![]() However, as individuals age, their immunity wanes (black wavy lines). After infection, they recover (dot-dashed orange lines) fully immune ( S 5). As individuals age, susceptible ones with incomplete immunity, including naive ( S 1), some ( S 2), moderate ( S 3), and vaccine-induced ( S 4) immunity, can be infected (red solid line) and become infectious. Recovery from disease leads to a fully immune state (orange dash-dotted line). I 1, I 2, I 3, and I 4 (red shaded boxes) represent infected individuals with typically severe symptoms who are maximally infectious, moderate symptoms and reduced infectiousness, mild symptoms and even less infectiousness, and neither symptoms nor infectiousness, respectively (we set I 5 = 0 in the text for ease of notation). S 1, S 2, S 3, S 4, and S 5 (blue shaded boxes) represent susceptible individuals who are immunologically naive, have some immunity, are moderately immune, were recently vaccinated, and are fully immune, respectively. The height of the bars in the top row indicate the total proportion in each age class while the bottom row is normalized by age group. (Column (B)) Colors represent the level of symptoms and transmissibility: severe symptoms and full transmissibility I 1 (red), moderate symptoms and transmissibility I 2 (orange), mild symptoms and low transmissibility I 3 (yellow), and neither symptoms nor transmissibility I 4 (light blue). (Column (A)) Colors represent the level of susceptibility: fully susceptible S 1 (red), low partial immunity S 2 (orange), medium partial immunity S 3 (yellow), vaccinated immunity S 4 (light blue), and complete immunity S 5 (blue). The proportion of susceptible (A) or infected (B) individuals from the total population of each status with no vaccination (A1)-(B1), with primary vaccination only (A2)-(B2), with primary vaccination plus one booster dose (A3)-(B3), with primary vaccination plus two booster doses (A4)-(B4). ![]() Colors from Brewer (2013).ĭistribution of individuals in each age class by immune status. ![]() The height of the bars in the top row indicates the total proportion in each age class while the bottom row is normalized by age group. The proportion of susceptible (A) or infected (B) individuals from the total population of each status with no vaccination (A1)-(B1), with primary vaccination alone (A2)-(B2), with primary vaccination plus one booster dose (A3)-(B3), with primary vaccination plus two booster doses (A4)-(B4). All rights reserved.ĭistribution of individuals in each age class by immune status. Because pertussis comprises a spectrum of symptoms, only the most severe of which are medically attended, accurate models are needed to design optimal vaccination programs where surveillance is less effective.Īge- and immunity-structured population Immuno-epidemiology Mathematical epidemiology Vaccination Waning and boosting of immunity.Ĭopyright © 2020 The Authors. As one example, we compare simulations with the experience of Sweden following resumption of pertussis vaccination after the hiatus from 1979 to 1996, reproducing the observations leading health authorities to introduce booster doses among school-aged children and adolescents in 20, respectively. ![]() The resurgences of pertussis that have been observed wherever effective vaccination programs have reduced typical disease among young children follow from these processes. We also model age, which affects contact, vaccination and possibly waning rates. We quantify these phenomena in a model population composed of individuals whose susceptibility, infectiousness, and symptoms all vary with immune status. Symptoms, and concomitantly infectiousness, depend on residual immunity. Immunity following natural infection or immunization may wane, increasing susceptibility to infection with time since infection or vaccination. ![]()
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