TY - JOUR
T1 - Stochastic model of an influenza epidemic with drug resistance
AU - Xu, Y.
AU - Allen, Linda
AU - Perelson, A.
N1 - Funding Information:
Portions of this work were done under the auspices of the US Department of Energy under contract DE-AC52-06NA25396 and supported in part by NIH Grant AI28433 (ASP). LJSA acknowledges support from NSF Grant DMS-0201105. We thank an anonymous referee for helpful suggestions on this research.
PY - 2007/9/7
Y1 - 2007/9/7
N2 - A continuous-time Markov chain (CTMC) model is formulated for an influenza epidemic with drug resistance. This stochastic model is based on an influenza epidemic model, expressed in terms of a system of ordinary differential equations (ODE), developed by Stilianakis, N.I., Perelson, A.S., Hayden, F.G., [1998. Emergence of drug resistance during an influenza epidemic: insights from a mathematical model. J. Inf. Dis. 177, 863-873]. Three different treatments-chemoprophylaxis, treatment after exposure but before symptoms, and treatment after symptoms appear, are considered. The basic reproduction number, R0, is calculated for the deterministic-model under different treatment strategies. It is shown that chemoprophylaxis always reduces the basic reproduction number. In addition, numerical simulations illustrate that the basic reproduction number is generally reduced with realistic treatment rates. Comparisons are made among the different models and the different treatment strategies with respect to the number of infected individuals during an outbreak. The final size distribution is computed for the CTMC model and, in some cases, it is shown to have a bimodal distribution corresponding to two situations: when there is no outbreak and when an outbreak occurs. Given an outbreak occurs, the total number of cases for the CTMC model is in good agreement with the ODE model. The greatest number of drug resistant cases occurs if treatment is delayed or if only symptomatic individuals are treated.
AB - A continuous-time Markov chain (CTMC) model is formulated for an influenza epidemic with drug resistance. This stochastic model is based on an influenza epidemic model, expressed in terms of a system of ordinary differential equations (ODE), developed by Stilianakis, N.I., Perelson, A.S., Hayden, F.G., [1998. Emergence of drug resistance during an influenza epidemic: insights from a mathematical model. J. Inf. Dis. 177, 863-873]. Three different treatments-chemoprophylaxis, treatment after exposure but before symptoms, and treatment after symptoms appear, are considered. The basic reproduction number, R0, is calculated for the deterministic-model under different treatment strategies. It is shown that chemoprophylaxis always reduces the basic reproduction number. In addition, numerical simulations illustrate that the basic reproduction number is generally reduced with realistic treatment rates. Comparisons are made among the different models and the different treatment strategies with respect to the number of infected individuals during an outbreak. The final size distribution is computed for the CTMC model and, in some cases, it is shown to have a bimodal distribution corresponding to two situations: when there is no outbreak and when an outbreak occurs. Given an outbreak occurs, the total number of cases for the CTMC model is in good agreement with the ODE model. The greatest number of drug resistant cases occurs if treatment is delayed or if only symptomatic individuals are treated.
KW - Continuous-time Markov chain
KW - Drug resistance
KW - Final size
KW - Influenza epidemic
UR - http://www.scopus.com/inward/record.url?scp=34547691348&partnerID=8YFLogxK
U2 - 10.1016/j.jtbi.2007.05.009
DO - 10.1016/j.jtbi.2007.05.009
M3 - Article
C2 - 17582443
VL - 248
SP - 179
EP - 193
JO - Journal of Theoretical Biology
JF - Journal of Theoretical Biology
IS - 1
ER -