Biomedical subjects

Murray E Alexander

Publications and source records attributed to Murray E Alexander.

3 recordsLinked to original sources

PubMed2006

Bifurcations of an epidemic model with non-linear incidence and infection-dependent removal rate.

An epidemic model with a generalized non-linear incidence is extended to incorporate the effect of an infection-dependent removal strategy, which is defined as a function of the number of infected individuals. It is assumed that the removal rate decreases from a maximum capacity for removing infected individuals as their number increases. The existence and stability of the associated equilibria are analysed, and the basic reproductive number (R0) is formulated. It is shown that R0 is independent of the functional form of the incidence, but depends on the removal rate. Normal forms are derived to show the different types of bifurcation the model undergoes, including transcritical, generalized Hopf (Bautin), saddle-node and Bogdanov-Takens. A degenerate Hopf bifurcation at the Bautin point, where the first Lyapunov coefficient vanishes, is discussed. Sotomayor's theorem is applied to establish a saddle-node bifurcation at the turning point of backward bifurcation. The Bogdanov-Takens normal form is derived, from which the local bifurcation curve for a family of homoclinic orbits is formulated. Bifurcation diagrams and numerical simulations, using parameter values estimated for some infectious diseases, are also presented to provide more intuition to the theoretical findings. The results show that sufficiently increasing the removal rate can reduce R0 below a subthreshold domain, which leads to disease eradication.

Communicable Diseases↗

PubMed2004

Modelling strategies for controlling SARS outbreaks.

Severe acute respiratory syndrome (SARS), a new, highly contagious, viral disease, emerged in China late in 2002 and quickly spread to 32 countries and regions causing in excess of 774 deaths and 8098 infections worldwide. In the absence of a rapid diagnostic test, therapy or vaccine, isolation of individuals diagnosed with SARS and quarantine of individuals feared exposed to SARS virus were used to control the spread of infection. We examine mathematically the impact of isolation and quarantine on the control of SARS during the outbreaks in Toronto, Hong Kong, Singapore and Beijing using a deterministic model that closely mimics the data for cumulative infected cases and SARS-related deaths in the first three regions but not in Beijing until mid-April, when China started to report data more accurately. The results reveal that achieving a reduction in the contact rate between susceptible and diseased individuals by isolating the latter is a critically important strategy that can control SARS outbreaks with or without quarantine. An optimal isolation programme entails timely implementation under stringent hygienic precautions defined by a critical threshold value. Values below this threshold lead to control, but those above are associated with the incidence of new community outbreaks or nosocomial infections, a known cause for the spread of SARS in each region. Allocation of resources to implement optimal isolation is more effective than to implement sub-optimal isolation and quarantine together. A community-wide eradication of SARS is feasible if optimal isolation is combined with a highly effective screening programme at the points of entry.

Computer Simulation↗

PubMed2004

Affine registration: a comparison of several programs.

Several registration programs with an affine model for the displacement field were tested on various 2D and 3D MRI of the same modality. The following programs were considered: AIR 3.0 (Woods, J. Comp. Assist. Tomogr, 22(1): 139-152, 1998), COCGV (Ostuni, JMRI, 7(2): 410-415, 1997), FLIRT (Jenkinson, Med. Image Analysis, 5(2): 143-156, 2001), Intramodal Registration (Thevenaz, IEEE Trans. Image Proc., 7(1): 27-41, 1998), SPM (Friston, Human Brain Mapping, 2: 165-189, 1995), and Patch Algorithm (Zhilkin, MRI 18(9): 1143-1150, 2000). Although some of these programs can perform multimodal registration, none was used in such a mode. This paper attempts a fair comparison of the performance of the Patch Algorithm with other programs. However, different settings of the programs' parameters may further improve the quality of the registration and/or change execution speed. The registered images, the CPU time required to perform the registration, and the error between the registered and reference images, are presented. Most of the programs give comparable accuracies of registration, but their execution times vary considerably. In general the AIR and Patch Algorithm require the least time. The Patch Algorithm can be easily parallelizable on a multi-processor computer.

Algorithms↗