Traveling Waves and Estimation of Minimal Wave Speed for a Diffusive Influenza Model with Multiple Strains.

Traveling Waves and Estimation of Minimal Wave Speed for a Diffusive Influenza Model with Multiple Strains. Bull Math Biol. 2020 Sep 13;82(9):121 Authors: Chen G, Fu X, Sun M Abstract Antiviral treatment remains one of the key pharmacological interventions against influenza pandemic. However, widespread use of antiviral drugs brings with it the danger of drug resistance evolution. To assess the risk of the emergence and diffusion of resistance, in this paper, we develop a diffusive influenza model where influenza infection involves both drug-sensitive and drug-resistant strains. We first analyze its corresponding reaction model, whose reproduction numbers and equilibria are derived. The results show that the sensitive strains can be eliminated by treatment. Then, we establish the existence of the three kinds of traveling waves starting from the disease-free equilibrium, i.e., semi-traveling waves, strong traveling waves and persistent traveling waves, from which we can get some useful information (such as whether influenza will spread, asymptotic speed of propagation, the final state of the wavefront). On the other hand, we discuss three situations in which semi-traveling waves do not exist. When the control reproduction number [Formula: see text] is larger than 1, the conditions for the existence and nonexistence of traveling waves are determined completely by the reproduction numbers [Formula: see text], [Formula: see text] and the...
Source: Bulletin of Mathematical Biology - Category: Bioinformatics Authors: Tags: Bull Math Biol Source Type: research