Prescribed vector abundance · Host-vector model

Simulation inputs

Model parameters

Year French department

β_hv host → vector transmission β_vh vector → host transmission γ day⁻¹ host recovery rate Host → vector pressure

Introduction of one infectious host 30 May 2022 t₀ is restricted to the scientific window used in the DISTIGRI notebook.

Selected department data

Host population: —
Area: —
Host density used: —
Host density (CSV): —
σ*: —

The supplied CSV labels the population column “Population_2023”; this value is retained unchanged while vector and temperature series are selected for the chosen year.

Scientific formulation and data treatment

The host system is SIR. The vector population satisfies V_S(t)+V_I(t)=V(t), with V(t) prescribed from DISTIGRI.

For the linear mode, λ_HV=β_hvH_I. The shrinking mode replaces H_I below one infectious host per department area by H_I²/H*.

DISTIGRI V(t) is already a vector density in km⁻² and is used directly, without division by department area. Vector abundance is regularised on the notebook scientific window using the manuscript’s boundary-corrected Gaussian procedure so that V′(t)+μ(t)V(t)≥0. Adult mortality μ(t) is obtained from the supplied iso-50 longevity curve.

Numerical output

Epidemic trajectories conditional on introduction date t₀

The curves below are the epidemic trajectories obtained for the selected introduction date t₀. Move the slider on the vector time axis to change t₀ and recompute the simulation.

Cumulative human cases at T —

ℛ_l(t₀) —

—

V_S(t), V_I(t), V(t)

Stacked vector compartments: Vₛ(t)+Vᵢ(t)=V(t). The black dashed curve is the prescribed total V(t); the slider selects the introduction date t₀.

ℛ_l(t)

Local reproduction index of the corresponding frozen linear model for a hypothetical introduction on each date. The horizontal reference is ℛ_l=1; the vertical marker gives the selected t₀.

N_S(t), N_I(t), N_R(t)

Human compartment sizes. Nₛ(t) is hidden by default so the epidemic dynamics remain visible; click its legend entry to display it.

IntegratorCrank-Nicolson + Newton-Raphson

Δt0.01 day

Scientific window—

Displayed axis1 Jan - 31 Dec 2022

Epidemic trajectories conditional on introduction date t₀

VS(t), VI(t), V(t)

ℛl(t)

NS(t), NI(t), NR(t)

V_S(t), V_I(t), V(t)

ℛ_l(t)

N_S(t), N_I(t), N_R(t)