---

Discontinuity, Nonlinearity, and Complexity 10(4) (2021) 681--691 | DOI:10.5890/DNC.2021.12.008

C. Muzvondiwa, A.A. Adeniji , I. Fedotov, M.Y. Shatalov, A.C. Mkolesia

Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria, P/Bag X380, South Africa

Download Full Text PDF

 

Abstract

Substantial frameworks for a predator prey dynamical model have been developed in the past. A Method for estimating parameters of a constrained dynamical model with incomplete data assuming information about predator (known) and prey (unknown) was investigated. Unknown parameters for the dynamical model was estimated using undetermined Lagrangian multiplier method. The method for estimating the parameters are based on the construction of a quadratic goal function minimization from a set of ordinary differential equations. A non-homogeneous system was generated using ordinary least square method applied to the goal function in order to estimate the parameters. The derivation of the parameters process was one of the inverse problem and the model with estimated parameters gave some satisfactory fit.

References

1. [1]	Shatalov, M., Demidov, A., and Fedotov, I. (2015), Parameters estimation of equations of chemical kinetics and mathematical biology in the case of incomplete experimental data, { Pleiades Publishing}, {\bf 50}(2), 148-157.

2. [2]	Shatalov, M.Yu, Demidov, A.S., and Fedotov, I.A. (2014), Estimating the Parameters of Chemical Kinetics Equations from the Partial Information about Their Solution, Pleiades Publishing, {\bf 50}(2), 148-157.

3. [3]	Gomez, J.R. and Velez, S.M.C. (2010), Parameter estimation of a predator-prey model using a genetic algorithm, { Ingenier\{\i}a Matem\{a}tica, Universidad EAFIT}, Medell\{\i}n, Colombia. %

4. [4]

5. [5]	Qureshi, S. and Yusuf, A. (2019), Modeling chickenpox disease with fractional derivatives: From caputo to atangana-baleanu, { Chaos, Solitons $\&$ Fractals}, Elsevier, {\bf 122}, 111-118.

6. [6]	Qureshi, S., Yusuf, A., Shaikh, A.A., Inc, M., and Baleanu, D. (2019), Fractional modeling of blood ethanol concentration system with real data application, { Chaos: An Interdisciplinary Journal of Nonlinear Science}, AIP Publishing LLC, {\bf 29}(1), 013143.

7. [7]	Adeniji, A.A., Fedotov, I., Shatalov, M.Y., and Mkolesia, A.C.P.G. (2018), Numerical investigation of diffusive predator-prey model with application to annular habitat, { Far East Journal of Mathematical Sciences (FJMS)}, Pushpa Publishing House, {\bf 109}(2), 343-335 . %\{\i}n,

8. [8]	Lotka, A.J. (1925), { Principles of physical biology} Baltimore, Waverly.

9. [9]	Volterra, V. (1927), Variazioni e fluttuazioni del numero dindividui in specie animali conviventi, C. Ferrari.

10. [10]	Pistorious, C. (1996), { A Lotka-Volterra model for multiscale technological interaction, Modelling competition symbiosis and predator prey model.} Oxford, United Kingdom. %

11. [11]

12. [12]	Dimentberg, M.F. (2002), Lotka-Volterra System in a Random Environment, { Physical Review E}, {\bf 65}(3). %

13. [13]

14. [14]	Mathye, P., Fedotov, I., and Shatalov, M. (2016), Identification of HIV Dynamic System in the case of Incomplete Experimental Data, { CSIR, Pretoria}, South Africa. %

15. [15]

16. [16]	Adeniji, A.A., Fedotov, I., and Shatalov, M.Y. (2018), Inverse problem of the Holling-Tanner model and its solution, { BIOMATH}, Pleiades Publishing, {\bf 7}(2), 1812057. %

17. [17]

18. [18]

    Adeniji, A.A., Shatalov, M.Y., Fedotov, I., and Mkolesia, A.C. (2020), Inverse problems of the Holling-Tanner model identification with incomplete information, { Discontinuity, Nonlinearity, and Complexity}, lhscientificpublishing. Discontinuity, Nonlinearity, and Complexity, acceptd for publication, 2020.