Agerelated Processes

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The age structure of PDE models facilitates the inclusion of parameters representing age-related processes of infection and disease (Anderson and May, 1991). These can be processes related to exposure, such as patterns of behavior and of contacts (including sexual contacts), or to the initial establishment and subsequent course of infection or to the transmission of infection from an infected individual as some function of processes of maturation or aging. Patterns of exposure will be determined by the changing intensity and patterns of social and familial contacts (and whether families are nuclear or extended) that an individual has through his or her lifetime, or by more specific patterns such as sexual partner choice and sexual lifestyles. Nursery and primary schools are prime points of contact for exchange of viruses for young children, though in different regions children may enter these institutions at different ages. Young adults may be more likely to have many sexual partners, or to have, for the first time, significant contacts with those from other parts of the country or the world during higher education, military service or travel (illustrative examples are, in Italy, a peak in measles cases in males at military age or, in the UK, recent outbreaks of mumps among university students). Older people are more likely to spend significant time in hospitals or nursing homes and be exposed to the particular range of infections which may have found a niche there among the frail and the sick. Examples of age-determined factors relating to establishment of disease are, for the very young, the degree of protection remaining from passive (i.e., maternal) antibody, or, for older individuals, the possibly decreasing degree of protection from acquired active immunity arising from past infection or from vaccination many years previously, or diminished lung function or reduced effectiveness of the mucous membranes leading to easier establishment of infections. Disease processes in many infections are age-determined; for example, for hepatitis B the age at infection is a very strong determinant of the risk of persistent infection—neonates and the very young being at very much greater risk than older children and adults even less so, although older individuals are significantly less responsive to HBV vaccine. In the case of varicella zoster (chicken pox virus), its secondary manifestation as shingles or zoster is essentially a disease of older ages (probably a result of reactivation following a diminution of immune function perhaps following ill health or simply as a result of loss of immune function with age) (Brisson et al., 2003).

Control measures also may be distributed according to age. For example often vaccination may be targeted at people of a specific age (e.g., young children for measles or the elderly for influenza) or a specific group (e.g., those with many sexual partners for hepatitis B). In such cases vaccination in the model can be effected by specifying a transition at a particular age to a vaccinated compartment for age cohort vaccination, or by specifying that those in a particular compartment are continuously vaccinated at a specified rate. Vaccination campaigns may also be simply effected in the computer program, providing the numerical solution to a model through the device of switching vaccination on and off at specified time points (Figure 15.8) (Manfredi et al., 2005).

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