|
L. J. S. Allen,
An Introduction to Stochastic Processes with Applications to Biology, 2$^{nd}$ edition, CRC Press, Boca Raton, FL, 2011.
|
|
L. J. S. Allen
and V. A. Bokil
, Stochastic models for competing species with a shared pathogen, Math. Biosci. Eng., 9 (2012)
, 461-485.
doi: 10.3934/mbe.2012.9.461.
|
|
L. J. S. Allen
and N. Kirupaharan
, Asymptotic dynamics of deterministic and stochastic epidemic models with multiple pathogens, Int. J. Numer. Anal. Modeling, 2 (2005)
, 329-344.
|
|
L. J. S. Allen
and G. E. Lahodny
, Extinction thresholds in deterministic and stochastic epidemic models, J. Biol. Dyn., 6 (2012)
, 590-611.
|
|
R. M. Anderson
and R. M. May
, The invasion, persistence, and spread of iufectious diseases within animal and plant communites, Phil. Trans. R. Soc. London B, 314 (1986)
, 533-570.
|
|
Y. L. Cai
, Y. Cai
, M. Banerjee
and W.M. Wang
, A stochastic sirs epidemic model with infectious force under intervention strategies, J. Differential Equaitons, 259 (2015)
, 7463-7502.
doi: 10.1016/j.jde.2015.08.024.
|
|
Y. L. Cai
, Y. Kang
and W. M. Wang
, A stochastic sirs epidemic model with nonlinear incidence rate, Appl. Math. Comput., 305 (2017)
, 221-240.
doi: 10.1016/j.amc.2017.02.003.
|
|
J. Chattopadhyay
and O. Arino
, A predator-prey model with disease in the prey, Nonlinear Anal., 36 (1999)
, 747-766.
doi: 10.1016/S0362-546X(98)00126-6.
|
|
K. P. Das
, A study of chaotic dynamics and its possible control in a predator-prey model with disease in the predator, J. Dyn. Control Syst., 21 (2015)
, 605-624.
doi: 10.1007/s10883-015-9283-6.
|
|
K. P. Das
, A study of harvesting in a predator-prey model with disease in both populations, Math. Methods Appl. Sci., 39 (2016)
, 2853-2870.
doi: 10.1002/mma.3735.
|
|
K. S. Dorman
, J. S. Sinsheimer
and K. Lange
, In the garden of branching processes, SIAM Rev., 46 (2004)
, 202-229.
doi: 10.1137/S0036144502417843.
|
|
R. Durrett
, Special invited paper: Coexistence in stochastic spatial models, Ann. Appl. Probab., 19 (2009)
, 477-496.
doi: 10.1214/08-AAP590.
|
|
D. T. Gillespie,
Markov Processes: An Introduction for Physical Scientists, Academic Press, Inc., Boston, MA, 1992.
|
|
B. S. Goh,
Management and Analysis of Biological Populations, Elsevier Sci. Pub. Com., Amsterdam, 1980.
|
|
B. S. Goh
, Global stability in two species interactions, J. Math. Biol., 3 (1976)
, 313-318.
doi: 10.1007/BF00275063.
|
|
F. M. D. Gulland, The impact of infectious diseases on wild animal populations–a review,
Ecology of Infectious Diseases in Natural Populations. (B. T. Grenfell and A. P. Dobson,
eds). Cambridge: Cambridge University Press, 1995, 20–51.
|
|
W. J. Guo
, Y. L. Cai
, Q. M. Zhang
and W. M. Wang
, Stochastic persistence and stationary distribution in an sis epidemic model with media coverage, Physica A: Statistical Mechanics and its Applications, 492 (2018)
, 2220-2236.
doi: 10.1016/j.physa.2017.11.137.
|
|
P. Haccou, P. Jagers and V. A. Vatutin,
Branching Processes Variation, Growth, and Extinction of Populations, Cambridge University Press, Cambridge; IIASA, Laxenburg, 2007.
|
|
K. P. Hadeler
and H. I. Freedman
, Predator-prey populations with parasitic infection, J. Math. Biol., 27 (1989)
, 609-631.
doi: 10.1007/BF00276947.
|
|
J. K. Hale
and P. Waltman
, Persistence in infinite-dimensional systems, SIAM J. Math. Anal., 20 (1989)
, 388-395.
doi: 10.1137/0520025.
|
|
L. T. Han
and Z. E. Ma
, Four predator prey models with infectious diseases, Math. Comput. Modelling, 34 (2001)
, 849-858.
doi: 10.1016/S0895-7177(01)00104-2.
|
|
L. T. Han
, Z. E. Ma
and T. Shi
, An sirs epidemic model of two competitive species, Math. Comput. Modelling, 37 (2003)
, 87-108.
doi: 10.1016/S0895-7177(03)80008-0.
|
|
L. T. Han
and A. Pugliese
, Epidemics in two competing species, Nonlinear Anal., 10 (2009)
, 723-744.
doi: 10.1016/j.nonrwa.2007.11.005.
|
|
M. Haque
, A predator-prey model with disease in the predator species only, Nonlinear Anal.: Real World Appl., 11 (2010)
, 2224-2236.
doi: 10.1016/j.nonrwa.2009.06.012.
|
|
M. Haque
and E. Venturino
, An ecoepidemiological model with disease in predator: The ratio-dependent case, Math. Meth. Appl. Sci., 30 (2007)
, 1791-1809.
doi: 10.1002/mma.869.
|
|
H. W. Hethcote
, W. D. Wang
, L. T. Han
and Z. E. Ma
, A predator-prey model with infected prey, Theor. Popul. Biol., 66 (2004)
, 259-268.
|
|
D. J. Higham
, Modeling and simulating chemical reactions, SIAM Rev., 50 (2008)
, 347-368.
doi: 10.1137/060666457.
|
|
M. Kimmel and D. Axelrod,
Branching Processes in Biology, Springer-Verlag, NewYork, 2002.
doi: 10.1007/b97371.
|
|
N. Lanchier
and C. Neuhauser
, A spatially explicit model for competition among specialists and generalists in a heterogeneous environment, Ann. Appl. Probab., 16 (2006)
, 1385-1410.
doi: 10.1214/105051606000000394.
|
|
N. Lanchier
and C. Neuhauser
, Stochastic spatial models of host-pathogen and host-mutualist interactions. i, Ann. Appl. Probab., 16 (2006)
, 448-474.
doi: 10.1214/105051605000000782.
|
|
Q. Liu
, D. Q. Jiang
, N. Z. Shi
, T. Hayat
and A. Alsaedi
, The threshold of a stochastic sis epidemic model with imperfect vaccination, Math. Comput. Simulation, 144 (2018)
, 78-90.
doi: 10.1016/j.matcom.2017.06.004.
|
|
M. Liu
, C. Bai
and Y. Jin
, Population dynamical behavior of a two-predator one-prey stochastic model with time delay, Discrete Contin. Dyn. Syst., 37 (2017)
, 2513-2538.
doi: 10.3934/dcds.2017108.
|
|
M. Liu
, X. He
and J. Yu
, Dynamics of a stochastic regime-switching predator-prey model with harvesting and distributed delays, Nonlinear Anal. Hybrid Syst., 28 (2018)
, 87-104.
doi: 10.1016/j.nahs.2017.10.004.
|
|
M. Liu
and M. Fan
, Stability in distribution of a three-species stochastic cascade predator-prey system with time delays, IMA J. Appl. Math., 82 (2017)
, 396-423.
doi: 10.1093/imamat/hxw057.
|
|
R. K. McCormack
and L. J. S. Allen
, Disease emergence in multi-host epidemic models, Math. Med. Biol., 24 (2007)
, 17-34.
|
|
S. Sarwardi
, M. Haque
and E. Venturino
, Global stability and persistence in lg-holling type ii diseased predator ecosystems, J. Biol. Phys., 37 (2011)
, 91-106.
|
|
H. R. Thieme
, Covergence results and a Poincaré-Bendixson trichotomy for asymptotically autonomous differential equations, J. Math. Biol., 30 (1992)
, 755-763.
doi: 10.1007/BF00173267.
|
|
H. R. Thieme
, Persistence under relaxed point-dissipativity (with application to an endemic model), SIAM J. Math. Anal., 24 (1993)
, 407-435.
doi: 10.1137/0524026.
|
|
E. Venturino
, The influence of diseases on lotka-volterra systems, Rocky Mountain J. Math, 24 (1994)
, 381-402.
doi: 10.1216/rmjm/1181072471.
|
|
E. Venturino
, Epidemics in predator-prey models: disease in the predators, IMA J. Math. Appl. Med. Biol., 19 (2002)
, 185-205.
|
|
P. Whittle
, The outcome of a stochastic epidemic: A note on bailey's paper, Biometrika, 42 (1955)
, 116-122.
doi: 10.1093/biomet/42.1-2.116.
|
|
Y. N. Xiao
and L. S. Chen
, Modeling and analysis of a predator-prey model with disease in the prey, Math. Biosci., 171 (2001)
, 59-82.
doi: 10.1016/S0025-5564(01)00049-9.
|
|
R. Xu
and S. H. Zhang
, Modelling and analysis of a delayed predator-prey model with disease in the predator, Appl. Math. Comput., 224 (2013)
, 372-386.
doi: 10.1016/j.amc.2013.08.067.
|
|
Y. Yuan
and L. J. S. Allen
, Stochastic models for virus and immune system dynamics, Math. Biosci, 234 (2011)
, 84-94.
doi: 10.1016/j.mbs.2011.08.007.
|