Mathematical Modeling, Analysis, and Optimal Control of Abstinence Behavior of Registration on the Electoral Lists

Abstract

We propose a mathematical model that describes the dynamics of citizens who have the right to register on the electoral lists and participate in the political process and the negative influence of abstainers, who abstain from registration on the electoral lists, on the potential electors. By using Routh–Hurwitz criteria and constructing Lyapunov functions, the local stability and the global stability of abstaining-free equilibrium and abstaining equilibrium are obtained. We also study the sensitivity analysis of the model parameters to know the parameters that have a high impact on the reproduction number ℜ0. In addition, we propose an optimal strategy for an awareness program that helps politicians and officials to increase the rate of citizens registered on the electoral lists with an optimal effort. Pontryagin’s maximum principle is used to characterize the optimal controls, and the optimality system is solved by an iterative method. Finally, some numerical simulations are performed to verify the theoretical analysis using Matlab.

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

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“…At this case it is considered that N is constant. For t ∈ [0, T ], the adjoint equations and transversality conditions can be obtained by using Pontryagin's maximum principle [5,10,11,13,23] such that…”

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

“…For the adjoint equations and transversality conditions can be obtained by using Pontryagin’s maximum principle [5] , [10] , [23] such that …”