Metering effects in population systems
Pages: 1365  1379,
Issue 5/6,
October/December
2013
doi:10.3934/mbe.2013.10.1365 Abstract
References
Full text (515.0K)
Related Articles
Erika T. Camacho  School of Mathematical & Natural Sciences, Arizona State University, 4701 W. Thunderbird Rd, Glendale, AZ, 85306, United States (email)
Christopher M. KribsZaleta  Mathematics Department, University of Texas at Arlington, Box 19408, Arlington, TX 760190408, United States (email)
Stephen Wirkus  School of Mathematical & Natural Sciences, Arizona State University, 4701 W. Thunderbird Rd, Glendale, AZ, 85306, United States (email)
1 
A. S. Ackleh, B. G. Fitzpatrick, S. Scribner, J. J. Thibodeaux and N. Simonsen, Ecosystem modeling of college drinking: Parameter estimation and comparing models to data, Mathematical and Computer Modelling, 50 (2009), 481997. 

2 
R. P. Agarwal, D. Franco and D. ORegan, Singular boundary value problems for first and second order impulsive differential equations, Aequationes Mathematicae, 69 (2005), 8396. 

3 
E. Aguirre, T. Smith, J. Stancil and N. Davidenko, Differential equation models of neoadjuvant chemotherapeutic treatment strategies for stage III breast cancer, Biometrics Unit Technical Report BU1522M, Cornell University, 1999. Available from: http://mtbi.asu.edu/. 

4 
L. Almada, E. Camacho, R. Rodriguez, M. Thompson and L. Voss, Deterministic and smallworld network models of college drinking patterns, 2006. Available from: http://www.public.asu.edu/ etcamach/AMSSI/reports/alcohol2006.pdf. 

5 
D. Bainov and P. Simeonov, "Systems with Impulsive Effect: Stability, Theory and Applications,'' Ellis Horwood, Chichester, 1989. 

6 
D. Bainov and P. Simeonov, "Theory of Impulsive Differential Equations: Periodic Solutions and Applications,'' Longman, Harlow, 1993. 

7 
F. Brauer and C. CastilloChavez, "Mathematical Models in Population Biology and Epidemiology,'' Springer, New York, 2012. 

8 
N. F. Britton, "Essential Mathematical Biology,'' SpringerVerlag, 2003. 

9 
B. Brogliato, "Nonsmooth Mechanics,'' $2^{nd}$ edition, Springer, Berlin, 1999. 

10 
R. T. Bupp, D. S. Bernstein, V. S. Chellaboina and W. M. Haddad, Resetting virtual absorbers for vibration control, Journal of Vibration and Control, 6 (2000), 6183. 

11 
E. T. Camacho, "Mathematical Models of Retinal Dynamics," Ph.D. thesis, Center for Applied Mathematics, Cornell University, Ithaca, NY, 2003. 

12 
E. T. Camacho, The development and interaction of terrorist and fanatic groups, Communications in Nonlinear Science and Numerical Simulation, 18 (2013), 30863097. 

13 
E. C. Chang and C. Yap. Competitive online scheduling with level of service, Journal of Scheduling, 6 (2003), 251267. 

14 
N. P. Chau, Destabilising effect of period harvest on population dynamics, Ecological Modelling, 127 (2000), 19. 

15 
G. Chowell and H. Nishiura, Quantifying the transmission potential of pandemic influenza, Physics of Life Reviews, 5 (2008), 5077. 

16 
M. Chrobak, L. Epstein, J. Noga, J. Sgall, R. van Stee, T. Tich\'y and N. Vakhania, Preemptive scheduling in overloaded systems, Journal of Computer and System Sciences, 2380 (2003), 183197. 

17 
F. Dercole, A. Gragnani and S. Rinaldi, Bifurcation analysis of piecewise smooth ecological models, Theoretical Population Biology, 72 (2007), 197213. 

18 
O. Diekmann, J. A. P. Heesterbeek and J. A. J. Metz, On the definition and the computation of the basic reproduction ratio $R_0$ in models for infectious diseases in heterogeneous population, Journal of Mathematical Biology, 28 (1990), 365382. 

19 
A. d'Onofrio, On pulse vaccination strategy in the SIR epidemic model with vertical transmission, Applied Mathematics Letters, 18 (2005), 729732. 

20 
D. B. Forger and D. Paydarfar, Starting, stopping, and resetting biological oscillators: In search of optimal perturbations, Journal of Theoretical Biology, 230 (2004), 521532. 

21 
S. Gao, L. Chen, J. J. Nieto and A. Torres, Analysis of a delayed epidemic model with pulse vaccination and saturation incidence, Vaccine, 24 (2006), 60376045. 

22 
S. Gao, Z. Teng, J. J. Nieto and A. Torres, Analysis of an SIR epidemic model with pulse vaccination and distributed time delay, Journal of Biomedicine and Biotechnology, 2007, Article ID 64870, 10 pp. 

23 
B. González, E. HuertaSánchez, A. OrtizNieves, T. VázquezÁlvarez and C. KribsZaleta, Am I too fat? Bulimia as an epidemic, Journal of Mathematical Psychology, 47 (2003), 515526. 

24 
V. Křivan Optimal foraging and predatorprey dynamics, Theoretical Population Biology, 49 (1996), 265290. 

25 
A. R. Ives, K. Gross and V. A. A. Jansen, Periodic mortality events in predatorprey systems, Ecology, 81 (2000), 33303340. 

26 
A. Lakmeche and O. Arino, Nonlinear mathematical model of pulsed therapy of heterogeneous tumors, Nonlinear Analysis: Real World Applications, 2 (2001), 455465. 

27 
V. Lakshmikantham, D. D. Bainov and P. S. Simeonov, "Theory of Impulsive Differential Equations," World Scientific, Singapore, 1989. 

28 
W. Li and H. Huo, Global attractivity of positive periodic solutions for an impulsive delay periodic model of respiratory dynamics, Journal of Computational and Applied Mathematics, 174 (2005), 227238. 

29 
J. D. Logan and W. Wolesensky, Accounting for temperature in predator functional responses, Natural Resource Modeling, 20 (2007), 549574. 

30 
R. M. Lopez, B. R. Morin and S. K. Suslov, On logistic models with timedependent coefficients and some of their applications, arXiv:1008.2534. 

31 
L. Lu, S. Chu, S. Yeh and C. Peng, Modeling and experimental verification of a variablestiffness isolation system using a leverage mechanism, Journal of Vibration and Control, 17 (2011), 18691885. 

32 
S. Maggi and S. Rinaldi, A secondorder impact model for forest fire regimes, Theoretical Population Biology, 70 (2006), 174182. 

33 
E. S. Meadows and T. A. Badgwell, Feedback through steadystate target optimization for nonlinear model predictive control, Journal of Vibration and Control, 4 (1998), 6174. 

34 
S. Mondie, R. Lozano and J. Collado, Resetting processmodel control for unstable systems with delay, Proceedings of the 40th IEEE Conference on Decision and Control, 3 (2001), 22472252. 

35 
J. J. Nieto, Basic theory for nonresonance impulsive periodic problems of first order, Proceedings of the American Mathematical Society, 125 (1997), 25992604. 

36 
J. J. Nieto and D. O'Regan, Variational approach to impulsive differential equations, Nonlinear Analysis: Real World Applications, 10 (2009), 680690. 

37 
J. C. Panetta, A mathematical model of periodically pulsed chemotherapy: Tumor recurrence and metastasis in a competition environment, Bulletin of Mathematical Biology, 58 (1996), 425447. 

38 
J. C. Panetta, A mathematical model of drug resistant: Heterogeneous tumors, Mathematical Biosciences, 147 (1998), 4161. 

39 
T. C. Reluga, Analysis of periodic growth disturbance models, Theoretical Population Biology, 66 (2004), 151161. 

40 
M. G. Roberts and B. T. Grenfell, The population dynamics of nematode infections of ruminants: Periodic perturbations as a model for management, Mathematical Medicine and Biology, 8 (1991), 8393. 

41 
M. G. Roberts and B. T. Grenfell, The population dynamics of nematode infections of ruminants: The effect of seasonally in the freeliving stages, Mathematical Medicine and Biology, 9 (1992), 2941. 

42 
M. G. Roberts and J. A. P. Heesterbeek, A simple parasite model with complicated dynamics, Journal of Mathematical Biology, 37 (1998), 272290. 

43 
A. M. Samoilenko and N. A. Perestyuk, "Impulsive Differential Equations,'' World Scientific, Singapore, 1995. 

44 
R. Scribner, A. S. Ackleh, B. G. Fitzpatrick, G. Jacquez, J. J. Thibodeaux, R. Rommel and N. Simonsen, A systems approach to college drinking: Development of a deterministic model for testing alcohol control policies, Journal of Studies on Alcohol and Drugs, 70 (2009), 805821. 

45 
B. Shulgin, L. Stone and Z. Agur, Pulse vaccination strategy in the SIR epidemic model, Bulletin of Mathematical Biology, 60 (1998), 126. 

46 
D. W. Stephens and J. R. Krebs, "Foraging Theory," Princeton University Press, Princeton, 1986. 

47 
J. S. Tsai, F. Chen, S. Guo, C. Chen and L. Shieh, A novel tracker for a class of sampleddata nonlinear systems, Journal of Vibration and Control, 17 (2011), 81101. 

48 
P. Van den Driessche and J. Watmough, Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, 180 (2002), 2948. 

49 
A. Winfree, "The Geometry of Biological Time," $2^{nd}$ edition, Springer, New York, 2001. 

50 
J. Yan, A. Zhao and J. J. Nieto, Existence and global attractivity of positive periodic solution of periodic singlespecies impulsive LotkaVolterra systems, Mathematical and Computer Modelling, 40 (2004), 509518. 

51 
W. Zhang and M. Fan, Periodicity in a generalized ecological competition system governed by impulsive differential equations with delays, Mathematical and Computer Modelling, 39 (2004), 479493. 

52 
H. Zhang, L. S. Chen and J. J. Nieto, A delayed epidemic model with stagestructure and pulses for management strategy, Nonlinear Analysis: Real World Applications, 9 (2008), 17141726. 

53 
X. Zhang, Z. Shuai and K. Wang, Optimal impulsive harvesting policy for single population, Nonlinear Analysis: Real World Applications, 4 (2003), 639651. 

Go to top
