Simultaneous effect of disease and toxicant on a plant population: a model
DOI:
https://doi.org/10.14419/gjma.v2i2.2561Abstract
In this paper, we have studied the effect of disease separately on the plant population and the simultaneous effect of diseaseand toxicant on plant population. The disease is caused to the plants by vector population and toxicants are effecting the total plant density directly through air. The local and global stability conditions for both the models have been derived and numerical simulation is done using MATLAB software.
Keywords: Plant population, Vector population, Disease, Toxicant, Stability.
References
Hallam, T.G., Clark, C.E., Lassiter, R.R : Effects of toxicant on populations: a qualitative approach I. Equillibrium environmental expose. Ecol. Modelling 18, 291-304 (1983).
Hallam, T.G., Clark, C.E., Jordan, G.S : Effects of toxicant on populations: a qualitative approach II. First order Kinetics. J. MAth. Biol. 18, 25-37 (1983).
Hallam, T.G., De Luna, J.T : Effects of toxicant on populations: a qualitative approach III. Environmental and food chain pathways. J. Theor. Biol. 109, 411-429 (1984).
Hallam, T.G., MA Zhien : Persistence in population models with demographic °uctuations. J. math. Biol. 24, 327-339(1986).
De Luna, J.T., Hallam T.G : Effects of toxicant on populations: a qualitative approach III. resource-consumer-Toxicant models. Ecol. Modelling 35, 249-273 (1987).
Debasis Mukherjee, Persistence and global stability of a population in a polluted environment with delay, journal of biological Systems. 10, 225-232 (2002).
Zhien Ma, G.Cui, W.Wang, Persistence and extinction of a population in a polluted environment, math. Biosci. 101, 75 (1990).
Camphell C.L, Madden LV, Introduction to plant Disease Epidemiology, New York, USA: Wiley, (1990).
Hughes G, Madden LV, Aggregation and incidence of disease. Plant Pathology 41, 657-60, (1992).
Hughes G, Madden LV, Using the beta-binomial distribution to describe aggregated patterns of disease incidence. Phytopathology, 83, 759-63 (1993).
Hughes G, Madden LV, Comment- Using spatial and temporal patterns of Armillaria root disease to formulate management recommendations for Ontario's black spruce (Picea mariana) seed orchard. Canasian Journal of Forest Research 28, 153-8 (1998).
Madden LV, Hughes G, Plant disease incidence : distributions, heterogeneity, and temporal analysis. Annual Review of Phytopathology 33, 529-64 (1995).
Madden LV, Nault LR, Murral DJ, Apelt MR, Spatial Pattern Analysis of the incidence of aster yellows disease in lettuce. Researches on population Ecology 37, 279-89 (1995).
Madden LV, Pirone TP, Raccah B, Analysis of spatial patterns of virus-induced tobacco plants. Phytopathology 77,1409-17 (1987).
H.R. Thieme, 1992, Convergence results and a Poincare-Bendixon trichotomy for asymptotically autonomous differential equations. J. Math. Biol., 30, pp. 755-763.
L. Han, Z. Ma, H.W. Hethcote, 2001, Four predator-prey models with infectious diseases. Math. Comp. Modelling, 34, pp. 849-858.
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