https://www.selleckchem.com/TGF-beta.html Finally, numerical simulations are performed to support our analytical findings. It was found out that the long-term memory has no effect on the stability of the equilibrium points. However, for increased values of the fractional derivative order parameter, each solution reaches its equilibrium state more rapidly. Furthermore, it was observed that an increase of the media awareness parameter, decreases the magnitude of infected individuals, and consequently, the height of the epidemic peak. We assessed left ventricular (LV) function and central hemodynamic effects in patients with a heart rate (HR) at rest of≥70 beats per minute (bpm) and chronic coronary syndrome (CCS) after long-term treatment with ivabradine compared to placebo by cardiac magnetic resonance (CMR) imaging. In a randomized, double-blinded, prospective cross-over design, 23 patients (18 male, 5 female) were treated with ivabradine (7.5mg bid) or placebo for 6months. CMR imaging was performed at baseline and after 6 and 12months to determine LV functional parameters.Mean resting HR on treatment with ivabradine was 58±8.2bpm and 70.2±8.3bpm during placebo (p<0.0001).There was no difference in systolic LV ejection fraction (ivabradine 57.4±11.2% vs placebo 53.0±10.9%, p=0.18), indexed end-diastolic (EDVi) or end-systolic volumes (ESVi). Indexed stroke volume (SVi) (ml/m ) remained unchanged after treatment with ivabradine. Volume time curve parameters reflecting systolic LV function (peak ejection rate and time) were unaffected by ivabradine, while both peak filling rate (PFR) and PFR/EDV were significantly increased. Mean aortic velocity (cm/s) was significantly reduced during treatment with ivabradine (ivabradine 6.7±2.7 vs placebo 9.0±3.4, p=0.01). Aortic flow parameters were correlated to parameters of vascular stiffness. The strongest correlation was revealed for mean aortic velocity with aortic distensibility (AD) (r=-0.86 [-0.90 to -0.85], p<0.0001). Lon