A Dynamical Analysis of a Mathematical Model on Type-2 Diabetic From Obestiy

The aim of this research is to construct a model for type-2 diabeticfrom obesity using parameters based on the female population in India.We have introduced two control variables as diet with physicalactivity and medication. The positive endemic equilibrium is obtained.The local and global stability of the model are analyzed withsome specific conditions. Numerical simulations are carried out to exhibitthe flow of variables with controls. Our study mainly highlightsthe awareness of metabolic risk by healthy diet, physical activitiesand medications

An Optimal Harvesting Strategy of a Three Species Syn-ecosystem with Commensalism and Stochasticity

In this paper we have studied the stability of three typical species syn-ecosystem. The system comprises of one commensal S1 and two hosts S2 and S3 . Both S2 and S2 benefit S1 without getting themselves affected either positively or adversely. Further S2 is a commensal of S3 and S3 is a host of both S1 and S2. Limited resources have been considered for all the three species in this case. The model equations of the system constitute a set of three first order non-linear ordinary differential equations. The possible equilibrium points of the model are identified. We have also studied the local and global stabilities. We have analyzed the bionomic equilibrium and optimal harvesting strategy using Pontryagin’s maximum principle. We have investigated the inhabitant intensities of the fluctuations (variances) around the positive equilibrium due to noise and have investigated the stability. We have also checked the MATLAB numerical simulations for stability of the system

Optimal harvesting strategy and stochastic analysis for a two species commensaling system

AbstractIn this paper, we have considered a mathematical model of commensalism between two species (S1 and S2) with a limited resource of food, in addition the paper also highlights how the commensal and host species are harvested. The model is characterized by a couple of first order non-linear differential equations. Here, the stable equilibrium point is identified and its stability (both local and global) criteria are discussed (both analytical and numerical). An optimal harvesting strategy is being conversed using Pontriyagin’s maximum principle. We have explored the stochastic stability by finding the corresponding variances. Finally numerical simulations illustrate the effectiveness of our results

An Optimal Harvesting Strategy of a Three Species Syn-ecosystem with Commensalism and Stochasticity

Abstract In this paper we have studied the stability of three typical species syn-ecosystem. The system comprises of one commensal 1 S and two hosts 2 S and 3 S . Both 2 S and 3 S benefit 1 S without getting themselves affected either positively or adversely. Further 2 S is a commensal of 3 S and 3 S is a host of both 1 S and 2 S . Limited resources have been considered for all the three species in this case. The model equations of the system constitute a set of three first order non-linear ordinary differential equations. The possible equilibrium points of the model are identified. We have also studied the local and global stabilities. We have analyzed the bionomic equilibrium and optimal harvesting strategy using Pontryagin's maximum principle. We have investigated the inhabitant intensities of the fluctuations (variances) around the positive equilibrium due to noise and have investigated the stability. We have also checked the MATLAB numerical simulations for stability of the system