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Bull Math Biol. 2011 May;73(5):1101-17. doi: 10.1007/s11538-010-9554-z. Epub 2010 Jun 17.

Effect of vaccination in environmentally induced diseases.

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  • 1Department of Mathematics and Gonda Brain Research Center, Bar Ilan University, Ramat Gan, 52900, Israel.


Along with the constant improvement in hygiene in the last few decades there has been a continuous increase in the incidence of particular diseases, mainly of autoimmune or allergic etiology, but also of diseases caused by infectious agents, such as listeriosis. We here present a model for the effect of exposure to agents causing or inducing the disease on the incidence of morbidity. The proposed model is an expansion of the SIR model to non-contagious diseases and aims to estimate the balance between immunization and disease probability. The model results indicate that, paradoxically in a wide range of parameters, a decrease in exposure to the disease inducing agent results in an increase in disease incidence. This can occur if: (a) the probability of developing disease, given an exposure to the agent increases with age, (b) immunity to the agent is long. The inverse relation between exposure and disease incidence results from a decrease in the adult immunized population following a previous decrease in the exposure rate. Therefore, a lower exposure can lead to lower incidence in the short term but to higher incidence in the long term.

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