Modeling and Simulation Study of the Population Dynamics of Commensal-Host-Parasite System
American Journal of Applied Mathematics
Volume 6, Issue 3, June 2018, Pages: 97-108
Received: Apr. 30, 2018; Accepted: Jun. 1, 2018; Published: Jul. 5, 2018
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Geremew Kenassa Edessa, Department of Mathematics, Wollega University, Nekemte, Ethiopia
Boka Kumsa, Department of Mathematics, Wollega University, Nekemte, Ethiopia
Purnachandra Rao Koya, Department of Mathematics, Hawassa University, Hawassa, Ethiopia
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This paper deals with the modeling and simulation study of Commensal-host species system together with the inclusion of parasite population. The model comprises of three populations viz. Host, Commensal and Parasite. The Commensal population gets benefit from Host population but the former do not do any harm to the latter. The parasite population gets benefit and also do harm to Host population. However, the Commensal population only harms the parasites. The mathematical model is comprised of a system of three first order non-linear ordinary differential equations. Mathematical analysis of the model is conducted. Positivity and boundedness of the solution have been verified and thus shown that the model is physically meaningful and biologically acceptable. Scaled model is constructed so as to reduce the number of model parameters. Equilibrium points of the model are identified and stability analysis is conducted. Simulation study is conducted in order to support the mathematical analysis. In the present model the Commensal population lies higher and the parasite population lies below respectively the host population. This fact is well supported by the mathematical analysis as well as simulation study. The results of analysis and simulation are presented and discussed lucidly in the text of the paper.
Commensalism, Parasite, Stability, Eco-epidemiology, Numerical Simulation
To cite this article
Geremew Kenassa Edessa, Boka Kumsa, Purnachandra Rao Koya, Modeling and Simulation Study of the Population Dynamics of Commensal-Host-Parasite System, American Journal of Applied Mathematics. Vol. 6, No. 3, 2018, pp. 97-108. doi: 10.11648/j.ajam.20180603.11
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May R. M. and Anderson R. M. (1978). Regulation and stability of host-parasite population interactions: II, Destabilizing processes, Journal of Animal Ecology, 47, 249-67.
AlyssaLois M. (2016). Non-native parasite enhances susceptibility of host to native predators, Springer-Verlag, Berlin, Heidelberg.
R. Bhattacharyya, and B. Mukhopadhyay, on an eco-epidemiological model with prey harvesting and predator switching: local and global perspectives, Nonlinear Anal.: RWA 11 (2010) 3824.
Hassell M. P. and May R. M. Stability in insect host-parasite models. J. Animal. Ecol.42, 693–726 (1973).
Hatcher M. J., Dick J. T. A., Dunn A. M. (2012). Disease emergence and invasions. Funct Ecol 26:1275–1287.
E. Venturino. The influence of diseases on Lotka–Volterra systems, Rocky Mt. J. Math. 24(1994) 381–402.
P. J. Hudson, and A. P. Dobson, D. Newborn, Do parasites make Prey more vulnerable to predation?Red-grouse and parasites, J. Anim. Ecol. 61 (1992) 681–692.
M. Haque, and E. Venturino, Modelling disease spreading in symbiotic communities, Wildlife: Destruction, Conservation and Biodiversity, Nova Science Publishers, USA, 2009.
Sule H., Muhamad, R., and Omar D. Parasitism rate, host stage preference and functional response of Tamarixiaradiata on Diaphorinacitri. Int. J. Agric. Biol. 16 (2014) 783–788.
J. H. P. Dawes and M. O. Souza (2013). A derivation of Hollings type I, II and III functional responses in predator-prey systems, 327, 11-22.
Poulin R (2007). Evolutionary Ecology of Parasites, 2ed, Princeton University Press, Princeton.
Fanghong Zhang and Cuncheng Jin. Analysis of an eco-epidemiological model with Disease in the prey and predator. (2017) 73-79.
Sen P., Das k. Simultaneous Effects of Prey Defence and Predator Infection on a Predator Prey System. Ann. Bio. Sci., 2017, 5 (1):37-46
Kwiatkowski M., Engelstadter J. and Vorburger C. On genetic specificity in symbiont-mediated host-parasite co evolution. PLoS Comp. Biol. 8(2012).
Auld S. K. J. R., Hall S. R. & Duffy M. A. Epidemiology of a Daphnia-multi parasite system and its implications for the Red Queen. (2012).
N. Bame, S. Bowong, J. Mbang, G. Sallet, J. J. Tewa, Global stability analysis for SEIS models with n latent classes, Math. Biosci. Eng. 5 (N1) (2008) 20–33.
Jean Jules Tewa. Mathematical analysis of two-patch model of tuberculosis disease with staged progression, Appl. Math. Model. 36 (2012) 5792–5807.
Chakra M. A., Hil be, C. and Treutlen A. Plastic behaviors in hosts promote the emergence of retaliatory parasites, Sci. Rep. 4, 4251 (2014).
Eswarappa S. M., Estrela S. & Brown S. P. Within-host dynamics of multi-species infections: Facilitation, competition and virulence. (2012).
Tompkins D. M., White A. R. & Boots M. Ecological replacement of native red squirrels by invasive greys driven by disease. Ecol. Lett. 6, 189–196 (2003).
Geremew K, N. Phani Kumar, Boka K. Dynamics of Commensalism Interaction with Linear and Holling Type II Functional Responses by the Host to the Commensal Species, (2017) 23-34.
C. S. Gokhale (2013). Lotka-Volterra dynamics kills the Red Queen: population size fluctuations and associated stochasticity dramatically change host parasite co evolution. BMC Evolutionary Biology, 13: 254.
E. Decaestecker. (2013). Damped long-term host-parasite Red Queen co- evolutionary dynamics: a reflection of dilution effects? Ecology Letters, 16: 1455-1462.
J. Moore. Parasites and the Behavior of Animals, Oxford University Press, 2002.
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