Free Access
Issue
Math. Model. Nat. Phenom.
Volume 11, Number 1, 2016
Reviews in mathematical modelling
Page(s) 49 - 90
DOI https://doi.org/10.1051/mmnp/201611104
Published online 03 December 2015
  1. V. Ajraldi, M. Pittavino, E. Venturino. Modelling herd behavior in population systems. Nonlinear Analysis Real World Applications, 12 (2011), 2319–2338. [CrossRef] [MathSciNet] [Google Scholar]
  2. H. R., Akcakaya. Population cycles of mammals: evidence for ratio-dependent predator-prey hypothesis. Ecol. Monogr., 62 (1992) 119–142. [CrossRef] [Google Scholar]
  3. W. C. Allee. The Social Life of Animals. New York: Norton and Co. (1938). [Google Scholar]
  4. R. M. Anderson, R. M. May. The invasion, persistence and spread of infectious diseases within animal and plant communities. Philos. Trans. R. Soc. London B, 314 (1986), 533–570. [CrossRef] [Google Scholar]
  5. O. Arino, M. Delgado, M. Molina-Becerra. Asymptotic behaviour of disease-free equilibriums of an age-structured predator-prey model with disease in the prey. Discrete and Continuous Dynamical Systems Series B, 4 (2004), 501–515. [CrossRef] [Google Scholar]
  6. R. A. Armstrong, R. McGehee. Competitive exclusion. The American Naturalist, 115 (1980), 151–170. [CrossRef] [Google Scholar]
  7. P. Auger, R. Mchich, T. Chowdhury, G. Sallet, M. Tchuente, J. Chattopadhyay. Effects of a disease affecting a predator on the dynamics of a predator-prey system. Journal of Theoretical Biology, 258 (2009), 344–351. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  8. N. Bairagi, P.K. Roy, J. Chattopadhyay. Role of infection on the stability of a predator-prey system with several response functions–A comparative study. Journal of Theoretical Biology, 248 (2007), 10–25. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  9. N. Bairagi, S. Chaudhuri, J. Chattopadhyay. Harvesting as a disease control measure in an eco-epidemiological system – A theoretical study. Mathematical Biosciences, 217 (2009), 134–144. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  10. N. Bairagi, R.R. Sarkar, J. Chattopadhyay. Impacts of incubation delay on the dynamics of an eco-epidemiological system–A theoretical study. Bulletin of Mathematical Biology, 70 (2008), 2017–2038. DOI: 10.1007/s11538-008-9337-y [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  11. M. Banerjee, E. Venturino. A phytoplankton–toxic phytoplankton–zooplantkon model. Ecological Complexity, 8 (2011), 239–248. [CrossRef] [Google Scholar]
  12. A. M. Bate, F. M. Hilker. Complex dynamics in an eco-epidemiological model. Bull. Math. Biol., 75 (2013), 2059–2078. DOI: 10.1007/s11538-013-9880-z [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  13. A. M. Bate, F. M. Hilker. Predator-prey oscillations can shift when diseases become endemic. Journal of Theoretical Biology, 316 (2013), 1–8. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  14. A. M. Bate, F. M. Hilker. Disease in group-defending prey can benefit predators. Theor. Ecol., 7 (2014), 87–100. DOI: 10.1007/s12080-013-0200-x [CrossRef] [Google Scholar]
  15. S. Bhattacharyya, D. K. Bhattacharya. Pest control through viral disease: mathematical modeling and analysis. J. Theor. Biol., 238 (2006), 177–196. [CrossRef] [PubMed] [Google Scholar]
  16. J. Beddington. Mutual interference between parasites or predators and its effect on searching efficiency. J.Anim. Ecol., 51 (1975), 331–340. [CrossRef] [Google Scholar]
  17. E. Beltrami, T.O. Carroll. Modelling the role of viral disease in recurrent phytoplankton blooms. J. Math. Biol., 32 (1994), 857–863. [CrossRef] [Google Scholar]
  18. S. Belvisi, E. Venturino. An ecoepidemic model with diseased predators and prey group defense. SIMPAT, 34 (2013), 144–155. DOI: 10.1016/j.simpat.2013.02.004 [Google Scholar]
  19. E. Beretta, Y. Kuang. Modeling and analysis of a marine bacteriophage infection. Math. Biosci., 149 (1998), 57–76. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  20. A. Berruti, V. La Morgia, E. Venturino, S. Zappalà. Competition among invasive and native species: the case of European and mountain hares, CMMSE 14, July 3rd-7th, 2014, Costa Ballena, Rota, Cádiz (Spain), (J. Vigo-Aguiar, I.P. Hamilton, J. Medina, P. Schwertfeger, W. Sproessig, M. Demiralp, E. Venturino, V.V. Kozlov, P. Oliveira Editors) v. I, 170–181. [Google Scholar]
  21. F. Bianco, E. Cagliero, M. Gastelurrutia, E. Venturino. Metaecoepidemic models: infected and migrating predators. Int. J. Comp. Math., 89(13-14) (2012), 1764–1780. [CrossRef] [Google Scholar]
  22. C. Bosica, A. De Rossi, N. L. Fatibene, M. Sciarra, E. Venturino. Two-strain ecoepidemic systems: the obligated mutualism case. Applied Math. Inf. Sci. 9(4), (2015) 1677–1685. [Google Scholar]
  23. P. A. Braza. Predator-prey dynamics with square root functional responses. Nonlinear Analysis: Real World Applications, 13 (2012), 1837–1843. [CrossRef] [MathSciNet] [Google Scholar]
  24. I. M. Bulai, R. Cavoretto, B. Chialva, D. Duma, E. Venturino. Comparing disease control policies for interacting wild populations. Nonlinear Dynamics, 79 (2015), 1881–1900. [CrossRef] [Google Scholar]
  25. S. Busenberg, P. van den Driessche. Analysis of a disease transmission model in a population with varying size. J. of Math. Biology, 28 (1990), 257–270. [CrossRef] [Google Scholar]
  26. E. Cagliero, E. Venturino. Ecoepidemics with infected prey in herd defence: the harmless and toxic cases. International Journal of Computer Mathematics, (2015), to appear. DOI: 10.1080/00207160.2014.988614 [Google Scholar]
  27. R. Cavoretto, S. Collino, B. Giardino, E. Venturino. A two-strain ecoepidemic competition model. Theoretical Ecology, 8(1) (2015), 37–52. DOI: 10.1007/s12080-014-0232-x [CrossRef] [Google Scholar]
  28. R. Cavoretto, A. De Rossi, E. Perracchione, E. Venturino, Reliable approximation of separatrix manifolds in competition models with safety niches, to appear in International Journal of Computer Mathematics. [Google Scholar]
  29. S. Chatterjee, J. Chattopadhyay. Role of migratory bird population in a simple eco-epidemiological model. Mathematical and Computer Modelling of Dynamical Systems: Methods, Tools and Applications in Engineering and Related Sciences, 13 (2007), 99–114. DOI: 10.1080/13873950500303352 [Google Scholar]
  30. S. Chatterjee, K. Das, J. Chattopadhyay. Time delay factor can be used as a key factor for preventing the outbreak of a disease–Results drawn from a mathematical study of a one season eco-epidemiological model. Nonlinear Analysis: Real World Applications, 8 (2007), 1472–1493. [CrossRef] [MathSciNet] [Google Scholar]
  31. S. Chatterjee, M. Isaia, E. Venturino. Spiders as biological controllers in the agroecosystem. Journal of Theoretical Biology 258 (2009), 352–362. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  32. J. Chattopadhyay, O. Arino. A predator-prey model with disease in the prey. Nonlinear Analysis, 36 (1999), 747–766. [CrossRef] [MathSciNet] [Google Scholar]
  33. J. Chattopadhyay, N. Bairagi. Pelicans at risk in Salton sea - an eco-epidemiological model. Ecological Modelling, 136 (2001), 103–112. [CrossRef] [Google Scholar]
  34. J. Chattopadhyay, S. Chatterjee, E. Venturino. Patchy agglomeration as a transition from monospecies to recurrent plankton blooms. Journal of Theoretical Biology, 253 (2008), 289–295. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  35. J. Chattopadhyay, R.R. Sarkar, G. Ghosal. Removal of infected prey prevent limit cycle oscillations in an infected prey-predator system - a mathematical study. Ecological Modelling, 156 (2002), 113–121. [CrossRef] [Google Scholar]
  36. J. Chattopadhayay, R. R. Sarkar, S. Mandal. Toxin-producing Plankton May Act as a Biological Control for Planktonic Blooms-Field Study and Mathematical Modelling. J. Theor. Biol., 215 (2002), 333–344. doi:10.1006/jtbi.2001.2510 [CrossRef] [PubMed] [Google Scholar]
  37. J. Chattopadhyay, R. R. Sarkar, S. Pal. Dynamics of nutrient-phytoplankton interaction in the presence of viral infection. BioSystems, 68 (2003), 5–17. [CrossRef] [PubMed] [Google Scholar]
  38. S. Chaudhuri, A. Costamagna, E. Venturino. Epidemics spreading in predator-prey systems. Int. J. Comp. Math., 89 (2012), 561–584. [CrossRef] [Google Scholar]
  39. S. Chaudhuri, J. Chattopadhyay, E. Venturino. Toxic phytoplankton-induced spatiotemporal patterns. J. of Biological Physics, 38 (2012), 331–348. [CrossRef] [PubMed] [Google Scholar]
  40. S. Chaudhuri, A. Costamagna, E. Venturino. Ecoepidemics overcoming the species-barrier and being subject to harvesting. Mathematical Medicine and Biology, 30 (2013), 73–93. doi:10.1093/imammb/dqr026 [CrossRef] [MathSciNet] [Google Scholar]
  41. C. Clark. Mathematical bioeconomics: the optimal management of renewable resources. Wiley, New York, (1976). [Google Scholar]
  42. C. Cosner, D. L. De Angelis. Effects of spatial grouping on the functional response of predators. Theoretical Population Biology, 56 (1999), 65–75. [CrossRef] [PubMed] [Google Scholar]
  43. K. p. Das, S. Roy, J. Chattopadhyay. Effect of disease-selective predation on prey infected by contact and external sources. BioSystems, 95 (2009), 188–199 [CrossRef] [PubMed] [Google Scholar]
  44. K. p. Das, J. Chattopadhyay. Role of environmental disturbance in an eco-epidemiological model with disease from external source. Math. Meth. Appl. Sci., 35 (2012), 659–675 [Google Scholar]
  45. K. p. Das, K. Kundu, J. Chattopadhyay. A predator-prey mathematical model with both the populations affected by diseases. Ecological Complexity, 8 (2011), 68–80. [CrossRef] [Google Scholar]
  46. D. De Angelis, R. Goldstein, and R. O’Neill. A model for trophic interaction. Ecology, 56 (1975), 881–892. [CrossRef] [Google Scholar]
  47. A. De Rossi, F. Lisa, L. Rubini, A. Zappavigna, E. Venturino. A food chain ecoepidemic model: infection at the bottom trophic level. Ecological Complexity 21 (2015) 233–245. [CrossRef] [Google Scholar]
  48. M. Delgado, M. Molina-Becerra, A. Suarez. Relating disease and predation: equilibria of an epidemic model. Math. Methods Appl. Sci., 28 (2005), 349–362. [CrossRef] [Google Scholar]
  49. B. Dennis. Allee effects: population growth, critical density, and the chance of extinction. Nat. Res. Model., 3 (1989), 481–538. [Google Scholar]
  50. J. Z. Farkas, A. Y. Morozov. Modelling Effects of Rapid Evolution on Persistence and Stability in Structured Predator-Prey Systems. Math. Model. Nat. Phenom., 9(3) (2014), 26–46. doi: 10.1051/mmnp/20149303 [CrossRef] [EDP Sciences] [Google Scholar]
  51. L. Ferreri, E. Venturino. Cellular automata for contact ecoepidemic processes in predator-prey systems. Ecological Complexity, 13 (2013), 8–20. [CrossRef] [Google Scholar]
  52. Q.L. Gao, H.W. Hethcote. Disease transmission models with density dependent demographics. J. Math. Biol., 30 (1992), 717–731. [MathSciNet] [PubMed] [Google Scholar]
  53. S. A. H. Geritz, M. Gyllenberg. Group defence and the predator’s functional response. J. Math. Biol., 66 (2013), 705–717. DOI: 10.1007/s00285-012-0617-7 [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  54. G. Gimmelli, B. W. Kooi, E. Venturino. Ecoepidemic models with prey group defense and feeding saturation. Ecological Complexity, 22 (2015), 50–58. [CrossRef] [Google Scholar]
  55. E. González-Olivares, R. Ramos-Jiliberto. Dynamic consequences of prey refuges in a simple model system: more prey, fewer predators and enhanced stability. Ecological Modelling, 166 (2003), 135–146. [CrossRef] [Google Scholar]
  56. E. González-Olivares, R. Ramos-Jiliberto. Comments to the effect of prey refuge in a simple predator-prey model. Ecological Modelling, 232 (2012), 158–160. [CrossRef] [Google Scholar]
  57. D. Greenhalgh, M. Haque. A predator-prey model with disease in the prey species only. Math. Meth. Appl. Science, 30 (2007), 911–929. [CrossRef] [Google Scholar]
  58. M. E. Gurtin, R. C. McCamy. Nonlinearly age-dependent population dynamics. Archs. Ration. Mech. Analysis, 54 (1974), 281–300. [CrossRef] [Google Scholar]
  59. M. Gyllenberg, J. Hemminki, T. Tammaru. Allee effects can both conserve and create spatial heterogeneity in population densities. Theor. Pop. Biol., 56 (1999), 231–242. [CrossRef] [Google Scholar]
  60. K.P. Hadeler, H.I. Freedman. Predator-prey population with parasitic infection. J. Math. Biol., 27 (1989), 609–631. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  61. L. Han, Z. Ma, H.W. Hethcote. Four predator prey models with infectious diseases. Math. Comp. Modelling, 30 (2001), 849–858. [CrossRef] [Google Scholar]
  62. I. Hanski, M. Gilpin (Editors) Metapopulation biology: ecology, genetics and evolution, Academic Press, London (1997). [Google Scholar]
  63. I. Hanski, A. Moilanen, T. Pakkala, M. Kuussaari. Metapopulation persistence of an endangered butterfly: a test of the quantitative incidence function model. Conservation Biology, 10 (1996), 578–590. [CrossRef] [Google Scholar]
  64. M. Haque, J. Chattopadhyay. Influences of non-linear incidence rate in an eco-epidemiological model of the Salton Sea. Nonlinear Studies, 10 (2003), 373–388. [MathSciNet] [Google Scholar]
  65. M. Haque, S. Rahman, E. Venturino. Comparing functional responses in predator-infected eco-epidemics models. BioSystems, 114 (2013), 98–117. [CrossRef] [PubMed] [Google Scholar]
  66. M. Haque, S. Sarwardi, S. Preston, E. Venturino. Effect of delay in a Lotka-Volterra type predator-prey model with a transmissible disease in the predator species. Mathematical Biosciences, 234 (2011), 47–57. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  67. M. Haque, J. Zhen, E. Venturino. An epidemiological predator-prey model with standard disease incidence. Mathematical Methods in the Applied Sciences, 32 (2009), 875–898. [CrossRef] [Google Scholar]
  68. M. Haque, E. Venturino. The role of transmissible diseases in the Holling-Tanner predator-prey model. Theoretical Population Biology, 70 (2006), 273–288. [CrossRef] [PubMed] [Google Scholar]
  69. M. Haque, E. Venturino. Increase of the prey may decrease the healthy predator population in presence of a disease in the predator. HERMIS, 7 (2006), 39–60. [Google Scholar]
  70. M. Haque, E. Venturino. An ecoepidemiological model with disease in the predator: the ratio-dependent case. Math. Meth. Appl. Sci., 30 (2007), 1791–1809. [CrossRef] [Google Scholar]
  71. M. Haque, E. Venturino. Effect of parasitic infection in the Leslie-Gower predator-prey model. Journal of Biological Systems, 16 (2008), 445–461. [CrossRef] [Google Scholar]
  72. M. Haque, E. Venturino. Mathematical models of diseases spreading in symbiotic communities. in J.D. Harris, P.L. Brown (Editors), Wildlife: Destruction, Conservation and Biodiversity, NOVA Science Publishers, New York, (2009) 135–179. [Google Scholar]
  73. H. W. Hethcote. The mathematics of infectious diseases. SIAM Review, 42 (2000), 599–653. [CrossRef] [MathSciNet] [Google Scholar]
  74. H. W. Hethcote, H. W. Stech, and P. van den Driessche. Periodicity and stability in epidemic models: A survey. In Differential Equations and Applications in Ecology, Epidemics and Population Problems, S. N. Busenberg and K. L. Cooke, eds., Academic Press, New York (1981), 65–82. [Google Scholar]
  75. H.W. Hethcote, W. Wang, L. Han, Z. Ma. A predator prey model with infected prey. Theoretical Population Biology, 66 (2004), 259–268. [CrossRef] [PubMed] [Google Scholar]
  76. F. M. Hilker. Population collapse to extinction: the catastrophic combination of parasitism and Allee effect. Journal of Biological Dynamics, 4 (2010), 86–101. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  77. F. M. Hilker, M. Langlais, H. Malchow. The Allee Effect and Infectious Diseases: Extinction, Multistability, and the (Dis-)Appearance of Oscillations. The American Naturalist, 173 (2009), 72–88. [CrossRef] [PubMed] [Google Scholar]
  78. F. M. Hilker, H. Malchow. Strange Periodic Attractors in a Prey-Predator System with Infected Prey. Mathematical Population Studies, 13 (2006), 119–134. DOI: 10.1080/08898480600788568 [CrossRef] [MathSciNet] [Google Scholar]
  79. F. M. Hilker, H. Malchow, M. Langlais, S. V. Petrovskii. Oscillations and waves in a virally infected plankton system: Part II: Transition from lysogeny to lysis. Ecological Complexity, 3 (2006), 200–208. [CrossRef] [Google Scholar]
  80. F. Hilker, K. Schmitz. Disease-induced stabilization of predator-prey cycles. Journal of Theoretical Biology, 255 (2008), 299–306. [CrossRef] [PubMed] [Google Scholar]
  81. I. S. Hotopp, H. Malchow, E. Venturino. Switching feeding among sound and infected prey in ecoepidemic systems. Journal of Biological Systems, 18 (2010), 727–747. DOI: 10.1142/S0218339010003718. [CrossRef] [MathSciNet] [Google Scholar]
  82. Y.H. Hsieh, C.K. Hsiao. A predator-prey model with disease infection in both populations. Mathematical Medicine and Biology, 25 (2008), 247–266. [CrossRef] [Google Scholar]
  83. S. Jana, T. K. Kar. Modeling and analysis of a prey-predator system with disease in the prey. Chaos, Solitons & Fractals, 47 (2013), 42–53. [CrossRef] [MathSciNet] [Google Scholar]
  84. S. Jana, T.K. Kar. A mathematical study of a prey-predator model in relevance to pest control. Nonlinear Dynamics, 74 (2013), 667–683. [CrossRef] [Google Scholar]
  85. A. Kacha, M. H. Hbid, R. Bravo. Mathematical study of bacteria-fish model with level of infection structure. Nonlinear Analysis: Real World Applications, 10 (2009), 1662–1678. [CrossRef] [MathSciNet] [Google Scholar]
  86. Y. Kang, S. K. Sasmal, A. M. Bhowmick, J. Chattopadhyay. Dynamics of a predator-prey system with prey subject to Allee effects and disease. Mathematical Biosciences and Engineering, 11 (2014), 877–918. [CrossRef] [MathSciNet] [Google Scholar]
  87. T. K. Kar, S. Jana. Application of three controls optimally in a vector-borne disease–a mathematical study. Commun. Nonlinear Sci. Numer. Simul. 18 (2013), 2868–2884. [CrossRef] [Google Scholar]
  88. T. K. Kar, S. Jana. A theoretical study on mathematical modelling of an infectious disease with application of optimal control. BioSystems 111 (2013), 37–50. [CrossRef] [PubMed] [Google Scholar]
  89. Q.J.A. Khan, E. Balakrishnan, G.C. Wake. Analysis of a predator-prey system with predator switching. Bull. Math. Biol., 66 (2004), 109–123. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  90. Q.J.A. Khan, B.S. Bhatt, R.P. Jaju. Switching model with two habitats and a predator involving group defence. J. of Nonlinear Mathematical Physics, 5 (1998), 212–223. [CrossRef] [Google Scholar]
  91. B. W., Kooi, G. A. K., van Voorn, K. p. Das. Stabilization and complex dynamics in a predator-prey model with predator suffering from an infectious disease. Ecol. Complexity, 8 (2011), 113–122. [CrossRef] [Google Scholar]
  92. M. A. Lewis, P. Kareiva. Allee dynamics and the spread of invading organisms. Theor. Popul. Biol., 43 (1993), 141–158. [CrossRef] [Google Scholar]
  93. J. Liu. Stability and Hopf bifurcation in a prey-predator system with disease in the prey and two delays. Abstract and Applied Analysis, (2014), Article ID 624546, 15 pages. DOI: 10.1155/2014/624546 [Google Scholar]
  94. Z. Ma, S. Wang, Z. Li. The effect of prey refuge in a simple predator-prey model. Ecological Modelling, 222 (2011), 3453–3454. [CrossRef] [Google Scholar]
  95. H. Malchow H. F. M. Hilker, S. V. Petrovskii, K. Brauer Oscillations and waves in a virally infected plankton system: Part I: The lysogenic stage. Ecological Complexity, 1 (2004), 211–223. [CrossRef] [Google Scholar]
  96. H. Malchow, F. M. Hilker, R. R. Sarkar, K. Brauer. Spatiotemporal patterns in an excitable plankton system with lysogenic viral infection. Mathematical and Computer Modelling, 42 (2005), 1035–1048. [CrossRef] [Google Scholar]
  97. H. Malchow, S. Petrovskii, E. Venturino. Spatiotemporal patterns in Ecology and Epidemiology. CRC, Boca Raton, (2008). [Google Scholar]
  98. J. Mena-Lorca, H. W. Hethcote. Dynamic models of infectious diseases as regulator of population sizes. J. Math. Biology, 30 (1992), 693–716. [Google Scholar]
  99. A. Molter, M. Rafikov. Nonlinear optimal control of population systems: applications in ecosystems. Nonlinear Dynamics, 76 (2014), 1141–1150. [CrossRef] [Google Scholar]
  100. M. Rafikov, J. C. Silveira. On dynamical behavior of the sugarcane borer – Parasitoid agroecosystem, Ecological Complexity, 18 (2014), 67–73. [CrossRef] [Google Scholar]
  101. A. Morozov. Revealing the role of predator-dependent disease transmission in the epidemiology of a wildlife infection: a model study. Theoretical Ecology, 5 (2012), 517–532. [CrossRef] [Google Scholar]
  102. A.Y. Morozov. Emergence of Holling type III zooplankton functional response: Bringing together field evidence and mathematical modelling. Journal of Theoretical Biology, 265 (2010), 45–54. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  103. N. M. Oliveira, F. M. Hilker. Modelling Disease Introduction as Biological Control of Invasive Predators to Preserve Endangered Prey. Bulletin of Mathematical Biology, 72 (2010), 444–468. DOI: 10.1007/s11538-009-9454-2 [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  104. S. Palomino Bean, A.C.S. Vilcarromero, J.F.R. Fernandes, O. Bonato. Co-existẽncia de Espécies em Sistemas Presa-predador com Switching (Species coexistence in predator-prey systems with switching). TEMA Tend. Mat. Apl. Comput., 7 (2006), 317–326. [CrossRef] [MathSciNet] [Google Scholar]
  105. E. Renshaw. Modelling biological populations in space and time. Cambridge Univ. Press, Cambridge, UK (1991). [Google Scholar]
  106. M.G. Roberts, J.A.P. Heesterbeek. Characterizing the next-generation matrix and basic reproduction number in ecological epidemiology. J. Math. Biol., 66 (2013), 1045–1064, DOI: 10.1007/s00285-012-0602-1 [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  107. T. Romano, M. Banerjee, E. Venturino. A comparison of several plankton models for red tides. in G. Kehayias (Editor) Zooplankton: Species Diversity, Distribution and Seasonal Dynamics, Nova Science Publishers, Hauppauge, NY, 2014, 19-63. ISBN: 978-1-62948-720-5 [Google Scholar]
  108. M.L. Rosenzweig, R.H. MacArthur. Graphical representation and stability conditions of predator-prey interactions. Am. Nat., 97 (1963), 209–223. [CrossRef] [Google Scholar]
  109. S. Roy, S. Alam, J. Chattopadhyay. Competitive effects of toxin-producing phytoplankton on overall plankton populations in the Bay of Bengal. Bull. Math. Biol., 68 (2006), 2303–2320. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  110. S. Roy, J. Chattopadhyay. Disease-selective predation may lead to prey extinction. Math. Meth. Appl. Sci., 28 (2005), 1257–1267. [CrossRef] [Google Scholar]
  111. G.D. Ruxton. Short term refuge use and stability of predator-prey models. Theoretical Population Biology, 47 (1995), 1–17. [CrossRef] [Google Scholar]
  112. R.A. Saenz, H.W. Hethcote. Competing species models with an infectious disease. Mathematical Biosciences and Engineering, 3 (2006), 219–235. [MathSciNet] [Google Scholar]
  113. R.R. Sarkar, S. Pal, J. Chattopadhyay. Role of two toxin-producing plankton and their effect on phytoplankton-zooplankton system, a mathematical study supported by experimental findings. BioSystems, 80 (2005), 11–13. [CrossRef] [PubMed] [Google Scholar]
  114. S. Sarwardi, M. Haque, E. Venturino. A Leslie-Gower Holling-type II ecoepidemic model. J. Applied Mathematics and Computing, 35 (2011), 263–280. DOI: 10.1007/s12190-009-0355-1 [CrossRef] [Google Scholar]
  115. S. Sarwardi, M. Haque, E. Venturino. Global stability and persistence in Leslie-Gower Holling type II diseased predator ecosystems. J. Biol. Phys., 37 (2011), 91–106. DOI: 10.1007/s10867-010-9201-9. [CrossRef] [PubMed] [Google Scholar]
  116. S. K. Sasmal, J. Chattopadhyay. An eco-epidemiological system with infected prey and predator subject to the weak Allee effect. Mathematical Biosciences, 246 (2013), 260–271. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  117. M. Semplice, E. Venturino. Travelling waves in plankton dynamics. Math. Model. Nat. Phenom., 8 (2013), No. 6, 64–79.DOI: 10.1051/mmnp/20138605. [CrossRef] [EDP Sciences] [Google Scholar]
  118. M. Sen, E. Venturino. A model for which toxic and non-toxic phytoplankton are indistinguishable by the zooplantkon. AIP Conf. Proc. 1479, ICNAAM 2012 (2012), T. Simos, G. Psihoylos, Ch. Tsitouras, Z. Anastassi (Editors), 1315–1318. doi: 10.1063/1.4756397 [Google Scholar]
  119. M. Sieber, F. M. Hilker. Prey, predators, parasites: intraguild predation or simpler community modules in disguise?. Journal of Animal Ecology, 80 (2011), 414–421. doi: 10.1111/j.1365-2656.2010.01788.x [CrossRef] [Google Scholar]
  120. M. Sieber, F. M. Hilker. The hydra effect in predator-prey models. J. Math. Biol., 64 (2012), 341–360. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  121. M. Sieber, H. Malchow, F. M. Hilker. Disease-induced modification of prey competition in eco-epidemiological models. Ecological Complexity, 18 (2014), 74–82. [CrossRef] [Google Scholar]
  122. I. Siekmann, H. Malchow, E. Venturino. An extension of the Beretta-Kuang model of viral diseases. Mathematical Biosciences and Engineering, 5 (2008), 549–565. [CrossRef] [MathSciNet] [Google Scholar]
  123. I. Siekmann, H. Malchow, E. Venturino. On competition of predators and prey infection, Ecological Complexity, 7 (2010), 446-457; doi:10.1016. [CrossRef] [Google Scholar]
  124. B.K. Singh, J. Chattopadhyay, S. Sinha. The role of virus infection in a simple phytoplankton zooplankton system. Journal of Theoretical Biology, 231 (2004), 153–166. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  125. D. Stiefs, E. Venturino, U. Feudel. Evidence of chaos in ecoepidemic models. Mathematical Biosciences and Engineering, 6 (2009), 855–871. [CrossRef] [MathSciNet] [Google Scholar]
  126. C. Tannoia, E. Torre, E. Venturino. An incubating diseased-predator ecoepidemic model. J. Biol. Phys., 38 (2012), 705–720. [CrossRef] [PubMed] [Google Scholar]
  127. M. Tansky. Switching effects in prey-predator system. J. Theor. Biol., 70 (1978), 263–271. [CrossRef] [PubMed] [Google Scholar]
  128. R.K. Upadhyay, N. Bairagi, K. Kundu, J. Chattopadhyay. Chaos in eco-epidemiological problem of the Salton Sea and its possible control. Applied Mathematics and Computation, 196 (2008), 392–401. [CrossRef] [Google Scholar]
  129. E. Venturino. The influence of diseases on Lotka-Volterra systems. Rocky Mountain J. of Mathematics, 24 (1994), 381–402. [CrossRef] [MathSciNet] [Google Scholar]
  130. E. Venturino. Epidemics in predator-prey models: disease in the prey. in Mathematical Population dynamics, Analysis of heterogeneity 1, in O. Arino, D. Axelrod, M. Kimmel, M. Langlais (Editors) (1995) 381–393. [Google Scholar]
  131. E. Venturino. The effects of diseases on competing species. Math. Biosc., 174 (2001), 111–131. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  132. E. Venturino. Epidemics in predator-prey models: disease in the predators. IMA J. Math. Appl. Med. and Biol., 19 (2002), 185–205. [CrossRef] [Google Scholar]
  133. E. Venturino. A stage-dependent ecoepidemic model. WSEAS Transactions on Biology and Biomedicine, 1 (2004), 449–454. [Google Scholar]
  134. E. Venturino. How diseases affect symbiotic communities. Math. Biosc., 206 (2007), 11–30. [CrossRef] [Google Scholar]
  135. E. Venturino. Ecoepidemic models with disease incubation and selective hunting. Journal of Computational and Applied Mathematics, 234 (2010), 2883–2901. [CrossRef] [Google Scholar]
  136. E. Venturino. A minimal model for ecoepidemics with group defense. J. of Biological Systems, 19 (2011), 763–785. [CrossRef] [MathSciNet] [Google Scholar]
  137. E. Venturino. Simple metaecoepidemic models. Bulletin of Mathematical Biology, 73 (2011), 917–950. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  138. E. Venturino. An ecogenetic model. Appl. Math. Letters, 25 (2012), 1230–1233. [CrossRef] [Google Scholar]
  139. E. Venturino, M. Isaia, F. Bona, S. Chatterjee, G. Badino. Biological controls of intensive agroecosystems: wanderer spiders in the Langa Astigiana. Ecological Complexity, 5 (2008), 157–164. [CrossRef] [Google Scholar]
  140. E. Venturino, S. Petrovskii. Spatiotemporal Behavior of a Prey-Predator System with a Group Defense for Prey. Ecological Complexity, 14 (2013), 37–47. doi: 10.1016/j.ecocom.2013.01.004 [CrossRef] [Google Scholar]
  141. C. Viberti, E. Venturino. An ecosystem with Holling type II response and predators’ genetic variability. Mathematical Modelling and Analysis, 19, (2014) 371–394. [CrossRef] [MathSciNet] [Google Scholar]
  142. P. Waltman. Competition models in population biology. SIAM, Philadelphia, 1983. [Google Scholar]
  143. Y. Wang, J. Wang. Influence of prey refuge on predator-prey dynamics. Nonlinear Dynamics, 67 (2012), 191–201. [CrossRef] [Google Scholar]
  144. J. A. Wiens. Metapopulation dynamics and landscape ecology, in I. A. Hanski, M. E. Gilpin (Ed.s), Metapolulation Biology: Ecology, Genetics and Evolution, San Diego: Academic Press (1997) 43–62. [Google Scholar]
  145. J. Zhen, M. Haque. Global stability analysis of an eco-epidemiological model of the Salton sea. Journal of Biological Systems, 14 (2006), 373–385. [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.