TY - JOUR
T1 - The dynamics of two viral infections in a single host population with applications to hantavirus
AU - Allen, Linda J.S.
AU - Langlais, Michel
AU - Phillips, Carleton J.
N1 - Funding Information:
L.J.S.A. was supported by a Texas Higher Education Coordinating Board ARP grant # 003644-0193 and a National Science Foundation grant DMS-9626417. We thank Pauline van den Driessche for suggesting applying the techniques in [52] . We especially thank the referees for their suggestions to include incomplete vertical transmission, additional references, and for their many helpful comments.
PY - 2003/12
Y1 - 2003/12
N2 - An SI epidemic model for a host with two viral infections circulating within the population is developed, analyzed, and numerically simulated. The model is a system of four differential equations which includes a state for susceptible individuals, two states for individuals infected with a single virus, one which is vertically transmitted and the other which is horizontally transmitted, and a fourth state for individuals infected with both viruses. A general growth function with density-dependent mortality is assumed. A special case of this model, where there is no coinfection and total cross immunity, is thoroughly analyzed. Several threshold values are defined which determine establishment of the disease and persistence at equilibrium for one or both of the infections within the host population. The model has applications to a hantavirus and an arenavirus that infect cotton rats. The hantavirus is transmitted horizontally whereas the arenavirus is transmitted vertically. It is shown through analysis and numerical simulations that both diseases can be maintained within a single host population, where individuals can be either infected with both viruses or with a single virus.
AB - An SI epidemic model for a host with two viral infections circulating within the population is developed, analyzed, and numerically simulated. The model is a system of four differential equations which includes a state for susceptible individuals, two states for individuals infected with a single virus, one which is vertically transmitted and the other which is horizontally transmitted, and a fourth state for individuals infected with both viruses. A general growth function with density-dependent mortality is assumed. A special case of this model, where there is no coinfection and total cross immunity, is thoroughly analyzed. Several threshold values are defined which determine establishment of the disease and persistence at equilibrium for one or both of the infections within the host population. The model has applications to a hantavirus and an arenavirus that infect cotton rats. The hantavirus is transmitted horizontally whereas the arenavirus is transmitted vertically. It is shown through analysis and numerical simulations that both diseases can be maintained within a single host population, where individuals can be either infected with both viruses or with a single virus.
KW - Coinfection
KW - Hantavirus
KW - Partial immunity
KW - SI epidemic model
KW - Vertical transmission
UR - http://www.scopus.com/inward/record.url?scp=0242522862&partnerID=8YFLogxK
U2 - 10.1016/j.mbs.2003.08.002
DO - 10.1016/j.mbs.2003.08.002
M3 - Article
C2 - 14583172
AN - SCOPUS:0242522862
VL - 186
SP - 191
EP - 217
JO - Mathematical Biosciences
JF - Mathematical Biosciences
SN - 0025-5564
IS - 2
ER -