Effect of viral infection on the generalized Gause model of predator-prey system. (English) Zbl 1041.92030
Summary: A generalized Gause model of predator-prey systems is revisited with an introduction of viral infection on the prey population. Stability behavior of such modified systems is carried out to observe the change of the dynamical behavior of the system. To substantiate the analytical results of this generalized susceptible prey, infected prey and predator population, numerical simulations of the model with specific growth and response functions are performed. Our observations suggest that the disease on prey population has a destabilizing or stabilizing effect depending on the level of force of infection and may act as a biological control for the persistence of the species.
MSC:
| 92D30 | Epidemiology |
| 92D40 | Ecology |
| 34D05 | Asymptotic properties of solutions to ordinary differential equations |
References:
| [1] | DOI: 10.1007/BF00168802 · Zbl 0825.92122 · doi:10.1007/BF00168802 |
| [2] | DOI: 10.1016/S0362-546X(98)00126-6 · Zbl 0922.34036 · doi:10.1016/S0362-546X(98)00126-6 |
| [3] | DOI: 10.1016/S0304-3800(01)00415-X · doi:10.1016/S0304-3800(01)00415-X |
| [4] | Chattopadhyay J., Korean J. Comp. Appl. Maths. 6 pp 601– |
| [5] | Freedman H. I., Deterministic Mathematical Models in Population Ecology (1980) · Zbl 0448.92023 |
| [6] | DOI: 10.5962/bhl.title.4489 · doi:10.5962/bhl.title.4489 |
| [7] | DOI: 10.2307/1087 · doi:10.2307/1087 |
| [8] | DOI: 10.1007/BF00276947 · Zbl 0716.92021 · doi:10.1007/BF00276947 |
| [9] | Kuang Y., J. Math. Biol. 28 pp 463– |
| [10] | DOI: 10.1016/S0065-2504(08)60288-3 · doi:10.1016/S0065-2504(08)60288-3 |
| [11] | E. Venturino, Mathematical Population Dynamics: Analysis of Heterogeneity, Vol. 1, Theory of Epidemics, eds. O. Arino (S. Wuerz, Winnipeg, 1995) pp. 381–393. |
| [12] | DOI: 10.1016/S0025-5564(01)00049-9 · Zbl 0978.92031 · doi:10.1016/S0025-5564(01)00049-9 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
