Analysis and Dynamics of Illicit Drug Use Described by Fractional Derivative with Mittag-Leffler Kernel

Illicit drug use is a significant problem that causes great material and moral losses and threatens the future of the society.For this reason,illicit drug use and related crimes are the most significant criminal cases examined by scientists.This paper aims at modeling the illegal drug use using the Atangana-Baleanu fractional derivative with Mittag-Leffler kernel.Also,in this work,the existence and uniqueness of solutions of the fractional-order Illicit drug use model are discussed via Picard-Lindelöf theorem which provides successive approximations using a convergent sequence.Then the stability analysis for both disease-free and endemic equilibrium states is conducted.A numerical scheme based on the known Adams-Bashforth method is designed in fractional form to approximate the novel Atangana-Baleanu fractional operator of order 0<a≤1.Finally,numerical simulation results based on different values of fractional order,which also serve as control parameter,are presented to justify the theoretical findings.

Pulmonary hypertension in extremely low birth weight infants:characteristics and outcomes

Background:To determine the characteristics and outcomes of pulmonary arterial hypertension(PAH)in extremely low birth weight(ELBW)infants.Methods:A retrospective case-control study of all ELBW infants admitted to a level III neonatal intensive care unit(NICU)between January 1,2003 and December 31,2010.Results:During the study period,450 ELBW infants were admitted.6.4%(29/450)were diagnosed with PAH and were matched to 26 controls.The mean gestational age of infants with PAH and their controls were similar[24.5±1.3 vs.24.9±1.8 weeks(P=0.26)];however the cases were smaller at birth than were controls[640.7±119.5 vs.727.0±184.5 g(P=0.04)].The diagnosis of PAH was made at a mean postnatal age of 131.8±53.7 days.Infants with PAH had a higher rate of intrauterine exposure to illicit maternal drug use[12/29(41%)vs.1/25(4%);P=0.001],a longer duration of initial mechanical ventilation[74.9±28.3 vs.59.1±27.8 days;(P=0.04)],a higher incidence of severe BPD[23/29(79%)vs.13/26(50%);P=0.02],and a greater NICU mortality rate[12/29(41%)vs.4/26(15%);P=0.04].Conclusion:PAH in ELBW infants is associated with maternal illicit drug use in pregnancy,longer exposure to mechanical ventilation,severe bronchopulmonary dysplasia and a significant increase in early mortality.