Susceptible-Infected-Treatment of Prey-Predator Population Model | Chapter 8 | Novel Research Aspects in Medicine and Medical Science Vol. 2

 This paper expresses a mathematical model accompanying Susceptible-Infected-Treatment under disease infection in martyr population. Moreover, we acquire that the prey species has a energetic illness, separating into classes of susceptible and infected cultures. One technique of control is self quarantining to separate active prey from diseased pillage, and another method is a situation that lowers the disease’s humanness rate. The system’s several equilibria are examined, and their balance analyses about the interior equilibrium are discussed. Routh-Hurwitz security criteria is secondhand for local stability analysis. Through mathematical analysis utilizing a simulated set of parameter principles, we have shown the examining results using Maple programmes.

Author(s) Details:

S. Saranya,
Annamalai University, Chidambaram, India.

S. Vijaya,
Annamalai University, Chidambaram, India.

E. Rekha,
Faculty of Science, Valalar Arts and Science College, Vadalur, Cuddalore, India.

Please see the link here: https://stm.bookpi.org/NRAMMS-V2/article/view/11804

Holling Type Response Function in Fishery Modelling with Optimal Harvesting Policy | Chapter 1 | Theory and Practices of Mathematics and Computer Science Vol. 6

We have considered in this paper a very general predator-prey system of the Holling type with selective harvesting and where both of the species follow logistic evolution. Along with the conditions of life, the uniform limits of the structure have been studied. In addition, the criteria for local stability of different equilibrium points were obtained and the global stability of the system was discussed, considering the appropriate Lyapunov function. After that, we studied the optimal harvesting strategy for the scheme using the Pontryagin Maximal Theory. Ultimately, some numerical examples have demonstrated the problem. Finally, with the aid of a numerical illustration, we discussed the problem by using arbitrary feasible parametric values and by using MATLAB, we observed from the stability diagram (Fig. 1) and phase portrait (Fig. 2) that the steady state value of the Prey population increases as the p values decrease. This is quite a positive outcome for the organisms' ecological survival. By integrating time delay and stochasticity into the framework, our model can be expanded.

Author (s) Details

Dipankar Sadhukhan
Department of Mathematics, Haldia Government College, Haldia-721657, W.B., India.

View Book :- https://stm.bookpi.org/TPMCS-V6/issue/view/6