A Note on Proportionate Mixing Assumption Revisited for a Model with Vertical Transmission

Abstract

We conditionally extend formulas of(Dietz and Schenzle, J. Math. Biol. 22: 117-120,1995) for the ”transmission potential” of an immunizing infection with pre-infection possible before birth and vertical transmission admitted. We look for minimum proportion to be covered to reduce basic reproduction rate below 1 by acting through vaccination. We present also a new criterion allowing the selection of an immunizing vaccination strategy by bringing the reproduction number below 1. We find that reduce vertical transmission, adds chances to eradicate disease. Moreover reduce age of vaccination reduces the minimum vaccination coverage inducing global immunization against disease by bringing down the basic reproduction number.

Keywords

• Transmission potential, minimum proportion for vaccination immunization, endemic disease, pre-infection