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  • Echinocytosis  (1)
  • Sexually transmitted diseases  (1)
  • Springer  (2)
  • American Society of Hematology
  • 1
    Electronic Resource
    Electronic Resource
    On the role of long incubation periods in the dynamics of acquired immunodeficiency syndrome (AIDS) (1989)
    Springer
    Journal of mathematical biology 27 (1989), S. 373-398 
    Details
    ISSN: 1432-1416
    Keywords: Acquired immunodeficiency syndrome (AIDS) ; Distributed delays ; Human immunodeficiency virus (HIV) ; Sexually transmitted diseases
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In this study, we investigate systematically the role played by the reproductive number (the number of secondary infections generated by an infectious individual in a population of susceptibles) on single group populations models of the spread of HIV/AIDS. Our results for a single group model show that if R ⩽ 1, the disease will die out, and strongly suggest that if R 〉 1 the disease will persist regardless of initial conditions. Our extensive (but incomplete) mathematical analysis and the numerical simulations of various research groups support the conclusion that the reproductive number R is a global bifurcation parameter. The bifurcation that takes place as R is varied is a transcritical bifurcation; in other words, when R crosses 1 there is a global transfer of stability from the infection-free state to the endemic equilibrium, and vice versa. These results do not depend on the distribution of times spent in the infectious categories (the survivorship functions). Furthermore, by keeping all the key statistics fixed, we can compare two extremes: exponential survivorship versus piecewise constant survivorship (individuals remain infectious for a fixed length of time). By choosing some realistic parameters we can see (at least in these cases) that the reproductive numbers corresponding to these two extreme cases do not differ significantly whenever the two distributions have the same mean. At any rate a formula is provided that allows us to estimate the role played by the survivorship function (and hence the incubation period) in the global dynamics of HIV. These results support the conclusion that single population models of this type are robust and hence are good building blocks for the construction of multiple group models. Our understanding of the dynamics of HIV in the context of mathematical models for multiple groups is critical to our understanding of the dynamics of HIV in a highly heterogeneous population.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00290636
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  • 2
    Electronic Resource
    Electronic Resource
    Local mechanical oscillations of the cell surface within the range 0.2–30 Hz (1990)
    Springer
    European biophysics journal 19 (1990), S. 93-99 
    Details
    ISSN: 1432-1017
    Keywords: Cell motility ; Cell surface light scattering ; Erythrocytes ; Cultured cells ; Spectrin abnormality ; Microspherocytosis ; Echinocytosis ; Membrane crosslinking
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Physics
    Notes: Abstract This paper describes transverse oscillations, within the range 0.2–30 Hz, of the surface of different animal cells: human and frog erythrocytes, human lymphocytes and monocytes, cultured 3T6 fibroblasts, and rat cardiomyocytes. The minimal area of the cell surface which undergoes unidirectional transverse movement is equal to or less than 0.5 × 0.5 μm. The amplitude of the oscillations recorded on larger surface areas is lower than on the smaller ones because of the averaging of solitary oscillations. The oscillation amplitude is different in different cells. The highest amplitude is recorded in human erythrocytes (350–400 nm), the lowest one, in fibroblasts, lymphocytes and monocytes (20–30 nm). The oscillations of the human erythrocyte are suppressed on hypotonic swelling, after hardening of the cell membrane owing to adsorption at the surface of the impermeable dye Heliogen Blue, by treatment of the cell with 0.01% glutaraldehyde, by treatment with 0.5 mM 4-hydroxymercurybenzoate, and after crenation caused by 1–2 mM 2,4-dinitrophenol. The amplitude of the surface oscillations is decreased in spectrin deficient erythrocytes obtained from patients with hereditary spherocytosis, which indicates an essential role for spectrin in the rapid oscillations of the erythrocyte surface.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00185092
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