An Epidemic Model With Post-Contact Prophylaxis of Distributed Length II. Stability and Oscillations if Treatment is Fully Effective
Mathematical modelling of natural phenomena, Tome 3 (2008) no. 7, pp. 267-293
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A possible control strategy against the spread of an infectious disease is the treatment with antimicrobials that are given prophylactically to those that had contact with an infective person. The treatment continues until recovery or until it becomes obvious that there was no infection in the first place. The model considers susceptible, treated uninfected exposed, treated infected, (untreated) infectious, and recovered individuals. The overly optimistic assumptions are made that treated uninfected individuals are not susceptible and treated infected individuals are not infectious. Since treatment lengths are considered that have an arbitrary distribution, the model system consists of ordinary differential and integral equations. We study the impact of the treatment length distribution on the large-time behavior of the model solutions, namely whether the solutions converge to an equilibrium or whether they are driven into undamped oscillations.
@article{10_1051_mmnp:2008052,
author = {H. R. Thieme and A. Tridane and Y. Kuang},
title = {An {Epidemic} {Model} {With} {Post-Contact} {Prophylaxis} of {Distributed} {Length} {II.} {Stability} and {Oscillations} if {Treatment} is {Fully} {Effective}},
journal = {Mathematical modelling of natural phenomena},
pages = {267--293},
year = {2008},
volume = {3},
number = {7},
doi = {10.1051/mmnp:2008052},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/mmnp:2008052/}
}
TY - JOUR AU - H. R. Thieme AU - A. Tridane AU - Y. Kuang TI - An Epidemic Model With Post-Contact Prophylaxis of Distributed Length II. Stability and Oscillations if Treatment is Fully Effective JO - Mathematical modelling of natural phenomena PY - 2008 SP - 267 EP - 293 VL - 3 IS - 7 UR - http://geodesic.mathdoc.fr/articles/10.1051/mmnp:2008052/ DO - 10.1051/mmnp:2008052 LA - en ID - 10_1051_mmnp:2008052 ER -
%0 Journal Article %A H. R. Thieme %A A. Tridane %A Y. Kuang %T An Epidemic Model With Post-Contact Prophylaxis of Distributed Length II. Stability and Oscillations if Treatment is Fully Effective %J Mathematical modelling of natural phenomena %D 2008 %P 267-293 %V 3 %N 7 %U http://geodesic.mathdoc.fr/articles/10.1051/mmnp:2008052/ %R 10.1051/mmnp:2008052 %G en %F 10_1051_mmnp:2008052
H. R. Thieme; A. Tridane; Y. Kuang. An Epidemic Model With Post-Contact Prophylaxis of Distributed Length II. Stability and Oscillations if Treatment is Fully Effective. Mathematical modelling of natural phenomena, Tome 3 (2008) no. 7, pp. 267-293. doi: 10.1051/mmnp:2008052
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