Optimal Control Strategy for a Discrete Time to the Dynamics of a Population of Diabetics with Highlighting the Impact of Living Environment

Abstract

Nowadays, Diabetes is one of the most common diseases, which has a huge and growing socio-economic burden affecting individuals, families, and the whole society. In this paper, we propose an optimal control approach modeling the evolution from pre-diabetes to diabetes with and without complications and the effect of living environment. We show the existence of an optimal control and then use a numerical implicit finite-difference method to monitor the size of population in each compartment.

A multi-age mathematical modeling of the dynamics of population diabetics with effect of lifestyle using optimal control

“…So, we defined the Hamiltonian H as follows: At this case it is considered that N is constant. For , the adjoint equations and transversality conditions can be obtained by using Pontryagin’s maximum principle [ 5 , 10 , 11 , 13 , 23 ] such that With the transversality conditions [ 48 ] at time T :…”

“…We use the Pontryagins maximum principle [ 13 ], for characterized the optimal controls. So, we defined the Hamiltonian H as follows: For , the adjoint equations and transversality conditions can be obtained by using Pontryagin’s maximum principle [ 5 , 10 , 11 , 13 , 50 ] such that For, the optimal controls u , v and w can be solved from the optimality condition we have By the bounds in U of the controls, it is easy to obtain and are given by ( 16 )–( 18 ) in the form of system. …”

“…Different simulations can be performed using different parameter values in Table 1 taken from [ 5 ]:…”

Optimal control approach of a mathematical modeling with multiple delays of the negative impact of delays in applying preventive precautions against the spread of the COVID-19 pandemic with a case study of Brazil and cost-effectiveness

“…The source of this virus was bats. Another virus of this strain is the Middle East Syndrome virus (MERS) [4] , [5] , [6] , [7] , which infected about 2498 people and resulted in the death of 858 people. The source of this virus was camels.…”

A Spatiotemporal Prey-Predator Discrete Model and Optimal Controls for Environmental Sustainability in the Multifishing Areas of Morocco

“…e numerical simulations of our strategies of control show that the control effect is effective if the strategies are used simultaneously. Other models from population dynamics and optimal control problems can be found in [55][56][57][58][59][60][61][62][63][64][65][66][67]. Basic notions and results concerning optimal control problems can be found in the books [68,69].…”