Modelling the spread of AIDS epidemic with vertical transmission

Naresh, Ram; Tripathi, Agraj; Omar, Sandip

doi:10.1016/j.amc.2005.11.041

Cited by 65 publications

(50 citation statements)

References 16 publications

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“…By the apriori boundedness of the state system, adjoint system and the resulting Lipschitz structure of the ODEs, we obtain the uniqueness of the optimal control for small T.The uniqueness of the optimal control follows from the uniqueness of the optimality system, which consist of (23), (24) and (25) with characterization (27) and (28). We impose a bound on the length of time interval in order to guarantee the uniqueness of the optimality system.…”

Section: Existence and Uniqueness Of The Controlmentioning

confidence: 99%

“…Mathematical models have become important tools in analyzing the spread and control of infectious diseases. Some examples on the use of mathematical model for the analyzes of treatment and control of infectious disease can be found in [11,13,16,17,21,27,28], etc. For instance, [13], based on results from the analysis and simulations of their HIV model, suggested universal HIV testing followed by an immediate commencement of antiretroviral therapy for those infected as a strategy to drive HIV epidemic towards elimination.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Optimal Control Analysis of an SIR Epidemic Model with Constant recruitment

Bakare

Nwagwo²,

Danso-Addo³

2014

International Journal of Applied Mathematical Research

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A mathematical model of an SIR epidemic model with constant recruitment and two control variables using control terms and a deterministic system of differential equation is presented and analyzed mathematically and numerically. We intend to control the susceptible and infected individuals with educational campaign and treatment strategies. We analyzed the model by non-dimensionalizing the system of equations of our SIR epidemic model and derived our basic reproduction number.We aim to minimize the total number of infective individuals and the cost associated with the use of educational campaign and treatment on [0, T ]. We used Pontryagin's maximum principle to characterize the optimal levels of the two controls. The resulting optimality system is solved numerically. The results show that the optimal combination of treatment and educational campaign strategy required to achieve the set objective will depend on the relative cost of each of the control measures. The results from our simulation is discussed.

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Section: Existence and Uniqueness Of The Controlmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal Control Analysis of an SIR Epidemic Model with Constant recruitment

Bakare

Nwagwo²,

Danso-Addo³

2014

International Journal of Applied Mathematical Research

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“…This models can be applied to epidemiology, which is defined by [12] as the study of the distribution and determinants of diseases both infectious and non-infectious. Mathematical models have been used extensively in research into the epidemiology of HIV/AIDS, to help improve our understanding of major contributing factors to its spread [17]. The goal of any modeling exercise is to extract as much information as possible from available data and provide an accurate representation of both the known and uncertainties of the epidemic [19].…”

Section: Mathematical Modeling and Epidemiologymentioning

confidence: 99%

Mathematical Modeling of the Spread of HIV/AIDS by Markov Chain Process

Titus¹

2016

AJAM

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Abstract:The spread of the Human Immunodeficiency Virus (HIV) and the resulting Acquired Immune Deficiency syndrome (AIDS) is a major health concern. Mathematical models are therefore commonly applied to understand the spread of the HIV epidemic. In this study, HIV dynamics is analyzed using a Stochastic Discrete-Time Markov Chain Mathematical Model. Demographic and epidemiological parameters that affect the model population dynamics were investigated. Well posedness of the model determined and the conditions for the existence and stability of disease-free and endemic equilibrium points proved, using the next generation matrix technique. The effect of various intervention strategies, were simulated by varying the parameters representing the possible strategies and comparing the respective values of the reproductive ratio . The numerical simulation results using intervention transition matrix showed that vertical transmission is the most sensitive parameter standing at 0.6 followed by the use of HAART at 0.4. This indicates the strategy which requires much effort to avert progression of infected individual to AIDS.

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“…The epidemic model in [16] considers a latent stage and vaccination of newborns and susceptible. In [18], it is assumed that the HIV epidemic spreads both through horizontal and vertical transmission; in [23], the immigration of infective individuals is considered, both models with a variable size population. The e¤ect of screening unaware infective individuals on the spread of HIV, in a constant population, is considered in the mathematical model proposed in [25].…”

Section: Introductionmentioning

confidence: 99%