Biomedical subjects

A B Gumel

Publications and source records attributed to A B Gumel.

4 recordsLinked to original sources

PubMed2006

Mathematical study of a staged-progression HIV model with imperfect vaccine.

A staged-progression HIV model is formulated and used to investigate the potential impact of an imperfect vaccine. The vaccine is assumed to have several desirable characteristics such as protecting against infection, causing bypass of the primary infection stage, and offering a disease-altering therapeutic effect (so that the vaccine induces reversal from the full blown AIDS stage to the asymptomatic stage). The model, which incorporates HIV transmission by individuals in the AIDS stage, is rigorously analyzed to gain insight into its qualitative features. Using a comparison theorem, the model with mass action incidence is shown to have a globally-asymptotically stable disease-free equilibrium whenever a certain threshold, known as the vaccination reproduction number, is less than unity. Furthermore, the model with mass action incidence has a unique endemic equilibrium whenever this threshold exceeds unity. Using the Li-Muldowney techniques for a reduced version of the mass action model, this endemic equilibrium is shown to be globally-asymptotically stable, under certain parameter restrictions. The epidemiological implications of these results are that an imperfect vaccine can eliminate HIV in a given community if it can reduce the reproduction number to a value less than unity, but the disease will persist otherwise. Furthermore, a future HIV vaccine that induces the bypass of primary infection amongst vaccinated individuals (who become infected) would decrease HIV prevalence, whereas a vaccine with therapeutic effect could have a positive or negative effect at the community level.

AIDS Vaccines↗

PubMed2005

A mathematical model for assessing control strategies against West Nile virus.

Since its incursion into North America in 1999, West Nile virus (WNV) has spread rapidly across the continent resulting in numerous human infections and deaths. Owing to the absence of an effective diagnostic test and therapeutic treatment against WNV, public health officials have focussed on the use of preventive measures in an attempt to halt the spread of WNV in humans. The aim of this paper is to use mathematical modelling and analysis to assess two main anti-WNV preventive strategies, namely: mosquito reduction strategies and personal protection. We propose a single-season ordinary differential equation model for the transmission dynamics of WNV in a mosquito-bird-human community, with birds as reservoir hosts and culicine mosquitoes as vectors. The model exhibits two equilibria; namely the disease-free equilibrium and a unique endemic equilibrium. Stability analysis of the model shows that the disease-free equilibrium is globally asymptotically stable if a certain threshold quantity (R0), which depends solely on parameters associated with the mosquito-bird cycle, is less than unity. The public health implication of this is that WNV can be eradicated from the mosquito-bird cycle (and, consequently, from the human population) if the adopted mosquito reduction strategy (or strategies) can make R0<1. On the other hand, it is shown, using a novel and robust technique that is based on the theory of monotone dynamical systems coupled with a regular perturbation argument and a Liapunov function, that if R0>1, then the unique endemic equilibrium is globally stable for small WNV-induced avian mortality. Thus, in this case, WNV persists in the mosquito-bird population.

Algorithms↗

PubMed2001

Numerical modelling of the perturbation of HIV-1 during combination anti-retroviral therapy.

A competitive, chaos-free, implicit, finite-difference method is developed and used for a novel deterministic model for the perturbation of HIV by combination antiretroviral therapy. The compartmental model monitors the interaction between HIV and CD4(+) T cells, its principal target and site of replication in vivo, in the presence of reverse transcription inhibitors and protease inhibitors. The model exhibits two steady states, an uninfected (trivial) steady state (with no virus present) and an endemically infected state (with virus and infected T cells present). Stability and bifurcation analyses together with numerical simulations of the resulting dynamical system are reported.

Anti-HIV Agents↗

PubMed1998

A sequential algorithm for the non-linear dual-sorption model of percutaneous drug absorption.

A sequential algorithm is developed for the non-linear dual-sorption model developed by Chandrasekaran et al. [1,2] which monitors pharmacokinetic profiles in percutaneous drug absorption. In the experimental study of percutaneous absorption, it is often observed that the lag-time decreases with the increase in the donor concentration when two or more donor concentrations of the same compound are used. The dual-sorption model has sometimes been employed to explain such experimental results. In this paper, it is shown that another feature observed after vehicle removal may also characterize the dual-sorption model. Soon after vehicle removal, the plots of the drug flux versus time become straight lines on a semilogarithmic scale as in the linear model, but the half-life is prolonged thereafter when the dual-sorption model prevails. The initial half-life after vehicle removal with a low donor concentration is longer than that with a higher donor concentration. These features, if observed in experiments, may be used as evidence to confirm that the dual-sorption model gives an explanation to the non-linear kinetic behaviour of a permeant.

Administration, Cutaneous↗