Deterministic-stochastic analysis of fractional differential equations malnutrition model with random perturbations and crossover effects

Abstract

To boost the handful of nutrient-dense individuals in the societal structure, adequate health care documentation and comprehension are permitted. This will strengthen and optimize the well-being of the community, particularly the girls and women of the community that are welcoming the new generation. In this article, we extensively explored a deterministic-stochastic malnutrition model involving nonlinear perturbation via piecewise fractional operators techniques. This novel concept leads us to analyze and predict the process from the beginning to the end of the well-being growth, as it offers the possibility to observe many behaviors from cross over to stochastic processes. Moreover, the piecewise differential operators, which can be constructed with operators such as classical, Caputo, Caputo-Fabrizio, Atangana-Baleanu and stochastic derivative. The threshold parameter is developed and the role of malnutrition in society is examined. Through a rigorous analysis, we first demonstrated that the stochastic model’s solution is positive and global. Then, using appropriate stochastic Lyapunov candidates, we examined whether the stochastic system acknowledges a unique ergodic stationary distribution. The objective of this investigation is to design a nutritional deficiency in pregnant women using a piecewise fractional differential equation scheme. We examined multiple options and outlined numerical methods of coping with problems. To exemplify the effectiveness of the suggested concept, graphical conclusions, including chaotic and random perturbation patterns, are supplied. Consequently, fractional calculus’ innovative aspects provide more powerful and flexible layouts, enabling us to more effectively adapt to the system dynamics tendencies of real-world representations. This has opened new doors to readers in different disciplines and enabled them to capture different behaviors at different time intervals.

Dynamic analysis and optimal control of stochastic information cross-dissemination and variation model with random parametric perturbations

“…The white noise, as well as the Lévy jump perturbations, were incorporated in all compartments of the proposed model. Adak et al(2020) [ 29 ] considered a stochastic extension of the deterministic model to capture the uncertainty or variation observed in the disease transmissibility.Chu et al(2023) [ 30 ] constructed an S f M b M g U malnutrition model with random perturbations and crossover effects, and using fractional differential equations analysis deterministic-stochastic model. Rashid et al(2023) [ 31 ] constructed an SI p I q I qp R p R q R qp B of the co-infection of the fractional pneumonia and typhoid fever disease stochastic model with cost-effective techniques and crossover effects.…”