scholarly journals The impact of nonlinear perturbation to the dynamics of HIV model

2021 ◽  
Author(s):  
Zhenfeng Shi ◽  
Daqing Jiang ◽  
Ningzhong Shi ◽  
Tasawar Hayat ◽  
Ahmed Alsaedi
Keyword(s):  
Nonlinear Perturbation ◽  
Hiv Model ◽  
The Impact

scholarly journals The impact of nonlinear perturbation to the dynamics of HIV model

2021 ◽  
Author(s):  
Zhenfeng Shi ◽  
Daqing Jiang ◽  
Ningzhong Shi ◽  
Tasawar Hayat ◽  
Ahmed Alsaedi
Keyword(s):  
Hiv Infection ◽  
Stochastic Model ◽  
Numerical Simulations ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Nonlinear Perturbation ◽  
Rigorous Analysis ◽  
Hiv Model ◽  
The Impact ◽  
Theoretical Results

In this paper, we developed and studied a stochastic HIV model with nonlinear perturbation. Through a rigorous analysis, we firstly showed that the solution of the stochastic model is positive and global. Then, by employing suitable stochastic Lyapunov functions, we prove that the stochastic model admit a unique ergodic stationary distribution. In addition, sufficient conditions for the extinction of HIV infection are derived. Finally, numerical simulations are employed to confirm our theoretical results.

scholarly journals Modeling the epidemiological impact of the UNAIDS 2025 targets to end AIDS as a public health threat by 2030

PLoS Medicine ◽  
2021 ◽  
Vol 18 (10) ◽  
pp. e1003831
Author(s):  
John Stover ◽  
Robert Glaubius ◽  
Yu Teng ◽  
Sherrie Kelly ◽  
Tim Brown ◽  
...  
Keyword(s):  
Public Health ◽  
Hiv Infections ◽  
Controlled Study ◽  
Access To Justice ◽  
People Living With Hiv ◽  
Hiv Model ◽  
Health Threat ◽  
Country Level ◽  
Public Health Threat ◽  
The Impact

Background UNAIDS has established new program targets for 2025 to achieve the goal of eliminating AIDS as a public health threat by 2030. This study reports on efforts to use mathematical models to estimate the impact of achieving those targets. Methods and findings We simulated the impact of achieving the targets at country level using the Goals model, a mathematical simulation model of HIV epidemic dynamics that includes the impact of prevention and treatment interventions. For 77 high-burden countries, we fit the model to surveillance and survey data for 1970 to 2020 and then projected the impact of achieving the targets for the period 2019 to 2030. Results from these 77 countries were extrapolated to produce estimates for 96 others. Goals model results were checked by comparing against projections done with the Optima HIV model and the AIDS Epidemic Model (AEM) for selected countries. We included estimates of the impact of societal enablers (access to justice and law reform, stigma and discrimination elimination, and gender equality) and the impact of Coronavirus Disease 2019 (COVID-19). Results show that achieving the 2025 targets would reduce new annual infections by 83% (71% to 86% across regions) and AIDS-related deaths by 78% (67% to 81% across regions) by 2025 compared to 2010. Lack of progress on societal enablers could endanger these achievements and result in as many as 2.6 million (44%) cumulative additional new HIV infections and 440,000 (54%) more AIDS-related deaths between 2020 and 2030 compared to full achievement of all targets. COVID-19–related disruptions could increase new HIV infections and AIDS-related deaths by 10% in the next 2 years, but targets could still be achieved by 2025. Study limitations include the reliance on self-reports for most data on behaviors, the use of intervention effect sizes from published studies that may overstate intervention impacts outside of controlled study settings, and the use of proxy countries to estimate the impact in countries with fewer than 4,000 annual HIV infections. Conclusions The new targets for 2025 build on the progress made since 2010 and represent ambitious short-term goals. Achieving these targets would bring us close to the goals of reducing new HIV infections and AIDS-related deaths by 90% between 2010 and 2030. By 2025, global new infections and AIDS deaths would drop to 4.4 and 3.9 per 100,000 population, and the number of people living with HIV (PLHIV) would be declining. There would be 32 million people on treatment, and they would need continuing support for their lifetime. Incidence for the total global population would be below 0.15% everywhere. The number of PLHIV would start declining by 2023.

Calcutta HIV Model Projections and the Impact of PrEP

2014 ◽  
Vol 30 (S1) ◽  
pp. A70-A71
Author(s):  
Zindoga Mukandavire ◽  
Kate Mitchell ◽  
Smarajit Jana ◽  
Peter Vickerman
Keyword(s):  
Hiv Model ◽  
The Impact

scholarly journals Mathematical Analysis and Clinical Implications of an HIV Model with Adaptive Immunity

2019 ◽  
Vol 2019 ◽  
pp. 1-19
Author(s):  
Jaouad Danane ◽  
Karam Allali
Keyword(s):  
Mathematical Model ◽  
Immune Response ◽  
Steady State ◽  
Adaptive Immunity ◽  
Reproduction Number ◽  
Adaptive Immune Response ◽  
Hiv Model ◽  
Adaptive Immune ◽  
The Impact ◽  
Ctl Immune Response

In this paper, a mathematical model describing the human immunodeficiency virus (HIV) pathogenesis with adaptive immune response is presented and studied. The mathematical model includes six nonlinear differential equations describing the interaction between the uninfected cells, the exposed cells, the actively infected cells, the free viruses, and the adaptive immune response. The considered adaptive immunity will be represented by cytotoxic T-lymphocytes cells (CTLs) and antibodies. First, the global stability of the disease-free steady state and the endemic steady states is established depending on the basic reproduction number R0, the CTL immune response reproduction number R1z, the antibody immune response reproduction number R1w, the antibody immune competition reproduction number R2w, and the CTL immune response competition reproduction number R3z. On the other hand, different numerical simulations are performed in order to confirm numerically the stability for each steady state. Moreover, a comparison with some clinical data is conducted and analyzed. Finally, a sensitivity analysis for R0 is performed in order to check the impact of different input parameters.

Analysis of an HIV model with distributed delay and behavior change

2015 ◽  
Vol 08 (02) ◽  
pp. 1550017
Author(s):  
Hasim A. Obaid ◽  
Rachid Ouifki ◽  
Kailash C. Patidar
Keyword(s):  
Response Function ◽  
Behavioral Change ◽  
Risky Behavior ◽  
Distributed Delay ◽  
Hiv Prevalence ◽  
Contact Rate ◽  
Threshold Values ◽  
Hiv Model ◽  
And Behavior ◽  
The Impact

We develop and analyze a mathematical model for the transmission dynamics of HIV that accounts for behavioral change. The contact rate is modeled by a decreasing function (response function) of HIV prevalence to reflect a reduction in risky behavior that results from the awareness of individuals to a higher HIV prevalence. The model also includes a distributed delay representing the time needed for individuals to reduce their risky behavior. We study mathematically and numerically the impact of the response function and the distributed delay on the model's dynamics. Threshold values for the delay at which the system destabilizes and periodic solutions can arise through Hopf bifurcation are determined.

Formation of Lunar Craters and Bright Rays as a Result of Meteorite Impacts

1962 ◽  
Vol 14 ◽  
pp. 415-418
Author(s):  
K. P. Stanyukovich ◽  
V. A. Bronshten
Keyword(s):  
Explosive Charge ◽  
The Moon ◽  
Meteorite Impacts ◽  
The Earth ◽  
Lunar Craters ◽  
The Impact

The phenomena accompanying the impact of large meteorites on the surface of the Moon or of the Earth can be examined on the basis of the theory of explosive phenomena if we assume that, instead of an exploding meteorite moving inside the rock, we have an explosive charge (equivalent in energy), situated at a certain distance under the surface.

The Geosciences Applied to Lunar Exploration

1962 ◽  
Vol 14 ◽  
pp. 169-257 ◽  
Author(s):  
J. Green
Keyword(s):  
Lunar Surface ◽  
Probable Mechanism ◽  
Point Of View ◽  
Lunar Exploration ◽  
Geological Model ◽  
Apply Geophysics ◽  
Surface Features ◽  
The Impact

The term geo-sciences has been used here to include the disciplines geology, geophysics and geochemistry. However, in order to apply geophysics and geochemistry effectively one must begin with a geological model. Therefore, the science of geology should be used as the basis for lunar exploration. From an astronomical point of view, a lunar terrain heavily impacted with meteors appears the more reasonable; although from a geological standpoint, volcanism seems the more probable mechanism. A surface liberally marked with volcanic features has been advocated by such geologists as Bülow, Dana, Suess, von Wolff, Shaler, Spurr, and Kuno. In this paper, both the impact and volcanic hypotheses are considered in the application of the geo-sciences to manned lunar exploration. However, more emphasis is placed on the volcanic, or more correctly the defluidization, hypothesis to account for lunar surface features.

Asteroid and Comet Impact Speeds upon Mars: Significance for Panspermia and the Supply of Organics

1997 ◽  
Vol 161 ◽  
pp. 197-201 ◽  
Author(s):  
Duncan Steel
Keyword(s):  
Probability Distributions ◽  
Regions Of Interest ◽  
Significant Fraction ◽  
Organic Chemicals ◽  
Impact Speed ◽  
The Mean ◽  
The Impact

AbstractWhilst lithopanspermia depends upon massive impacts occurring at a speed above some limit, the intact delivery of organic chemicals or other volatiles to a planet requires the impact speed to be below some other limit such that a significant fraction of that material escapes destruction. Thus the two opposite ends of the impact speed distributions are the regions of interest in the bioastronomical context, whereas much modelling work on impacts delivers, or makes use of, only the mean speed. Here the probability distributions of impact speeds upon Mars are calculated for (i) the orbital distribution of known asteroids; and (ii) the expected distribution of near-parabolic cometary orbits. It is found that cometary impacts are far more likely to eject rocks from Mars (over 99 percent of the cometary impacts are at speeds above 20 km/sec, but at most 5 percent of the asteroidal impacts); paradoxically, the objects impacting at speeds low enough to make organic/volatile survival possible (the asteroids) are those which are depleted in such species.

Organic Syntheses During the Impact of a Comet with a Gaseous Planet

1997 ◽  
Vol 161 ◽  
pp. 189-195
Author(s):  
Cesare Guaita ◽  
Roberto Crippa ◽  
Federico Manzini
Keyword(s):  
Polymeric Material ◽  
Molecular Form ◽  
Parent Compound ◽  
Blue Filter ◽  
Organic Syntheses ◽  
The Impact

AbstractA large amount of CO has been detected above many SL9/Jupiter impacts. This gas was never detected before the collision. So, in our opinion, CO was released from a parent compound during the collision. We identify this compound as POM (polyoxymethylene), a formaldehyde (HCHO) polymer that, when suddenly heated, reformes monomeric HCHO. At temperatures higher than 1200°K HCHO cannot exist in molecular form and the most probable result of its decomposition is the formation of CO. At lower temperatures, HCHO can react with NH3 and/or HCN to form high UV-absorbing polymeric material. In our opinion, this kind of material has also to be taken in to account to explain the complex evolution of some SL9 impacts that we observed in CCD images taken with a blue filter.

Hydrogen Cyanide Polymers from the Impact of Comet P/Shoemaker-Levy 9 on Jupiter

1997 ◽  
Vol 161 ◽  
pp. 179-187
Author(s):  
Clifford N. Matthews ◽  
Rose A. Pesce-Rodriguez ◽  
Shirley A. Liebman
Keyword(s):  
Amino Acids ◽  
Solar System ◽  
Hydrogen Cyanide ◽  
Nitrogen Heterocycles ◽  
Laboratory Studies ◽  
Heterogeneous Solids ◽  
The Many ◽  
Comet Halley ◽  
The Impact ◽  
By Products

AbstractHydrogen cyanide polymers – heterogeneous solids ranging in color from yellow to orange to brown to black – may be among the organic macromolecules most readily formed within the Solar System. The non-volatile black crust of comet Halley, for example, as well as the extensive orangebrown streaks in the atmosphere of Jupiter, might consist largely of such polymers synthesized from HCN formed by photolysis of methane and ammonia, the color observed depending on the concentration of HCN involved. Laboratory studies of these ubiquitous compounds point to the presence of polyamidine structures synthesized directly from hydrogen cyanide. These would be converted by water to polypeptides which can be further hydrolyzed to α-amino acids. Black polymers and multimers with conjugated ladder structures derived from HCN could also be formed and might well be the source of the many nitrogen heterocycles, adenine included, observed after pyrolysis. The dark brown color arising from the impacts of comet P/Shoemaker-Levy 9 on Jupiter might therefore be mainly caused by the presence of HCN polymers, whether originally present, deposited by the impactor or synthesized directly from HCN. Spectroscopic detection of these predicted macromolecules and their hydrolytic and pyrolytic by-products would strengthen significantly the hypothesis that cyanide polymerization is a preferred pathway for prebiotic and extraterrestrial chemistry.

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