Figure 1.
Nested Host-Parasite-Gene populations.
A) A host may carry susceptible and resistant parasites, a parasite can be either homozygous or heterozygous for the gene associated with resistance; B) Euler diagram of the host population. Alleles associated with drug resistance are initially concentrated within a sub-set (focus) of the host sub-population (target) that receives either annual chemotherapy or chemotherapy and vaccine every T (e.g. every 5) years.
Table 1.
Baseline parameters for the model.
Figure 2.
Allele frequency in worms outside of the primary focus of resistance.
Resistance can be fully recessive (A–B) or fully dominant (C–D). Annual chemotherapy is administered to 50% of the host population and no vaccination. Simulation parameters in Table 1. A) If resistance is a recessive character the allele frequency follows two different time-dynamics depending on the the degree of host-population mixing ρ: i) for ρ smaller than 69%, it grows fast and plateaus at a level inversely related to the value of ρ; ii) for ρ equal to or larger than 69%, a slow initial growth is followed by an accelerated growth. B) Non-monotonic relation between the allele frequency after 20 annual chemotherapy rounds and ρ. The maximum allele frequency is observed when ρ is equal to 85%. C) If resistance is a dominant character, the allele frequency grows at a rate inversely related to ρ. D) Negative monotonic relationship between the allele frequency after 20 annual chemotherapy rounds and ρ. The maximum allele frequency is observed when ρ is equal to 1.99% (homogeneous mixing case).
Figure 3.
Population-level vaccine effectiveness (VE), assuming that density dependence acts on the fecundity of established parasites, and that 50% of the host population is effectively vaccinated (Simulation parameters in Table 1).
Vaccines can reduce the host susceptibility to infection (A–B), by a proportion VS, or the female parasite reproductive rate (C–D), by a proportion VR, or the parasite lifespan (E–F), by a proportion VM. Vaccines reducing the parasite fecundity and vaccines reducing the parasite lifespan are more efficacious than vaccines reducing host susceptibility by the same proportion. Low reductions (<50%) in female reproductive rate have marginally higher impact than equal proportional reductions in adult worm lifespan. The impact on recessive alleles (A–C–D) grows with ρ, the degree of host-population mixing. The impact on dominant alleles increases with (B), decreases with (D) or is independent of (F) ρ, depending on the biological action of the vaccine.
Figure 4.
Impact of multi-target vaccines.
Vaccines simultaneously reducing fecundity (VR) and susceptibility (VS) (panels A–B) or fecundity, susceptibility, and parasite life-span (VM) (panels C–D) have the greatest potential. In this example, it is assumed that the vaccine reduces by the same proportion female worm fecundity, host susceptibility, and parasite lifespan. A and C refer to recessive alleles, B and D refer to dominant alleles.