11256

10347

كارشناسي ارشد

رياضي كاربردي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1394

نه، 90ص.

حميدرضا ظهوري زنگنه

به فارسي و انگليسي

رسول عاشقي، رضا مزروعي سبداني

1395/03/03

رياضي

ID10347

Bifurcation and complex dynamics of an SIR model with the impact of the number of hospital beds Soheila Mohammadi Kamal abadi s mohammadi@math iut ac ir December1 2015 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Hamid R Z Zangeneh HamidZ@cc iut ac ir MSC2010 37G15 37G10 34C07 Keywords SIR model Number of hospital beds Dynamics Backward bifurcation Saddle node bifurcation Hopf bifurcations Bogdanov Takens bifurcations Abstract In this paper we establish an SIR model with a standard incidence rate and a nonlinear recoveryrate formulated to consider the impact of available resources of the public health system especiallythe number of hospital beds The main assumption of this model is that the population comprisesthree subgroups the healthy individuals who are susceptible S to infection the already infected in dividuals I who can transmit the disease to the healthy ones and the individuals who are recovered R from the infection cycle One of the major undertakings of epidemiological modeling is to describe how changes in biologicalprocesses will e ect the characteristics of the infection dynamics at a population level R0 the basicreproductive ratio represents the expected number of new infections caused by each case of infectionat the start of an epidemic in a certain baseline population If R0 1 the number of infections afteran initial introduction grows creating an epidemic If R0 1 small initial introductions are not su ciently transmissible to cause an epidemic a new epidemic cannot be started and an endemic diseasewill fade out Thus many control policies have focused on reaching coverage levels su cient to reduceR0 below 1 Over the last 15 years one of the important issues in epidemiological modeling has beenunderstanding when and how the R0 can fail In particular some epidemic models can be bistable R0 1 is a su cient condition for avoiding an epidemic caused by the introduction of a small numberof initial cases but R0 1 is not a su cient condition for eradication of the disease once it is endemic One common way to identify bistable epidemic models is to look for backward bifurcations In SIRmodels the transcritical bifurcation at R0 1 typically has two locally stable branches a disease free

حميدرضا ظهوري زنگنه

رسول عاشقي، رضا مزروعي سبداني