Inverse problems in demography and biodemography

Inverse problems play important role in science and engineering. Estimation of boundary conditions on the temperature distribution inside a metallurgical furnace, reconstruction of tissue density inside body on plane projections obtained with x-rays are examples. The similar problems exist in demography in the form of projection and estimation of population age distributions and age-specific mortality rates. The problem of residual demography is estimation of demographic process in wild nature on its manifestation in marked subjects with unobserved age, which again is inverse problem. The article presents examples and the ways of solution the inverse problems in demography and biodemography, discusses the ways of improving results by combination of demographic and genetic data.

Senescence can play an essential role in modelling and estimation of vector based epidemiological indicators: demographical approach

In the paper basic epidemiological indicators, produced by an aging population of vectors, are calculated. In the study we follow two lines: calculations for demographically structured population and individual life-history approach. We discuss the advantages and limitations of these approaches and compare the results of our calculations with epidemiological indicators obtained for non-aging population of vectors.Gibraltar, age effect, disease control, gerontology

An Age-Structured Extension to the Vectorial Capacity Model

Vectorial capacity and the basic reproductive number (R(0)) have been instrumental in structuring thinking about vector-borne pathogen transmission and how best to prevent the diseases they cause. One of the more important simplifying assumptions of these models is age-independent vector mortality. A growing body of evidence indicates that insect vectors exhibit age-dependent mortality, which can have strong and varied affects on pathogen transmission dynamics and strategies for disease prevention.Based on survival analysis we derived new equations for vectorial capacity and R(0) that are valid for any pattern of age-dependent (or age-independent) vector mortality and explore the behavior of the models across various mortality patterns. The framework we present (1) lays the groundwork for an extension and refinement of the vectorial capacity paradigm by introducing an age-structured extension to the model, (2) encourages further research on the actuarial dynamics of vectors in particular and the relationship of vector mortality to pathogen transmission in general, and (3) provides a detailed quantitative basis for understanding the relative impact of reductions in vector longevity compared to other vector-borne disease prevention strategies.Accounting for age-dependent vector mortality in estimates of vectorial capacity and R(0) was most important when (1) vector densities are relatively low and the pattern of mortality can determine whether pathogen transmission will persist; i.e., determines whether R(0) is above or below 1, (2) vector population growth rate is relatively low and there are complex interactions between birth and death that differ fundamentally from birth-death relationships with age-independent mortality, and (3) the vector exhibits complex patterns of age-dependent mortality and R(0) ∼ 1. A limiting factor in the construction and evaluation of new age-dependent mortality models is the paucity of data characterizing vector mortality patterns, particularly for free ranging vectors in the field

Formulas for vectorial capacity in stable and stationary vector populations.

<p>Formulas for vectorial capacity in stable and stationary vector populations.</p

Vectorial capacity in a stable population for three mortality models (see Table 3 for functions).

<p>Parameters used in calculations are: exponential (dotted line, <i>g</i> = 0.0313), Gompertz (dashed line, α = 0.00662, <i>β</i> = 0.06234), and logistic (solid line, <i>α</i> = 0.00662, <i>β</i> = 0.06234, <i>s</i> = 1.073); taken from Styer et al. 2007a.</p

Hypothetical survivorship curves for different values of <i>H,</i> entropy.

<p>Hypothetical survivorship curves for different values of <i>H,</i> entropy.</p

Transmission dynamics when an infectious host is introduced at time = 0.

<p>(A) age-dependent mortality, <i>m = </i>1.5, (B) age-independent mortality <i>m</i> = 1.5, (C) age-dependent mortality, <i>m = </i>0.007, (D) age-independent mortality <i>m</i> = 0.007. Solid line denotes humans and dashed line mosquitoes.</p

Illustration of mortality models examined with different parameter values.

<p>Parameter values not listed; Gompertz: α = 0.01, declining: µ = 0.7, <i>g</i> = 0.1, logistic: <i>α = </i>0.007, <i>s</i> = 0.2, U-Shaped: <i>µ</i> = 0.001, <i>e₀</i> = 24, unimodal: <i>g</i> = 0.05, <i>e₀</i> = 30.</p