SIS Epidemic Models with Multiple Pathogen Strains

Abstract

The dynamics of discrete-time SIS epidemic models with multiple pathogen strains are studied. The population infected with these strains may be confined to one geographic region or patch or may disperse between two patches. The models are systems of difference equations. It is the purpose of this investigation to study the persistence and extinction dynamics of multiple pathogen strains in a single patch and in two patches. It is shown for the single patch model that the basic reproduction number determines which strain dominates and persists. The strain with the largest basic reproduction number is the one that persists and outcompetes all other strains, provided its magnitude is greater than one. However, in the two-patch epidemic model, both the dispersal probabilities and the basic reproduction numbers for each strain determine whether a strain persists. With two patches, there is a greater chance that more than one strain will coexist. Analytical results are complemented with numerical simulations to help illustrate both competitive exclusion and coexistence of pathogens strains within the host population.

Keywords:

• Competitive exclusion
• SIS epidemic model
• Patch model
• Lotka–Volterra competition model
• 39A11
• 97D30

Acknowledgements

This research was supported by a Texas Higher Education Coordinating Board ARP grant # 003644-0193 (L. J. S. Allen, S. M. Wilson and N. Kirupaharan) and a National Science Foundation grant, DMS-9626417 (L. J. S. Allen). We thank the referees for their helpful comments and suggestions.