabilities ranged between 0 and 1.

Epidemic parameters

• βᴵ::Array{Float64, 1}: Infectivity of infected.
• βᴬ::Array{Float64, 1}: Infectivity of asymptomatic.
• ηᵍ::Array{Float64, 1}: Exposed rate for each strata.
• αᵍ::Array{Float64, 1}: Asymptomatic infectious rate for each strata.
• μᵍ::Array{Float64, 1}: Infectious rate for each strata.
• θᵍ::Array{Float64, 1}: Direct death probability for each strata.
• γᵍ::Array{Float64, 1}: ICU probability for each strata.
• ζᵍ::Array{Float64, 1}: Pre-deceased rate for each strata.
• λᵍ::Array{Float64, 1}: Pre-hospitalized in ICU rate for each strata.
• ωᵍ::Array{Float64, 1}: Fatality probability in ICU for each strata.
• ψᵍ::Array{Float64, 1}: Death rate in iCU for each strata.
• χᵍ::Array{Float64, 1}: ICU discharge rate for each strata.
• T::Int64: Number of epidemic timesteps.

Compartmental evolution

• ρˢᵍ::Array{Float64, 3}: Matrix of size $G \times M \times T$ containing infomation about the evolution of fraction of suceptible individuals for each strata and patch.
• ρᴱᵍ::Array{Float64, 3}: Matrix of size $G \times M \times T$ containing infomation about the evolution of fraction of exposed individuals for each strata and patch.
• ρᴬᵍ::Array{Float64, 3}: Matrix of size $G \times M \times T$ containing infomation about the evolution of fraction of asymptomatic individuals for each strata and patch.
• ρᴵᵍ::Array{Float64, 3}: Matrix of size $G \times M \times T$ containing infomation about the evolution of fraction of symptomatic individuals for each strata and patch.
• ρᴾᴴᵍ::Array{Float64, 3}: Matrix of size $G \times M \times T$ containing infomation about the evolution of fraction of pre-hospitalized to ICU individuals for each strata and patch.
• ρᴾᴰᵍ::Array{Float64, 3}: Matrix of size $G \times M \times T$ containing infomation about the evolution of pre-deceased individuals for each strata and patch.
• ρᴴᴿᵍ::Array{Float64, 3}: Matrix of size $G \times M \times T$ containing infomation about the evolution of fraction of hospitalized in ICU patients who will recover for each strata and patch.
• ρᴴᴰᵍ::Array{Float64, 3}: Matrix of size $G \times M \times T$ containing infomation about the evolution of fraction of hospitalized in ICU patients who will not recover for each strata and patch.
• ρᴰᵍ::Array{Float64, 3}: Matrix of size $G \times M \times T$ containing infomation about the evolution of fraction of deceased individuals for each strata and patch.
• ρᴿᵍ::Array{Float64, 3}: Matrix of size $G \times M \times T$ containing infomation about the evolution of fraction of recovered individuals for each strata and patch.

Auxiliary

• CHᵢᵍ::Array{Float64, 2}: Fraction of securely confined individuals for each strata and patch.
• Qᵢᵍ::Array{Float64, 3}: Suceptible contacts available for each strata on a given patch.

Constructor

Use outer constructor Epidemic_Params for a proper initialization of this struct.

Epidemic_Params(βᴵ::Float64,
                βᴬ::Float64,
                ηᵍ::Array{Float64, 1},
                αᵍ::Array{Float64, 1},
                μᵍ::Array{Float64, 1},
                θᵍ::Array{Float64, 1},
                γᵍ::Array{Float64, 1},
                ζᵍ::Array{Float64, 1},
                λᵍ::Array{Float64, 1},
                ωᵍ::Array{Float64, 1},
                ψᵍ::Array{Float64, 1},
                χᵍ::Array{Float64, 1},
                G::Int64,
                M::Int64,
                T::Int64)

Constructor of the struct Epidemic_Params.

Arguments

• βᴵ::Float64: Infectivity of infected.
• βᴬ::Float64: Infectivity of asymptomatic.
• ηᵍ::Array{Float64, 1}: Vector of size $G$ with exposed rates for each strata.
• αᵍ::Array{Float64, 1}: Vector of size $G$ with asymptomatic infectious rates for each strata.
• μᵍ::Array{Float64, 1}: Vector of size $G$ with infectious rates for each strata.
• θᵍ::Array{Float64, 1}: Vector of size $G$ with direct death probabilities for each strata.
• γᵍ::Array{Float64, 1}: Vector of size $G$ with ICU probabilities for each strata.
• ζᵍ::Array{Float64, 1}: Vector of size $G$ with pre-deceased rates for each strata.
• λᵍ::Array{Float64, 1}: Vector of size $G$ with pre-hospitalized in ICU rates for each strata.
• ωᵍ::Array{Float64, 1}: Vector of size $G$ with fatality probabilities in ICU for each strata.
• ψᵍ::Array{Float64, 1}: Vector of size $G$ with death rates for each strata.
• χᵍ::Array{Float64, 1}: Vector of size $G$ with ICU discharge rates for each strata.
• G::Int64: Number of strata.
• M::Int64: Number of patches.
• T::Int64: Number of epidemic timesteps.

Return

Struct that contains the parameters related with the epidemic parameters and compartmental evolution.

Population_Params

Struct that contains the parameters related with geographical, population and mobility data.

Fields

• G::Int64: Number of population strata.
• M::Int64: Number of patches.
• nᵢ:Array{Float64, 1}: Population of each patch.
• nᵢᵍ:Array{Float64, 2}: Population of each strata on each patch.
• nᵢ_eff:Array{Float64, 1}: Effective population on each patch after taking into account mobility.
• nᵢᵍ_eff:Array{Float64, 1}: Effective population of each strata on each patch after taking into account mobility.
• N::Int64: Total population.
• Nᵍ::Array{Int64, 1}: Total population of each strata.
• pᵍ::Array{Float64, 1}: Vector with the degree of mobility of each strata.
• pᵍ_eff::Array{Float64, 1}: Vector with the current degree of mobility of each strata.
• edgelist::Array{Int64, 2}: Matrix with the directed edgelist between patches, where $L$ is the number of edges.
• Rᵢⱼ::Array{Float64, 1}: Vector with the transition probabilities for each edge in the edgelist.
• mobilityᵍ::Array{Float64, 1}: Effective mobility of each strata between patches (used to optimize performance).
• kᵍ::Array{Float64, 1}: Average number of contacts of each strata.
• kᵍ_h::Array{Float64, 1}: Average number of contacts at home of each strata.
• kᵍ_w::Array{Float64, 1}: Average number of contacts at work of each strata.
• kᵍ_eff::Array{Float64, 1}: Current average number of contacts of each strata.
• C::Array{Float64, 2}: Matrix with the probability of contact between different stratifications.
• zᵍ::Array{Float64, 1}: Nomalization factor each strata.
• normᵍ::Array{Float64, 2}: Normalization of each strata (used to optimize performance).
• sᵢ::Array{Float64, 1}: Surface of each patch.
• ξ::Float64: Densisty factor.
• σ::Float64: Average household size.

Constructor

Use outer constructor Population_Params for a proper initialization of this struct.

Population_Params(G::Int64,
                  M::Int64,
                  nᵢᵍ::Array{Float64, 2},
                  kᵍ::Array{Float64, 1},
                  kᵍ_h::Array{Float64, 1},
                  kᵍ_w::Array{Float64, 1},
                  C::Array{Float64, 2},
                  pᵍ::Array{Float64, 1},
                  edgelist::Array{Int64, 2},
                  Rᵢⱼ::Array{Float64, 1},
                  sᵢ::Array{Float64, 1},
                  ξ::Float64,
                  σ::Float64)

Constructor of the struct Population_Params.

Arguments

• G::Int64: Number of population strata.
• M::Int64: Number of patches.
• nᵢᵍ::Array{Float64, 2}: Matrix of size $G \times M$ with the population at each strata and patch.
• kᵍ::Array{Float64, 1}: Vector of size $G$ with the average number of contacts of each strata.
• kᵍ_h::Array{Float64, 1}: Vector of size $G$ with the average number of contacts at home of each strata.
• kᵍ_w::Array{Float64, 1}: Vector of size $G$ with the average number of contacts at work of each strata.
• C::Array{Float64, 2}: Matrix of size $G \times G$ with the probability of contact between different stratifications.
• pᵍ::Array{Float64, 1}: Vector of size $G$ with the degree of mobility of each strata ranged between 0 and 1.
• edgelist::Array{Int64, 2}: Matrix of size $L \times 2$ containing the directed edgelist between patches, where $L$ is the number of edges. The IDs of the patches have to go from $1$ to $M$.
• Rᵢⱼ::Array{Float64, 1}: Vector of size $L$ containing the transition probabilities for each edge in the edgelist.
• sᵢ::Array{Float64, 1}: Vector of size M with the surface of each patch.
• ξ::Float64: Density factor.
• σ::Float64: Average household size.

Return

Struct that contains the parameters related with geographical, population and mobility data.

compute_R_eff(epi_params::Epidemic_Params,
              population::Population_Params;
              τ::Int64 = 21)

Compute the effective reproduction number R.

Arguments

• epi_params::Epidemic_Params: Structure that contains all epidemic parameters and the epidemic spreading information.
• population::Population_Params: Structure that contains all the parameters related with the population.

Optional

• τ::Int64 = 21: kernel length.

Return

Tuple formed by:

• DataFrame containing information about the evolution of the effective reproduction number R for each strata and patch.
• DataFrame containing information about the evolution of the total effective reproduction number R.

reset_params!(epi_params::Epidemic_Params,
              population::Population_Params)

Reset the epidemic and population parameters to reuse the structure and avoid additional data allocations.

Arguments

• epi_params::Epidemic_Params: Structure that contains all epidemic parameters and the epidemic spreading information.
• population::Population_Params: Structure that contains all the parameters related with the population.

run_epidemic_spreading_mmca!(epi_params::Epidemic_Params,
                             population::Population_Params,
                             tᶜs::Array{Int64, 1},
                             κ₀s::Array{Float64, 1},
                             ϕs::Array{Float64, 1},
                             δs::Array{Float64, 1};
                             t₀::Int64 = 1,
                             verbose::Bool = false)

Computes the evolution of the epidemic spreading over time, updating the variables stored in epi_params. It provides the option of the application of multiple different containmnets at specific dates.

Arguments

• epi_params::Epidemic_Params: Structure that contains all epidemic parameters and the epidemic spreading information.
• population::Population_Params: Structure that contains all the parameters related with the population.
• tᶜs::Array{Int64, 1}: List of timesteps of application of containments.
• κ⁰s::Array{Float64, 1}: List of mobility reductions.
• ϕs::Array{Float64, 1}: List of permeabilities of confined households.
• δs::Array{Float64, 1}: List of social distancings.

Optional

• t₀::Int64 = 1: Initial timestep.
• verbose::Bool = false: If true, prints useful information about the evolution of the epidemic process.

run_epidemic_spreading_mmca!(epi_params::Epidemic_Params,
                             population::Population_Params;
                             tᶜ::Int64 = -1,
                             κ₀::Float64 = 0.0,
                             ϕ::Float64 = 1.0,
                             δ::Float64 = 0.0,
                             t₀::Int64 = 1,
                             verbose::Bool = false)

Computes the evolution of the epidemic spreading over time, updating the variables stored in epi_params. It also provides, through optional arguments, the application of a containmnet on a specific date.

Arguments

• epi_params::Epidemic_Params: Structure that contains all epidemic parameters and the epidemic spreading information.
• population::Population_Params: Structure that contains all the parameters related with the population.

Optional

• tᶜ::Int64 = -1: Timestep of application of containment, or out of timesteps range value for no containment.
• κ⁰::Float64 = 0.0: Mobility reduction.
• ϕ::Float64 = 1.0: Permeability of confined households.
• δ::Float64 = 0.0: Social Distancing.
• t₀::Int64 = 1: Initial timestep.
• verbose::Bool = false: If true, prints useful information about the evolution of the epidemic process.

set_initial_infected!(epi_params::Epidemic_Params,
                      population::Population_Params,
                      E₀::Array{Float64, 2},
                      A₀::Array{Float64, 2},
                      I₀::Array{Float64, 2})

Set the initial number of infected individuals on a population. They can be introduced as exposed (E), asymptomatic (A) or symptomatic (I) individuals.

Arguments

• epi_params::Epidemic_Params: Structure that contains all epidemic parameters and the epidemic spreading information.
• population::Population_Params: Structure that contains all the parameters related with the population.
• E₀::Array{Float64, 2}: Matrix of size $G \times M$ containing the number of exposed individuals of each strata on each patch.
• A₀::Array{Float64, 2}: Matrix of size $G \times M$ containing the number of asymptomatic infected individuals of each strata on each patch.
• I₀::Array{Float64, 2}: Matrix of size $G \times M$ containing the number of symptomatic infected individualsof each strata on each patch.

store_R_eff(epi_params::Epidemic_Params,
            population::Population_Params,
            suffix::String,
            folder::String;
            τ::Int64 = 21)

Compute and store the effective reproduction number R.

Arguments

• epi_params::Epidemic_Params: Structure that contains all epidemic parameters and the epidemic spreading information.
• population::Population_Params: Structure that contains all the parameters related with the population.
• suffix::String: String used to identify the experiment.
• folder::String: String containing the path where the results will be stored.

Optional

• τ::Int64 = 21: kernel length.

store_compartment(epi_params::Epidemic_Params,
                  population::Population_Params,
                  compartment::Char,
                  sufix::String,
                  folder::String)

Store the evolution of the given epidemic compartment for each strata and patch.

Arguments

• epi_params::Epidemic_Params: Structure that contains all epidemic parameters and the epidemic spreading information.
• population::Population_Params: Structure that contains all the parameters related with the population.
• compartment::String: String indicating the compartment, one of: "S", "E", "A", "I", "PH", "PD", "HR", "HD", "D", "R".
• suffix::String: String used to identify the experiment.
• folder::String: String containing the path to the folder where the results will be stored.