16,000 research outputs found
Transmission dynamics of HIV/AIDS with screening and non-linear incidence
This paper examines the transmission dynamics of HIV/AIDS with screening using non-linear incidence. A nonlinear mathematical model for the problem is proposed and analysed qualitatively using the stability theory of the differential equations. The results show that the disease free equilibrium is locally stable at threshold parameter less than unity and unstable at threshold parameter greater than unity. Globally, the disease free equilibrium is not stable due existence of forward bifurcation at threshold parameter equal to unity. However numerical results suggest that screening of unaware infectives has the effect of reducing the transmission dynamics of HIV/AIDS. Also, the effect of non-linear incidence parameters showed that transmission dynamics of HIV/AIDS will be lowered when infectives after becoming aware of their infection, do not take part in sexual interaction or use preventive measures to prevent the spreading of the infection. Numerical simulation of the model is implemented to investigate the sensitivity of certain key parameters on the transmission dynamics of HIV/AIDS with screening using non-linear incidence.Keywords: HIV/AIDS, Screening, Non-linear incidence, Reproduction number, Stabilit
Occurrence of HIV eradication for preexposure prophylaxis treatment with a deterministic HIV model
The authors examine the human immunodeficiency virus (HIV) eradication in this study using a mathematical model and analyse the occurrence of virus eradication during the early stage of infection. To this end they use a deterministic HIV-infection model, modify it to describe the pharmacological dynamics of antiretroviral HIV drugs, and consider the clinical experimental results of preexposure prophylaxis HIV treatment. They also use numerical simulation to model the experimental scenario, thereby supporting the clinical results with a model-based explanation. The study results indicate that the protocol employed in the experiment can eradicate HIV in infected patients at the early stage of the infection
Multiobjective optimization to a TB-HIV/AIDS coinfection optimal control problem
We consider a recent coinfection model for Tuberculosis (TB), Human
Immunodeficiency Virus (HIV) infection and Acquired Immunodeficiency Syndrome
(AIDS) proposed in [Discrete Contin. Dyn. Syst. 35 (2015), no. 9, 4639--4663].
We introduce and analyze a multiobjective formulation of an optimal control
problem, where the two conflicting objectives are: minimization of the number
of HIV infected individuals with AIDS clinical symptoms and coinfected with
AIDS and active TB; and costs related to prevention and treatment of HIV and/or
TB measures. The proposed approach eliminates some limitations of previous
works. The results of the numerical study provide comprehensive insights about
the optimal treatment policies and the population dynamics resulting from their
implementation. Some nonintuitive conclusions are drawn. Overall, the
simulation results demonstrate the usefulness and validity of the proposed
approach.Comment: This is a preprint of a paper whose final and definite form is with
'Computational and Applied Mathematics', ISSN 0101-8205 (print), ISSN
1807-0302 (electronic). Submitted 04-Feb-2016; revised 11-June-2016 and
02-Sept-2016; accepted for publication 15-March-201
Initiation of HIV therapy
In this paper, we numerically show that the dynamics of the HIV system is sensitive to both the initial condition and the system parameters. These phenomena imply that the system is chaotic and exhibits a bifurcation behavior. To control the system, we propose to initiate an HIV therapy based on both the concentration of the HIV-1 viral load and the ratio of the CD4 lymphocyte population to the CD8 lymphocyte population. If the concentration of the HIV-1 viral load is higher than a threshold, then the first type of therapy will be applied. If the concentration of the HIV-1 viral load is lower than or equal to the threshold and the ratio of the CD4 lymphocyte population to the CD8 lymphocyte population is greater than another threshold, then the second type of therapy will be applied. Otherwise, no therapy will be applied. The advantages of the proposed control strategy are that the therapy can be stopped under certain conditions, while the state variables of the overall system is asymptotically stable with fast convergent rate, the concentration of the controlled HIV-1 viral load is monotonic decreasing, as well as the positivity constraint of the system states and that of the dose concentration is guaranteed to be satisfied. Computer numerical simulation results are presented for an illustration
Sieve estimation of constant and time-varying coefficients in nonlinear ordinary differential equation models by considering both numerical error and measurement error
This article considers estimation of constant and time-varying coefficients
in nonlinear ordinary differential equation (ODE) models where analytic
closed-form solutions are not available. The numerical solution-based nonlinear
least squares (NLS) estimator is investigated in this study. A numerical
algorithm such as the Runge--Kutta method is used to approximate the ODE
solution. The asymptotic properties are established for the proposed estimators
considering both numerical error and measurement error. The B-spline is used to
approximate the time-varying coefficients, and the corresponding asymptotic
theories in this case are investigated under the framework of the sieve
approach. Our results show that if the maximum step size of the -order
numerical algorithm goes to zero at a rate faster than , the
numerical error is negligible compared to the measurement error. This result
provides a theoretical guidance in selection of the step size for numerical
evaluations of ODEs. Moreover, we have shown that the numerical solution-based
NLS estimator and the sieve NLS estimator are strongly consistent. The sieve
estimator of constant parameters is asymptotically normal with the same
asymptotic co-variance as that of the case where the true ODE solution is
exactly known, while the estimator of the time-varying parameter has the
optimal convergence rate under some regularity conditions. The theoretical
results are also developed for the case when the step size of the ODE numerical
solver does not go to zero fast enough or the numerical error is comparable to
the measurement error. We illustrate our approach with both simulation studies
and clinical data on HIV viral dynamics.Comment: Published in at http://dx.doi.org/10.1214/09-AOS784 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Estimation of constant and time-varying dynamic parameters of HIV infection in a nonlinear differential equation model
Modeling viral dynamics in HIV/AIDS studies has resulted in a deep
understanding of pathogenesis of HIV infection from which novel antiviral
treatment guidance and strategies have been derived. Viral dynamics models
based on nonlinear differential equations have been proposed and well developed
over the past few decades. However, it is quite challenging to use experimental
or clinical data to estimate the unknown parameters (both constant and
time-varying parameters) in complex nonlinear differential equation models.
Therefore, investigators usually fix some parameter values, from the literature
or by experience, to obtain only parameter estimates of interest from clinical
or experimental data. However, when such prior information is not available, it
is desirable to determine all the parameter estimates from data. In this paper
we intend to combine the newly developed approaches, a multi-stage
smoothing-based (MSSB) method and the spline-enhanced nonlinear least squares
(SNLS) approach, to estimate all HIV viral dynamic parameters in a nonlinear
differential equation model. In particular, to the best of our knowledge, this
is the first attempt to propose a comparatively thorough procedure, accounting
for both efficiency and accuracy, to rigorously estimate all key kinetic
parameters in a nonlinear differential equation model of HIV dynamics from
clinical data. These parameters include the proliferation rate and death rate
of uninfected HIV-targeted cells, the average number of virions produced by an
infected cell, and the infection rate which is related to the antiviral
treatment effect and is time-varying. To validate the estimation methods, we
verified the identifiability of the HIV viral dynamic model and performed
simulation studies.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS290 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Mathematical modelling of internal HIV dynamics
We study a mathematical model for the viral dynamics of HIV in an infected individual in the presence of HAART. The paper starts with a literature review and then formulates the basic mathematical model. An expression for R0, the basic reproduction number of the virus under steady state application of HAART, is derived followed by an equilibrium and stability analysis. There is always a disease-free equilibrium (DFE) which is globally asymptotically stable for R0 1 then some simulations will die out whereas others will not. Stochastic simulations suggest that if R0 > 1 those which do not die out approach a stochastic quasi-equilibrium consisting of random uctuations about the non-trivial deterministic equilibrium levels, but the amplitude of these uctuations is so small that practically the system is at the non-trivial equilibrium. A brief discussion concludes the paper
A Stochastic Model of Latently Infected Cell Reactivation and Viral Blip Generation in Treated HIV Patients
Motivated by viral persistence in HIV+ patients on long-term anti-retroviral treatment (ART), we present a stochastic model of HIV viral dynamics in the blood stream. We consider the hypothesis that the residual viremia in patients on ART can be explained principally by the activation of cells latently infected by HIV before the initiation of ART and that viral blips (clinically-observed short periods of detectable viral load) represent large deviations from the mean. We model the system as a continuous-time, multi-type branching process. Deriving equations for the probability generating function we use a novel numerical approach to extract the probability distributions for latent reservoir sizes and viral loads. We find that latent reservoir extinction-time distributions underscore the importance of considering reservoir dynamics beyond simply the half-life. We calculate blip amplitudes and frequencies by computing complete viral load probability distributions, and study the duration of viral blips via direct numerical simulation. We find that our model qualitatively reproduces short small-amplitude blips detected in clinical studies of treated HIV infection. Stochastic models of this type provide insight into treatment-outcome variability that cannot be found from deterministic models
Saturation Effects and the Concurrency Hypothesis: Insights from an Analytic Model
Sexual partnerships that overlap in time (concurrent relationships) may play
a significant role in the HIV epidemic, but the precise effect is unclear. We
derive edge-based compartmental models of disease spread in idealized dynamic
populations with and without concurrency to allow for an investigation of its
effects. Our models assume that partnerships change in time and individuals
enter and leave the at-risk population. Infected individuals transmit at a
constant per-partnership rate to their susceptible partners. In our idealized
populations we find regions of parameter space where the existence of
concurrent partnerships leads to substantially faster growth and higher
equilibrium levels, but also regions in which the existence of concurrent
partnerships has very little impact on the growth or the equilibrium.
Additionally we find mixed regimes in which concurrency significantly increases
the early growth, but has little effect on the ultimate equilibrium level.
Guided by model predictions, we discuss general conditions under which
concurrent relationships would be expected to have large or small effects in
real-world settings. Our observation that the impact of concurrency saturates
suggests that concurrency-reducing interventions may be most effective in
populations with low to moderate concurrency
Spread and Control of the Dynamics of HIV/AIDS-TB Co-infection in Ethiopia: A Mathematical Model Analysis
In this work we considered a nonlinear deterministic dynamical system to study the dynamics of HIV/AIDS-TB co-infection in Ethiopia. We found the system exhibit disease free equilibrium point and endemic equilibrium point. For the reproduction number the disease-free equilibrium point is locally asymptomatically stable and the endemic equilibrium point is locally asymptomatically unstable. We calculate basic reproduction number of the HIV/AIDS-TB co-infection dynamical system which depends on six parameters. Using real data collected from different sectors in Ethiopia we found that the numerical value of the basic reproduction number is. This shows that HIV/AIDS–TB co-infection spread in the society. Using sensitive analysis, we identify the most influential control parameter is the HIV/AIDS-TB co-infection transmission rate. The HIV/AIDS-TB co-infection transmission rate which numerical value to be 0.021. But the real value of is 0.74, to be 0.74 in to 0.021 by fixing the number of contacts for HIV/AIDS-TB co-infection we decrease the effective number of contacts for HIV/AIDS-TB co-infection 74 to 21. We also perform numerical simulation based on real data collected from different health sectors in Ethiopia.  
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