Dynamics of HIV/AIDS and TB Co-infection with Treatment Rate as Holling Type-II Function

2020 ◽  
pp. 343-358
Author(s):  
Rajiv Aggarwal ◽  
Tanvi ◽  
Tamas Kovacs
Keyword(s):  
Type Ii ◽  
Treatment Rate ◽  
Hiv Aids

Dynamic Behavior of an SIR Epidemic Model along with Time Delay; Crowley–Martin Type Incidence Rate and Holling Type II Treatment Rate

2019 ◽  
Vol 20 (7-8) ◽  
pp. 757-771 ◽  
Author(s):  
Abhishek Kumar ◽  
Nilam
Keyword(s):  
Incidence Rate ◽  
Time Lag ◽  
Type Ii ◽  
Functional Type ◽  
Sir Epidemic Model ◽  
Treatment Rate ◽  
Nonlinear Incidence Rate ◽  
Sir Epidemic ◽  
The Stability ◽  
Disease Free

Abstract In this article, we propose and analyze a time-delayed susceptible–infected–recovered (SIR) mathematical model with nonlinear incidence rate and nonlinear treatment rate for the control of infectious diseases and epidemics. The incidence rate of infection is considered as Crowley–Martin functional type and the treatment rate is considered as Holling functional type II. The stability of the model is investigated for the disease-free equilibrium (DFE) and endemic equilibrium (EE) points. From the mathematical analysis of the model, we prove that the model is locally asymptotically stable for DFE when the basic reproduction number {R_0} is less than unity ({R_0} \lt 1) and unstable when {R_0} is greater than unity ({R_0} \gt 1) for time lag \tau \ge 0. The stability behavior of the model for DFE at {R_0} = 1 is investigated using Castillo-Chavez and Song theorem, which shows that the model exhibits forward bifurcation at {R_0} = 1. We investigate the stability of the EE for time lag \tau \ge 0. We also discussed the Hopf bifurcation of EE numerically. Global stability of the model equilibria is also discussed. Furthermore, the model has been simulated numerically to exemplify analytical studies.

Stability of a Time Delayed SIR Epidemic Model Along with Nonlinear Incidence Rate and Holling Type-II Treatment Rate

2018 ◽  
Vol 15 (06) ◽  
pp. 1850055 ◽  
Author(s):  
Abhishek Kumar ◽  
Nilam
Keyword(s):  
Incidence Rate ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Type Ii ◽  
Treatment Rate ◽  
Nonlinear Incidence Rate ◽  
Number Formula ◽  
The Stability ◽  
Disease Free ◽  
The Basic Reproduction Number

In this paper, we present a mathematical study of a deterministic model for the transmission and control of epidemics. The incidence rate of susceptible being infected is very crucial in the spread of disease. The delay in the incidence rate is proved fatal. In the present study, we propose an SIR mathematical model with the delay in the infected population. We are taking nonlinear incidence rate for epidemics along with Holling type II treatment rate for understanding the dynamics of the epidemics. Model stability has been done by the basic reproduction number [Formula: see text]. The model is locally asymptotically stable for disease-free equilibrium [Formula: see text] when the basic reproduction number [Formula: see text] is less than one ([Formula: see text]). We investigated the stability of the model for disease-free equilibrium at [Formula: see text] equals to one using center manifold theory. We also investigated the stability for endemic equilibrium [Formula: see text] at [Formula: see text]. Further, numerical simulations are presented to exemplify the analytical studies.

Type II Solar Radio Bursts over Solar Cycle 21

1994 ◽  
Vol 144 ◽  
pp. 283-284
Author(s):  
G. Maris ◽  
E. Tifrea
Keyword(s):  
Solar Radio ◽  
Interplanetary Space ◽  
Impulsive Phase ◽  
Radio Bursts ◽  
Type Ii ◽  
Solar Radio Bursts ◽  
Strong Energy ◽  
Mass Ejection ◽  
Geophysical Effect ◽  
Radio Event

The type II solar radio bursts produced by a shock wave passing through the solar corona are one of the most frequently studied solar activity phenomena. The scientific interest in this type of phenomenon is due to the fact that the presence of this radio event in a solar flare is an almost certain indicator of a future geophysical effect. The origin of the shock waves which produce these bursts is not at all simple; besides the shocks which are generated as a result of a strong energy release during the impulsive phase of a flare, there are also the shocks generated by a coronal mass ejection or the shocks which appear in the interplanetary space due to the supplementary acceleration of the solar particles.

Heat-Etching with a Bullivant Type II Simple Freeze-Cleave Device

1970 ◽  
Vol 28 ◽  
pp. 106-107 ◽  
Author(s):  
Ronald S. Weinstein ◽  
N. Scott McNutt
Keyword(s):  
New Zealand ◽  
General Hospital ◽  
Massachusetts General Hospital ◽  
Type I ◽  
Type Ii ◽  
Collaborative Effort ◽  
Temperature And Pressure ◽  
The University

The Type I simple cold block device was described by Bullivant and Ames in 1966 and represented the product of the first successful effort to simplify the equipment required to do sophisticated freeze-cleave techniques. Bullivant, Weinstein and Someda described the Type II device which is a modification of the Type I device and was developed as a collaborative effort at the Massachusetts General Hospital and the University of Auckland, New Zealand. The modifications reduced specimen contamination and provided controlled specimen warming for heat-etching of fracture faces. We have now tested the Mass. General Hospital version of the Type II device (called the “Type II-MGH device”) on a wide variety of biological specimens and have established temperature and pressure curves for routine heat-etching with the device.

Ultrastructure of pulmonary microvasculature in acute endotoxemia

1978 ◽  
Vol 36 (2) ◽  
pp. 470-471
Author(s):  
R. G. Gerrity ◽  
M. Richardson
Keyword(s):  
Polymorphonuclear Leukocytes ◽  
Alveolar Epithelium ◽  
Endothelial Damage ◽  
Capillary Endothelium ◽  
Type Ii Cells ◽  
Type Ii ◽  
Interstitial Edema ◽  
Pulmonary Capillaries ◽  
Lung Ultrastructure ◽  
Fibrin Thrombi

Dogs were injected intravenously with E_. coli endotoxin (2 mg/kg), and lung samples were taken at 15 min., 1 hr. and 24 hrs. At 15 min., occlusion of pulmonary capillaries by degranulating platelets and polymorphonuclear leukocytes (PML) was evident (Fig. 1). Capillary endothelium was intact but endothelial damage in small arteries and arterioles, accompanied by intraalveolar hemorrhage, was frequent (Fig. 2). Sloughing of the surfactant layer from alveolar epithelium was evident (Fig. 1). At 1 hr., platelet-PML plugs were no longer seen in capillaries, the endothelium of which was often vacuolated (Fig. 3). Interstitial edema and destruction of alveolar epithelium were seen, and type II cells had discharged their granules into the alveoli (Fig. 4). At 24 hr. phagocytic PML's were frequent in peripheral alveoli, while centrally, alveoli and vessels were packed with fibrin thrombi and PML's (Fig. 5). In similar dogs rendered thrombocytopenic with anti-platelet serum, lung ultrastructure was similar to that of controls, although PML's were more frequently seen in capillaries in the former (Fig. 6).

Mitochondria microcrystals deposition in some inherited diseases of lipid metabolism.

1978 ◽  
Vol 36 (2) ◽  
pp. 256-257
Author(s):  
S. Laoussadi ◽  
A. Kahan ◽  
G. Aubouy ◽  
F. Delbarre
Keyword(s):  
Synovial Tissue ◽  
Storage Disease ◽  
Metabolic Diseases ◽  
Uranyl Acetate ◽  
List Type ◽  
Type Ii ◽  
Type Number ◽  
Lipid Storage Disease ◽  
Thin Sections ◽  
Mean Size

Several patients with Fabry's, Gaucher's diseases and hyperlipoproteinemia type II and with arthropatic manifestations were observed.As no histological explanation for these symptoms was available,an ultrastructural study of synovial tissue was done to establish an anatomoclinical relation.Material and Methods :synovial membrane samples were obtained by needle biopsies of the knee from three patients with arthropatic manifestations of each disease.They were fixed in 5% glutaraldehyde, postfixed in 1% osmium tetraoxyde and embedded in Epon 812. Thin sections coloured by uranyl acetate and lead citrate were observed with an Elmiskop I Siemens electron microscope.Two important phenomena were observed in synovial tissue:Specific patterns of each lipid storage disease,which are now well known.In all the three metabolic diseases, hydroxyapatite-like crystals were found. They are characterized by their intramitochondrial localization, without any relation with cristae,an anarchic disposition and a mean size of 550 A.Crystals may be found also free in the cytoplasm of synoviocytes Some micrographs suggest an evolution in four steps :a. mitochondria with only a few microcrystalsb. mitochondria stuffed with these structuresc. disruption of mitochondria membranesd. microcrystals appear free in the cytoplasm

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