Modeling the Effects of Climate on the Transmission Dynamics of High and Low Pathogenic Avian Influenza Using Computational Methods

Introduction

A mathematical model(ODE system) is used to describe the transmission dynamics of avian influenza among a non-migratory waterfowl population. The manuscript under the same title was submitted to Mathematical Bioscience in Fall 2025 (currently still under review). This repository stores all the computational tools the authors used to produce the analytical and numerical results.

Avian Influenza Dynamics Solver

To generate the transmission dynamics, the module named AIVDynamics.py can be downloaded into your directory to solve for the intended system. The module includes functions: Temp, Viral, Avian, and DynamicsSolver. To generate the solutions and dynamics plot, users only need to call the DynamicsSolver function along with their initial conditions and required parameters for high pathogenic virus. It is recommended that users review the docstrings of each function carefully.

$R_0$ Calculator

The calculation for the time-invariant basic reproduction number is shown in the manuscript; one can simply compute $R_0$ by using the formula and desired parameters in the manuscript. However, a module for such calculation is provided in this repository under the file name R0_calc.py. Note that this file also plots the basic reproduction number as a function of temperature for $R_0^{LPAI}$, $R_0^{HPAI}$, as well as $R_0^{model}$.

$R_i$ Calculation scheme and algorithm

$R_i$ denotes the invasion threshold, which can be defined as the ability of one pathogen to invade the susceptible population while other pathogens are at equilibrium. We use $R_i$ to emphasize the periodicity of this model along with the strain-wise competition. In this study, we use the method of linear periodic operators and Floquet theory to solve for $R_i$. The algorithm used to solve for the threshold value can be found in Safi et al(2012) and Wang et al(2008). The implementation of this algorithm for the two-strain invasion threshold can be found under the file name RiTwoStrain.py.