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We further allowed for a high or low rate of waning immunity and volunteer isolation at different times of the epidemic.
We then proceed to apply this methodology to our structured households models to investigate the impact of household size, within- and between-household transmission rates, rate of waning immunity, and infectious period distribution on dynamics.
This rate is higher than the one we used in the model but in fact the only difference expected by increasing the rate of waning immunity is a higher morbidity during the third wave and thus a higher CFR, but still lower then the CFR during the second wave.
The rate of waning vaccine-derived immunity was obtained by fitting an exponential curve to the estimated proportion of vaccinated individuals retaining immunity after 10, 20, 30, 50 and 70 years (95%, 90 %, 81 %, 74 and 68% respectively), obtanded using the Delphi method [ 24], yielding f = 0.005795 year-1.
We estimated the rate of transmission from short-cycle and long-cycle transmission, amplitude of seasonality in long-cycle transmission, rate of waning partial immunity, relative infectiousness of carriers, and a "reporting fraction" necessary to scale the predicted number of clinical infections in Blantyre district to the observed weekly number of culture-confirmed cases at QECH (Table 2).
44 The annual rate of waning of efficacy was based on the differential between the first and second season efficacy in a large Latin American trial 45 and converted into monthly rates for our model.
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Results showed that the efficacy of any immunization schedule was highly influenced by the rate at which immunity waned and that the benefit of a booster dose increased with increasing rates of waning immunity.
The peak of clinical malaria is again visible at low transmission, although this effect would be less pronounced for lower rates of waning immunity.
This has allowed us to quantify some basic behaviours of household structured dynamics; for example the impacts of varying within-household and between-household transmission rates and the role of waning immunity.
In general, estimation of the seasonality parameters A and φ is very sensitive to the rate of antibody waning.
The relative magnitude of oscillations in infected individuals is large and insensitive to changes in the rate of antibody waning.
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