A deterministic model for influenza infection with multiple strains and antigenic drift

Abstract

We describe a multiple strain Susceptible Infected Recovered deterministic model for the spread of an influenza subtype within a population. The model incorporates appearance of new strains due to antigenic drift, and partial immunity to reinfection with related circulating strains. It also includes optional seasonal forcing of the transmission rate of the virus, which allows for comparison between temperate zones and the tropics. Our model is capable of reproducing observed qualitative patterns such as the overall annual outbreaks in the temperate region, a reduced magnitude and an increased frequency of outbreaks in the tropics, and the herald wave phenomenon. Our approach to modelling antigenic drift is novel and further modifications of this model may help improve the understanding of complex influenza dynamics.

Keywords:

• influenza
• antigenic drift
• cross-immunity
• multiple strains
• seasonality

AMS Subject Classification:

• 92D30
• 92D15

Acknowledgements

We thank the reviewers for helpful comments. The initial idea for this work started during a summer program of the Mathematical and Theoretical Biology Institute (MTBI); we thank all institutions and persons that make MTBI possible. We also thank Carlos Castillo-Chavez for continued discussions and helpful suggestions. This work is partially supported by the NSF grant DMS-1022758.