TY - JOUR
T1 - SIS Epidemic Models with Multiple Pathogen Strains
AU - Allen, Linda J.S.
AU - Kirupaharan, Nadarajah
AU - Wilson, Sherri M.
N1 - Funding Information:
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.
PY - 2004/1
Y1 - 2004/1
N2 - 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.
AB - 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.
KW - Competitive exclusion
KW - Lotka-Volterra competition model
KW - Patch model
KW - SIS epidemic model
UR - http://www.scopus.com/inward/record.url?scp=0842346795&partnerID=8YFLogxK
U2 - 10.1080/10236190310001603680
DO - 10.1080/10236190310001603680
M3 - Article
AN - SCOPUS:0842346795
SN - 1023-6198
VL - 10
SP - 53
EP - 75
JO - Journal of Difference Equations and Applications
JF - Journal of Difference Equations and Applications
IS - 1
ER -