TY - JOUR
T1 - Asymptotic dynamics of deterministic and stochastic epidemic models with multiple pathogens
AU - Allen, Linda J.S.
AU - Kirupaharan, Nadarajah
N1 - Funding Information:
This research was partially supported by the National Science Foundation grant #DMS-0201105. We thank E. J. Allen and an anonymous referee for helpful suggestions on this work.
Publisher Copyright:
© 2005 Institute for Scientific Computing and Information.
PY - 2005
Y1 - 2005
N2 - Emerging diseases in animals and plants have led to much research on questions of evolution and persistence of pathogens. In particular, there have been numerous investigations on the evolution of virulence and the dynamics of epidemic models with multiple pathogens. Multiple pathogens are involved in the spread of many human diseases including influenza, HIV-AIDS, malaria, dengue fever, and hantavirus pulmonary syndrome [9, 15, 16, 23, 24, 27]. Un- derstanding the impact of these various pathogens on a population is partic- ularly important for their prevention and control. We summarize some of the results that have appeared in the literature on multiple pathogen models. Then we study the dynamics of a deterministic and a stochastic susceptible-infected epidemic model with two pathogens, where the population is subdivided into susceptible individuals and individuals infected with pathogen j for j = 1; 2. The deterministic model is a system of ordinary differential equations, whereas the stochastic model is a system of stochastic differential equations. The mod- els assume total cross immunity and vertical transmission. The conditions on the parameters for coexistence of two pathogens are summarized for the deter- ministic model. Then we compare the coexistence dynamics of the two models through numerical simulations. We show that the deterministic and stochas- tic epidemic models differ considerably in predicting coexistence of the two pathogens. The probability of coexistence in the stochastic epidemic model is very small. Stochastic variability results in extinction of at least one of the strains. Our results demonstrate the importance of understanding the dynam- ics of both the deterministic and stochastic epidemic models.
AB - Emerging diseases in animals and plants have led to much research on questions of evolution and persistence of pathogens. In particular, there have been numerous investigations on the evolution of virulence and the dynamics of epidemic models with multiple pathogens. Multiple pathogens are involved in the spread of many human diseases including influenza, HIV-AIDS, malaria, dengue fever, and hantavirus pulmonary syndrome [9, 15, 16, 23, 24, 27]. Un- derstanding the impact of these various pathogens on a population is partic- ularly important for their prevention and control. We summarize some of the results that have appeared in the literature on multiple pathogen models. Then we study the dynamics of a deterministic and a stochastic susceptible-infected epidemic model with two pathogens, where the population is subdivided into susceptible individuals and individuals infected with pathogen j for j = 1; 2. The deterministic model is a system of ordinary differential equations, whereas the stochastic model is a system of stochastic differential equations. The mod- els assume total cross immunity and vertical transmission. The conditions on the parameters for coexistence of two pathogens are summarized for the deter- ministic model. Then we compare the coexistence dynamics of the two models through numerical simulations. We show that the deterministic and stochas- tic epidemic models differ considerably in predicting coexistence of the two pathogens. The probability of coexistence in the stochastic epidemic model is very small. Stochastic variability results in extinction of at least one of the strains. Our results demonstrate the importance of understanding the dynam- ics of both the deterministic and stochastic epidemic models.
KW - Cross immunity
KW - Epidemic model
KW - Multiple pathogens
KW - Stochastic differential equation
KW - Vertical transmission
UR - http://www.scopus.com/inward/record.url?scp=85015746533&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:85015746533
VL - 2
SP - 329
EP - 344
JO - International Journal of Numerical Analysis and Modeling
JF - International Journal of Numerical Analysis and Modeling
SN - 1705-5105
IS - 3
ER -