Time scale theory on stability of explicit and implicit discrete epidemic models: applications to Swine flu outbreak.

Time scales theory has been in use since the 1980s with many applications. Only very recently, it has been used to describe within-host and between-hosts dynamics of infectious diseases. In this study, we present explicit and implicit discrete epidemic models motivated by the time scales modeling approach. We use these models to formulate the basic reproduction number, which determines whether an outbreak occurs or the disease dies out. We discuss the stability of the disease-free and endemic equilibrium points using the linearization method and Lyapunov function. Furthermore, we apply our models to swine flu outbreak data to demonstrate that the discrete models can accurately describe the epidemic dynamics. Our comparison analysis shows that the implicit discrete model can best describe the data regardless of the data frequency. In addition, we perform the sensitivity analysis on the key parameters of the models to study how these parameters impact the basic reproduction number.

Continuous and discrete modeling of HIV-1 decline on therapy.

Mathematical models have shed light on the dynamics of HIV- 1 infection in vivo. In this paper, we generalize continuous mathematical models of drug therapy for HIV-1 by Perelson et al. (Science 271:1582-1586, 1996) and Perelson and Nelson (SIAM Rev 41:3-44, 1999) on time scales, i.e., a nonempty closed subset of real numbers in order to derive new discrete models that predict the total concentration of plasma virus as a function of time. One of our main goals is to compare discrete mathematical models with the continuous model in Perelson et al. (1996) where HIV infected patients were given protease inhibitors and sampled frequently thereafter. For the comparison, we use experimental data collected in Perelson et al. (1996) and estimate the parameters such as the virion clearance rate and the rate of loss of infected cells by fitting the total concentration of plasma virus to this data set. Our results show that discrete systems describe the best fit. In the previous models of this study, the efficacy of protease inhibitor is assumed to be perfect. Motivated by Perelson and Nelson (1999), we end the paper with a mathematical model of imperfect protease inhibitor and reverse transcriptase (RT) inhibitor combination therapy of HIV-1 infection on time scales with its stability analysis.

Parameter identification for gompertz and logistic dynamic equations.

In this paper, we generalize and compare Gompertz and Logistic dynamic equations in order to describe the growth patterns of bacteria and tumor. First of all, we introduce two types of Gompertz equations, where the first type 4-paramater and 3-parameter Gompertz curves do not include the logarithm of the number of individuals, and then we derive 4-parameter and 3-parameter Logistic equations. We notice that Logistic curves are better in modeling bacteria whereas the growth pattern of tumor is described better by Gompertz curves. Increasing the number of parameters of Logistic curves give favorable results for bacteria while decreasing the number of parameters of Gompertz curves for tumor improves the curve fitting. Moreover, our results overshadow some of the existing results in the literature.

Proprotein Convertase Subtilisin/Kexin type 9 (PCSK9): Impact of PCSK9 on Major Adverse Cardiac and Cerebrovascular Events.

Statins are the most widely prescribed drugs to reduce serum low density lipoprotein cholesterol (LDL-C) by inhibiting 3-hydroxy-3-methyl-glutaryl-coenzyme A (HMG-CoA) reductase. LDL-C reduction is associated with a decreased risk of atherosclerotic cardiovascular disease (ASCVD), including cardiovascular disease (CVD) and stroke. Statins reduce LDL-C by 30 to 40%, and the combination with other lipid-lowering agents such as ezetimibe leads to a further reduction by 20 to 25%. However, even the combination of these two agents might not be sufficient in high risk patients to require aggressive LDL-C reduction. Therefore, starting from observations on individuals with loss-of-function in proprotein convertase subtilisin/kexin type 9 (PCSK9), which was associated with lower LDL-C levels and CVD rates, monoclonal antibodies (mAbs) against PCSK9 were developed. To date, two mAbs, alirocumab and evolocumab, have received approval by the US Food and Drug Administration (FDA) and the European Medicines Agency (EMA). In the present review we give an overview about pathophysiological and clinical aspects as well as evidence for these drugs with respect to cerebrovascular events.

[62-year old male patient with position-depending dyspnoe after hemipneumectomia]. / 62-jähriger Patient mit lageabhängiger Dyspnoe nach einseitiger Pneumektomie.

BACKGROUND: Dyspnoe is a symptom with a huge differential diagnostic spectrum. According to patients hemodynamic, acute forms can be caused by myocardial infarction, pulmonary embolism, pulmonary edema and heart rhythm disturbances while chronic forms can be caused by restrictive myocardial and pericardial diseases, hematooncological diseases, orthopedic deformations and chronic pulmonary diseases. The platypnea-orthodeoxia syndrome with underlying interatrial connection is a rare cause and need a special diagnostic work-up. CASE REPORT: A 62-year old male patient with previously known pneumectomy on right side due to underlying cancer presented with a 6-months history of increasing dyspnoe (NYHA III) on exertion and upright position. The physical examination just revealed a lack of ventilation on right side. The saturation drops from 97% in supine position to 68% in upright position. Transesophageal echocardiography revealed a compressed right atrium with a persisted foramen ovale (PFO) and atrial septal aneurysm resulting in a right-left shunt. After completing diagnostic work-up and excluding other possible causes for dyspnoe an interventional closure of interatrial connection was performed. Subsequently the symptoms of the patients resolved (NYHA I). CONCLUSION: The Platypnea-Orthodeoxia-Syndrome isa rare cause of dyspoe. The diagnosis can be made by echocardiography. Medical treatment of such disease is of less success, thus a closure of interatrial connection is recommended.

Use of a novel needle wire in patients undergoing transseptal puncture associated with severe septal tenting.

INTRODUCTION: An increasing number of patients undergo left atrial ablation procedures, since several approaches have proven efficacy in the treatment of atrial fibrillation. Although transseptal catheterization was generally shown be a safe technique, it harbors the principal risk of cardiac injury. Therefore, there is a need for a safe and effective tool to enable transseptal puncture in difficult cases as well. METHODS AND RESULTS: In 158 consecutive patients, a transseptal puncture was intended for mapping and ablation of left atrial tachycardias. In seven patients of this series transseptal puncture using different sheaths and needle designs, the operators failed to cross the interatrial septum as a result of severe tenting. Three patients were known to have a septal aneurysm; a redo procedure was performed in two patients. In the remaining patients, there was no obvious explanation for the difficulty in crossing the interatrial septum conventionally. In all seven patients, a 120-cm-long nitinol guidewire ("needle wire") with a 0.014-inch diameter was used to cross the atrial septum with the following idea: after tenting the fossa ovalis with the transseptal dilator and the Brockenbrough needle positioned just inside the tip, effortless advancement of the needle wire perforates the membranous fossa. Unsupported by the needle and dilator, the tip of the wire immediately assumes a "J" shape, rendering it incapable of further tissue penetration after its entry into the left atrium. In all seven patients, the needle wire could be placed into a left pulmonary vein. In five patients, a single attempt was sufficient to reach the left atrium with the wire, two patients needed two and three attempts, respectively. No complications occurred. CONCLUSIONS: Additional use of a needle wire to perform transseptal puncture in a subset of patients at higher risk for complications appears safe and effective.

Pulmonary vein isolation by duty-cycled bipolar and unipolar antrum ablation using a novel multielectrode ablation catheter system: first clinical results.

BACKGROUND: The electrical disconnection of the pulmonary veins (PV) plays an important role in the ablation strategy of paroxysmal atrial fibrillation (PAF). Circumferential antral ablation with a conventional ablation technique using a steerable ablation catheter is sometimes difficult to perform and does not always result in isolation of the targeted PV. METHODS: Patients with symptomatic PAF were treated with a novel circular mapping/ablation catheter (PVAC). Ablation was performed in the antral region of the PV with a power-modulated bipolar/unipolar RF generator using 8-10 W until isolation of the vein was achieved. Seven-day Holter monitor recordings were performed off antiarrhythmic drugs at 3 and 6 months after the initial procedure. A subgroup of patients had received an implantable recorder before ablation, and the device was interrogated at the same time. The primary objective of this study is acute isolation of the targeted PV, and the second objective is clinical efficacy with a short-term follow-up. RESULTS: In 73 patients, 290 PV could be reached with the PVAC. Antral ablation was performed in 244 PV showing PV potentials. Acutely, 243 PV (99%) were isolated with the PVAC after 21+/-7 energy applications per patient with a mean fluoroscopy time of 20+/-11 min. Total procedure time was 122+/-27 min. No complications were observed. Follow-up at 3 and 6 months showed freedom from AF in 61 of 73 (84%) patients and 38 of 45 patients (85%), respectively, off antiarrhythmic drugs. CONCLUSIONS: PV isolation by duty-cycled unipolar/bipolar RF ablation can be effectively and safely performed with a circular, decapolar catheter. Clinical results at 3 and 6 months after ablation are encouraging with the need for longer follow-up intervals.

Results of short-term and long-term pulmonary vein isolation for paroxysmal atrial fibrillation using duty-cycled bipolar and unipolar radiofrequency energy.

BACKGROUND: Electrical disconnection of the pulmonary veins (PV) plays an important role in the ablation of paroxysmal atrial fibrillation (AF). Antral ablation using a conventional steerable ablation catheter often is technically challenging and time consuming. METHODS: Eighty-eight patients (mean age 58 +/- 11 years) with symptomatic paroxysmal AF underwent ablation with a circular mapping/ablation decapolar catheter (PVAC). Ablation was performed in the antral region of the PVs with a power-modulated bipolar/unipolar radiofrequency (RF) generator using 8-10 W delivered simultaneously through 2-10 electrodes, as selected by the operator. Seven-day Holter monitor recordings were performed off antiarrhythmic drugs at 3-, 6-, and 12-month follow-up, and patients were requested to visit the hospital in the event of ongoing palpitations. All follow-up patients were divided into 2 groups: Group 1 with a follow-up of less than 1 year and group 2 patients completing a 1-year follow-up. RESULTS: Overall, 338 of 339 targeted PVs (99%) were isolated with the PVAC with a mean of 24 +/- 9 RF applications per patient, a mean total procedure time of 125 +/- 28 minutes, and a mean fluoroscopy time of 21 +/- 13 minutes. Freedom from AF off antiarrhythmic drugs was found in 82 and 79% of group 1 and group 2 patients, respectively. No procedure-related complications were observed. CONCLUSION: PV isolation by duty-cycled unipolar/bipolar RF ablation can be effectively and safely performed with a circular, decapolar catheter. Twelve-month follow-up data compare favorably with early postablation results, indicating stable effects over time.

Renovascular hypertension by two-kidney one-clip enhances endothelial progenitor cell mobilization in a p47phox-dependent manner.

BACKGROUND: Enhanced mechanical forces, e.g. in arterial hypertension, stimulate the formation of reactive oxygen species (ROS) by the NAD(P)H oxidase. Since bone marrow derived endothelial progenitor cells (EPCs) contribute to vascular remodeling and repair, we investigated whether renovascular hypertension stimulates EPC mobilization in a NAD(P)H oxidase-dependent manner. METHODS: Renovascular hypertension was induced by two-kidney one-clip (2K1C) in C57BL/6 (WT) and in mice lacking the p47phox subunit of the NAD(P)H oxidase (p47phox-/-). RESULTS: In WT, 2K1C increased blood pressure levels by 32.4 +/- 4 mmHg, which was associated with a four-fold increase in circulating EPCs (Sca-1+;Flk-1+). In p47phox-/- mice, the increase in blood pressure was significantly reduced (15.1 +/- 1.8 mmHg, P < 0.05) and not associated with increased EPCs. Inhibitors of the renin-angiotensin system (RAS) and nonspecific vasodilators normalized blood pressure and inhibited EPC mobilization in WT mice after 2K1C. In addition, p47phox deficiency and pharmacological ROS blockage abrogated 2K1C-induced blood pressure elevation and EPC mobilization. Stromal cell derived factor (SDF)-1 and matrix metalloproteinase (MMP)-9 activity in the bone marrow, required for EPC mobilization, were modulated in WT mice after 2K1C. In contrast, no alterations in SDF-1 and MMP-9 were observed in p47phox-/- mice. Moreover, enhanced migration of Lin- bone marrow mononuclear cells was observed when stimulated with plasma from 2K1C WT mice but not when stimulated with plasma from 2K1C p47phox-/- mice. CONCLUSION: Enhanced mechanical stretch in renovascular hypertension induces EPC mobilization in a p47phox-dependent manner, involving bone marrow SDF-1 and MMP-9 which may contribute to compensatory vascular adaptation in renovascular hypertension.

Mechanical stretch enhances mRNA expression and proenzyme release of matrix metalloproteinase-2 (MMP-2) via NAD(P)H oxidase-derived reactive oxygen species.

Mechanical stretch is a hallmark of arterial hypertension and leads to vessel wall remodeling, which involves matrix metalloproteinases (MMPs). Because mechanical stretch is further capable of inducing reactive oxygen species (ROS) formation via the NAD(P)H oxidase, we assessed whether mechanical stretch enhances MMP expression and activity in a NAD(P)H oxidase-dependent manner. Therefore, vascular smooth muscle cells (VSMCs) isolated from C57BL/6 mice were exposed to cyclic mechanical stretch. The impact of ROS was assessed using VSMCs isolated from p47phox-/- mice, deficient for a NAD(P)H oxidase subunit responsible for ROS formation. Transcript levels were investigated by cDNA array and confirmed by RT-PCR. ROS formation was determined by DCF fluoroscopy and MMP-2 activity by zymography. Mechanical stretch of wild-type VSMCs resulted in a rapid ROS formation and p47phox membrane translocation that is followed by an increase in Nox-1 transcripts. ROS formation was completely abrogated in p47phox-/- VSMCs. cDNA array further revealed an increase of MMP-2 mRNA in response to mechanical stretch, which was validated by RT-PCR. Using p47phox-/- VSMCs, this increase in MMP-2 mRNA was completely blunted. mRNA expression of tissue inhibitor of MMP-2 TIMP-1 and TIMP-2 and membrane-type 1 MMP was unaffected by mechanical stretch. Gelatinolytic activity of pro-MMP-2 has been increased rapidly in wild-type VSMCs and was completely abolished in p47phox-/- VSMCs. These results indicate that mechanical stretch induces ROS formation via the NAD(P)H oxidase and thereby enhances MMP-2 mRNA expression and pro-MMP-2 release. These results are consistent with the notion that in arterial hypertension, reactive oxygen species are involved in vascular remodeling via MMP activation. The full text of this article is available online at http://www.circresaha.org.