Fig. 3

Vaccine success rates depend on manual vaccinations and the reproductive properties of vaccine and helper. Each panel shows the results from hundreds of numerical simulations stopped at time 400. For each combination of b _M and b _MV tested, the proportion of bacterial hosts with vaccine over all infected bacteria (at time 400) is indicated with color – purple is best, yellow worst. Color opacity is scaled in proportion to the fraction of infected bacteria over all bacteria. As most simulations resulted in all or nearly all bacteria becoming infected with either vaccine or helper by time 400, most of the panel is solid color. The white space in the lower left region is highly transparent because those parameter values resulted in few bacteria infected; zones with intermediate levels of infection are narrow. Each panel assumes a fixed ratio of vaccine/helper output (b _VM :b _MV ) and a specific number of initial vaccinations (100 or 100,000), as indicated. Black circles indicate the approximate behavior of wildtype M13 and phagemid (a, c) and of engineered M13 and phagemid (b, d) and are placed on the panels most closely representing the empirical relationship of b _VM : b _MV . The benefit of engineering a vaccine with a large reproductive excess over helper is readily evident, as is the value of introducing larger numbers of vaccinations. Equations were those of (A1), with lethal virus omitted and all forms of vaccine-infected cells combined; parameter values were those of Table 4 in Appendix, except for b _M , b _MV and b _VM , which were varied and are given in the figure. The initial density of uninfected cells was 10⁸; vaccinated cells were introduced as H _VMS at time 0