Dynamics of low and high pathogenic avian influenza in wild and domestic bird populations

Last modified: 2014-03-31

#### Abstract

This talk introduces an avian influenza model which includes the dynamics of low pathogenic avian influenza (LPAI) and high pathogenic avian influenza (HPAI). The model structures the LPAI-recovered individuals by time-since-recovery and involves the cross-immunity that LPAI infection generates toward the HPAI. Reproduction numbers ( $\mathcal R_0^{L_w},\mathcal R_0^{H_w}$) and invasion reproduction numbers ($\hat{\mathcal R}_{H_w}, \hat{\mathcal R}_{L_w}$) ofLPAI and HPAI are computed. It is shown that the system has a unique disease-free equilibrium that is locally and globally stable if $\mathcal R_0^{L_w}<1$ and$\mathcal R_0^{H_w}<1$. If $\mathcal R_0^{L_w}>1$ a unique LPAI dominance equilibrium exists. Similarly, if $\mathcal R_0^{H_w}>1$ a unique HPAI dominance equilibrium exists. The equilibria are locally stable if $\hat{\mathcal R}_{H_w}<1$($\hat{\mathcal R}_{L_w}<1$ correspondingly). A unique coexistence equilibrium is present if both invasion numbers are larger than one. Simulations show that this coexistence equilibrium can lose stability and coexistence in the form of sustained oscillations is possible. Cross-immunity and duration of protectionincrease the probability of coexistence. Simulations also show that increasingLPAI transmission increases LPAI prevalence and decreases HPAI prevalence.This observation in part may explain why wild birds which have much higher transmission of LPAI compared to domestic birds also have much lower prevalence of HPAI.

#### Keywords

mathematical models, age-structured differential equations, reproduction number, invasion number, LPAI, HPAI, H5N1, avian influenza.