Harvesting as a disease control measure in an eco-epidemiological system – a theoretical study. (English) Zbl 1157.92030

Summary: Epidemiology and ecology are traditionally treated as independent research areas, but there are many commonalities between these two fields. It is frequently observed in nature that the former has an encroachment into the later and changes the system dynamics significantly. In population ecology, in particular, the predator-prey interaction in presence of parasites can produce more complex dynamics including switching of stability, extinction and oscillations. On the other hand, harvesting practices may play a crucial role in a host-parasite system. Reasonable harvesting can remove a parasite, in principle, from their host. We study theoretically the role of harvesting in a predator-prey-parasite system. Our study shows that, using impulsive harvesting effort as control parameter, it is not only possible to control the cyclic behavior of the system populations leading to the persistence of all species, but other desired stable equilibrium including disease-free can also be obtained.


92D40 Ecology
92D30 Epidemiology
93C95 Application models in control theory
93C15 Control/observation systems governed by ordinary differential equations
Full Text: DOI


[1] Amundsen, P.A.; Kristoffersen, R., Infection of white fish (coregonus iavaretus L.s.1): a case study in parasite control, Can. J. zoo., 68, 1187, (1990)
[2] Anderson, R.M.; May, R.M., The invasion, persistence, and spread of infectious diseases within animal and plant communities, Philos. trans. R. soc. lond. B, 314, 533, (1986)
[3] Bairagi, N.; Roy, P.K.; Chattopadhyay, J., Role of infection on the stability of a predator – prey system with several response functions – a comparative study, J. theoret. biol., 248, 10, (2007)
[4] Birkhoff, G.; Rota, G.C., Ordinary differential equations, (1989), Wiley Canada · Zbl 0183.35601
[5] Brauer, F.; Soudack, A.C., Constant-rate stocking of predator – prey systems, J. math. biol., 11, 1, (1981) · Zbl 0448.92020
[6] Brauer, F.; Soudack, A.C., Coexistence properties of some predator – prey systems under constant rate harvesting and stocking, J. math. biol., 12, 101, (1981) · Zbl 0482.92015
[7] Chattopadhyay, J.; Arino, O., A predator – prey model with disease in the prey, Nonlinear anal., 36, 747, (1999) · Zbl 0922.34036
[8] Chattopadhyay, J.; Ghosal, K.; Chaudhuri, K.S., Nonselective harvesting of a prey – predator community with infected prey, Korean J. comput. appl. math., 3, 601, (1999) · Zbl 0938.92031
[9] Chattopadhyay, J.; Bairagi, N., Pelicans at risk in salton sea – an eco-epidemiological study, Ecol. model., 136, 103, (2001)
[10] Chau, N.P., Destabilizing effect of periodic harvest, Ecol. model., 127, 1, (2000)
[11] Chaudhuri, K.S., A bioeconomic model of harvesting a multispecies fishery, Ecol. model., 32, 267, (1986)
[12] Chaudhuri, K.S.; Saha Roy, S., On the combined harvesting of a prey – predator system, J. biol. syst., 4, 3, 373, (1996)
[13] Clark, C.W., Mathematical bioeconomics: the optimal management of renewable resources, (1976), Wiley New York · Zbl 0364.90002
[14] Cohn, J.P., Saving the salton sea, Bioscience, 50, 4, 295, (2000)
[15] Costa, M.I.S., Harvesting induced fluctuations: insights from a threshold management policy, Math. biosci., 205, 77, (2007) · Zbl 1106.92069
[16] Courtney, W., Tilapias as exotic species in the americas, (), p. 18
[17] Culver, C.S.; Kuris, A.M., The apparent eradication of a locally established introduced marine pest, Biol. invasion, 2, 245, (2000)
[18] Dobson, A.P.; May, R.M., The effects of parasites on fish populations – theoretical aspects, Int. J. parasitol., 17, 363, (1987)
[19] Fenton, A.; Rands, S.A., The impact of parasite manipulation and predator foraging behavior on predator – prey communities, Ecology, 87, 11, 2832, (2006)
[20] Freedman, H.I., A model of predator – prey dynamics as modified by the action of parasite, Math. biosci., 99, 143, (1990) · Zbl 0698.92024
[21] Friend, M., Avian disease in the salton sea, Hydrobiologia, 473, 293, (2002)
[22] Goh, B.S.; Leitmann, G.; Vincent, T.L., Optimal control of a prey – predator system, Math. biosci., 190, 263, (1974) · Zbl 0297.92013
[23] B. Grenfell, M. Keeling, in: R.M. May, R.A. McLean (Eds.), Dynamics of Infectious Disease in Theoretical Ecology, third ed., Oxford University Press Inc., New York, 2007, p. 132.
[24] Hadeler, K.P.; Freedman, H.I., Predator – prey population with parasite infection, J. math. biol., 27, 609, (1989) · Zbl 0716.92021
[25] Hall, S.R.; Duffy, M.A.; Caceres, C.E., Selective predation and productivity jointly drive complex behavior in host – parasite systems, Am. nat., 165, 1, 70, (2005)
[26] S. Horvitz, Salton Sea 101. Available from: <http://www.saltonseainfo.com/SS101/ss101.html>.
[27] Hethcote, H.W.; Wang, W.; Han, L.; Ma, Z., A predator – prey model with infected prey, Theoret. popul. biol., 66, 259, (2004)
[28] Holmes, J.C.; Bethel, W.M.; Canning, E.V.; Wright, C.A., Modification of intermediate host behavior by parasites, Behavioral aspects of parasite transmission, Supplementary I to zoological for Linnean socitey, 51, 123, (1972)
[29] Hudson, P.J.; Dobson, A.P.; Newborn, D., Prevention of population cycles by parasite removal, Science, 282, 2256, (1998)
[30] Ianelli, J.; Lamberson, R.H., History and future of models in fisheries science, Nat. resour. model., 16, 4, 1, (2003)
[31] Jonzen, N.; Ranta, E.; Lundberg, P.; Kaitala, V.; Linden, H., Harvesting induced fluctuations?, Wildlife biol., 9, 59, (2003)
[32] Jost, C.; Arino, O.; Arditi, R., About deterministic extinction in ratio-dependent predator – prey models, Bull. math. biol., 61, 19, (1999) · Zbl 1323.92173
[33] Kaiser, J., Salton sea: battle over a dying sea, Science, 284, 5411, 28, (1999)
[34] Kot, M., Elements of mathematical ecology, (2001), Cambridge University Cambridge
[35] Lafferty, K.D., Foraging on prey that are modified by parasites, Am. nat., 140, 854, (1992)
[36] Lafferty, K.D.; Morris, A.K., Altered behaviour of parasitized killfish increases susceptibility to predation by bird final hosts, Ecology, 77, 1390, (1996)
[37] Lafferty, K.D.; Kuris, A.M., How environmental stress affects the impacts of parasites?, Limnol. oceanogr., 44, 925, (1999)
[38] Martin, A.; Ruan, S., Predator – prey models with delay and prey harvesting, J. math. biol., 43, 3, 247, (2001) · Zbl 1008.34066
[39] McCallum, H.; Gerber, L.; Jani, A., Does infectious diseases influence the efficacy of marine protected areas? A theoretical framework, J. appl. ecol., 42, 688, (2005)
[40] Mesterton-Gibbons, M., On the optimal policy for combined harvesting of predator and prey, Nat. resour. model., 3, 63, (1988)
[41] Mesterton-Gibbons, M., A technique for finding optimal two-species harvesting policies, Nat. resour. model., 92, 235, (1996)
[42] Packer, C.; Holt, R.D.; Hudson, P.J.; Lafferty, K.D.; Dobson, A.P., Keeping the herds healthy and alert: implications of predator control for infectious disease, Ecol. lett., 6, 792, (2003)
[43] Potts, G.R.; Tapper, S.C.; Hudson, P.J., Population fluctuations in red grouse: analysis of bag records and a simulation model, J. anim. ecol., 53, 21, (1984)
[44] G. Slack, Salton Sea Sickness, Pacific Discovery, Winter, 1997.
[45] E. Venturino, Epidemics in predator – prey models: disease in the prey, in: O. Arino, D. Axelrod, M. Kimmel, M. Langlais (Eds.), Mathematical Population Dynamics: Analysis of Heterogeneity, vol. 1, Wuerz Publishing, Winnipeg, 1995, p. 381. · Zbl 1014.92036
[46] Venturino, E., Epidemics in predator – prey models: disease in the predators, IMA J. math. appl. med. biol., 19, 85, (2002) · Zbl 1014.92036
[47] Xiao, Y.; Chen, L., Modelling and analysis of a predator – prey model with disease in the prey, Math. biosci., 171, 59, (2001) · Zbl 0978.92031
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