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Author (up) Aracena, J.; Demongeot, J.; Fanchon, E.; Montalva, M. pdf  doi
openurl 
  Title On the number of different dynamics in Boolean networks with deterministic update schedules Type
  Year 2013 Publication Mathematical Biosciences Abbreviated Journal Math. Biosci.  
  Volume 242 Issue 2 Pages 188-194  
  Keywords Boolean network; Update schedule; Update digraph; Dynamics  
  Abstract Deterministic Boolean networks are a type of discrete dynamical systems widely used in the modeling of genetic networks. The dynamics of such systems is characterized by the local activation functions and the update schedule, i.e., the order in which the nodes are updated. In this paper, we address the problem of knowing the different dynamics of a Boolean network when the update schedule is changed. We begin by proving that the problem of the existence of a pair of update schedules with different dynamics is NP-complete. However, we show that certain structural properties of the interaction digraph are sufficient for guaranteeing distinct dynamics of a network. In [1] the authors define equivalence classes which have the property that all the update schedules of a given class yield the same dynamics. In order to determine the dynamics associated to a network, we develop an algorithm to efficiently enumerate the above equivalence classes by selecting a representative update schedule for each class with a minimum number of blocks. Finally, we run this algorithm on the well known Arabidopsis thaliana network to determine the full spectrum of its different dynamics. (C) 2013 Elsevier Inc. All rights reserved.  
  Address Univ Concepcion, CI2MA, Concepcion, Chile, Email: jaracena@ing-mat.udec.cl;  
  Corporate Author Thesis  
  Publisher Elsevier Science Inc Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0025-5564 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000317164700008 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 275  
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Author (up) Kapitanov, G.; Alvey, C.; Vogt-Geisse, K.; Feng, Z.L. pdf  doi
openurl 
  Title An Age-Structured Model For The Coupled Dynamics Of Hiv And Hsv-2 Type
  Year 2015 Publication Mathematical Biosciences And Engineering Abbreviated Journal Math. Biosci. Eng.  
  Volume 12 Issue 4 Pages 803-840  
  Keywords HIV; HSV-2; mathematical epidemiology; co-infection; population dynamics; basic reproduction number; invasion reproduction number; partial differential equations; sensitivity analysis; age-structure; sexually transmitted diseases  
  Abstract Evidence suggests a strong correlation between the prevalence of HSV-2 (genital herpes) and the perseverance of the HIV epidemic. HSV-2 is an incurable viral infection, characterized by periodic reactivation. We construct a model of the co-infection dynamics between the two diseases by incorporating a time-since-infection variable to track the alternating periods of infectiousness of HSV-2. The model considers only heterosexual relationships and distinguishes three population groups: males, general population females, and female sex workers. We calculate the basic reproduction numbers for each disease that provide threshold conditions, which determine whether a disease dies out or becomes endemic in the absence of the other disease. We also derive the invasion reproduction numbers that determine whether or not a disease can invade into a population in which the other disease is endemic. The calculations of the invasion reproduction numbers suggest a new aspect in their interpretation – the class from which the initial disease carrier arises is important for understanding the invasion dynamics and biological interpretation of the expressions of the reproduction numbers. Sensitivity analysis is conducted to examine the role of model parameters in influencing the model outcomes. The results are discussed in the last section.  
  Address [Kapitanov, Georgi; Alvey, Christina; Vogt-Geisse, Katia; Feng, Zhilan] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA, Email: georgi.i.kapitanov@grnail.com;  
  Corporate Author Thesis  
  Publisher Amer Inst Mathematical Sciences Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 1547-1063 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000354138400012 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 488  
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Author (up) Towers, S.; Vogt Geisse, K.; Chia-Chun, T.; Han, Q.; Feng, Z.L. pdf  doi
openurl 
  Title The Impact Of School Closures On Pandemic Influenza: Assessing Potential Repercussions Using A Seasonal Sir Model Type
  Year 2012 Publication Mathematical Biosciences And Engineering Abbreviated Journal Math. Biosci. Eng.  
  Volume 9 Issue 2 Pages 413-430  
  Keywords Pandemic influenza; epidemic model; dynamic systems  
  Abstract When a new pandemic influenza strain has been identified, mass-production of vaccines can take several months, and antiviral drugs are expensive and usually in short supply. Social distancing measures, such as school closures, thus seem an attractive means to mitigate disease spread. However, the transmission of influenza is seasonal in nature, and as has been noted in previous studies, a decrease in the average transmission rate in a seasonal disease model may result in a larger final size. In the studies presented here, we analyze a hypothetical pandemic using a SIR epidemic model with time- and age-dependent transmission rates; using this model we assess and quantify, for the first time, the the effect of the timing and length of widespread school closures on influenza pandemic final size and average peak time. We find that the effect on pandemic progression strongly depends on the timing of the start of the school closure. For instance, we determine that school closures during a late spring wave of an epidemic can cause a pandemic to become up to 20% larger, but have the advantage that the average time of the peak is shifted by up to two months, possibly allowing enough time for development of vaccines to mitigate the larger size of the epidemic. Our studies thus suggest that when heterogeneity in transmission is a significant factor, decisions of public health policy will be particularly important as to how control measures such as school closures should be implemented.  
  Address [Towers, Sherry; Geisse, Katia Vogt; Chia-Chun, Tsai; Han, Qing; Feng, Zhilan] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA, Email: stowers@purdue.edu  
  Corporate Author Thesis  
  Publisher Amer Inst Mathematical Sciences Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 1547-1063 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000301177600010 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 198  
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