Although vaccines against measles have been routinely applied over a quarter of a century, measles is still persistent in Israel, with major epidemics roughly every 5 years. Recent serological analyses have shown that only 85% of Israelis aged 18 years have anti-measles IgG antibodies. Considering the high transmissibility of the virus and the high level of herd immunity required for disease eradication, the Israeli vaccination policy against measles is now being reevaluated. Motivated by theoretical studies of populations in perturbed environments, we examined the possibility of replacing the conventional cohort vaccination strategy by a pulse strategy--i.e., periodic vaccination of several age cohorts at the same time. Numerical studies of a deterministic age-structured model suggest that vaccination, which renders immunity to no more than 85% of the susceptible children aged 1-7 years, once every 5 years will suffice to prevent epidemics in Israel, where infection rate is highest amongst schoolchildren. The model suggests that by using such a strategy the density of susceptible individuals is always kept below the threshold above which recurrent epidemics will be maintained. Analysis of simpler, non-age-structured, models serves to clarify the basic properties of the proposed strategy. Our theoretical results indicate that the advantages and disadvantages of a pulse strategy should be seriously examined in Israel and in countries with similar patterns of measles virus transmission.

The humoral immune response to antigenic challenge involves a Darwinian process of somatic mutations and selection for B-cells carrying higher affinity antibodies. Insufficient knowledge about this process may hamper the use genetically engineered antibodies for vaccination. The aim of the present work is to circumvent some of the experimental difficulties in the study of affinity maturation by investigating this system mathematically. Using dynamic programming methods we look for mutation rate as a function of clone size, which maximizes the probability that the required antibody structure is generated before the pathogen kills the host. We show analytically that the globally optimal strategy for a fast production of high affinity antibodies is to utilize a step-function mutation rate, i.e., a minimal mutation rate in early stages of the immune response, followed by the maximal possible rate when the proliferating B-cells population size exceeds a given threshold. Based on the methodology we have followed it may be concluded that the good performance of this simple, thrifty, two-stage strategy cannot be improved by evolutionary development of a more complex control of the response. Laboratory experiments are suggested for testing the validity of our theoretical results.

Efficient immune response often depends on the production of high affinity antibodies. We show analytically that the optimal strategy for a fast production of high affinity antibodies is to utilize a step-function mutation rate, i.e. a minimal mutation rate in early stages of the immune response, followed by a discontinuous switch to the maximal possible rate when the proliferating population of B-cells exceeds a threshold value. Our results are in accordance with the biological observations concerning the time of onset of the hypermutation process, and with the mutation rate during the later stages of the primary immune response. Indeed the hypermutation process plays a crucial role in responding to a prevailing pathogen at each round of immune response, and not only for coping with future infections. Moreover, as the effect of hypermutations is shown to be crucially dependent on the number of proliferating B-cells, its onset is not expected to depend on an external signal, but rather to be related to the clone's age. This suggests that the onset is host species specific, rather than pathogen specific. Another implication of the present results is that activation of hypermutations before the B-cell population has reached the critical size may impede the efficiency of the response.