Fig 1.
Transmissible vaccine model diagram.
Graphical representation of the general framework for the transmissible vaccine model. The model consists of Susceptible individuals (S), Pathogen-infected individuals (P), Vaccine-infected individuals (V), and Recovered individuals (R). Individuals enter the system through birth into the susceptible class at the seasonally variable rate b(t) (Eq 1), all individuals leave the system through disease-independent mortality (d) and infected individuals may experience additional disease-dependent mortality at rate (ν). Other important parameters are the transmission rate of the pathogen (βP), recovery from the pathogen (γP), direct-vaccination (Eq 2), transmission of the vaccine (βV), and loss of vaccine transmissibility (γV). Further details of the model can be found in the main text and the full system of equations can be found in the S1 Appendix. These figures were created with BioRender.com.
Table 1.
Table of model parameters and biological interpretation.
Fig 2.
Transferable vaccine model diagram.
Graphical representation of the general framework for the transferable vaccine model. The model consists of Susceptible individuals (S), Pathogen-infected individuals (P), and Recovered individuals (R). In addition, we track individuals that have gel on them, that is, Pathogen-infected individuals with gel (Pg) and Recovered individuals with gel (Rg). There is no Susceptible class with gel because we assume animals to which gel is applied are also directly vaccinated and thus move directly to the recovered and gelled class (rightmost arrow). Individuals are born into the Susceptible class at a seasonally variable rate b(t) (Eq 1) and all individuals leave the system through disease-independent mortality (d) and infected individuals may experience additional disease-dependent mortality at rate (ν). Other important parameters are the transmission rate of the pathogen (βP), recovery from the pathogen (γP), direct-vaccination (Eq 2), transmission of the vaccine-laced gel (βg), deterioration of gel (γg), and removal of gel via grooming behaviors (α). Further details of the model can be found in the main text and the full system of equations can be found in the S1 Appendix. These figures were created with BioRender.com.
Fig 3.
Temporal dynamics of immunity.
The temporal dynamics of immunity for standard, transferable, and transmissible vaccines in the absence of a pathogen. For each type of vaccine, 250 vaccines are distributed on day 200. The colored lines represent the number of immune individuals in the population over three years of repeated vaccination for either a standard vaccine, transferable vaccine, transmissible vaccine with R0,V < 1, and a transmissible vaccine with R0,V > 1. R0,V of the standard, transferable, strongly transmissible, and weakly transmissible are: (0, 1.5, 1.5, and 0.75) respectively. The remaining parameters are: an average population size of 2000 individuals (), s = 3, an average lifespan of 1 year (d = 1/365), R0,P = 2, 250 vaccines are distributed each year (NV = 250), individuals can disseminate vaccine for 21 days on average (γV = 21−1), individuals remain infectious with the pathogen for 21 days on average (γP = 21−1), the transferable vaccine is groomed off individuals after 6 days on average (α = 1/15000, and the pathogen is non-virulent (ν = 0).
Fig 4.
R0,V and the importance of timing vaccine delivery.
Optimal timing for self-disseminating vaccines as a function of vaccine R0,V. Solid lines represent the level of pathogen reduction achieved for a given date of vaccine introduction for different vaccine R0,V. The grey region outlined by the dashed lined represents the seasonal birthing season where day 1 corresponds to the first day of the birthing season. Additional parameters used were: an average population size of 2000 individuals (), s = 3, an average lifespan of 1 year (d = 1/365), R0,P = 2, 250 vaccines are distributed each year (NV = 250), individuals can disseminate vaccine for 21 days on average (γV and γg = 21−1), individuals remain infectious with the pathogen for 21 days on average (γP = 21−1), the transferable vaccine is groomed off individuals after 6 days on average (α = 1/15000, and the pathogen is non-virulent (ν = 0).
Fig 5.
Level of pathogen reduction across various R0,V, tv, and Vl.
Level of pathogen reduction achieved for both transmissible vaccines and transferable vaccines at different times (tv) and for different durations of a vaccination campaign (Vl). The R0 in the figure refers to the vaccine R0. The remaining parameters used were: an average population size of 2000 individuals (), s = 3, an average lifespan of 1 year (d = 1/365), R0,P = 2, 250 vaccines are distributed each year (NV = 250), individuals can disseminate vaccine for 21 days on average (γV and γg = 21−1), individuals remain infectious with the pathogen for 21 days on average (γP = 21−1), the transferable vaccine is groomed off individuals after 6 days on average (α = 1/15000, and the pathogen is non-virulent (ν = 0).
Fig 6.
Pathogen reduction across different vaccine infectious periods.
Level of pathogen reduction achieved across various times of vaccination with different vaccine recovery rates indicated by the different colors. The vaccine recovery rate controls the length of time that the vaccine can disseminate to other individuals in the population. Solid lines represent the level of pathogen reduction achieved for a given date of vaccine introduction. The grey region outlined by the dashed line represents the birthing season where day 1 corresponds to the first day of the birthing season. The remaining parameters are: an average population size of 2000 individuals (), s = 3, an average lifespan of 1 year (d = 1/365), R0,V = 1.5, R0,P = 2, 250 vaccines are distributed each year (NV = 250), individuals remain infectious with the pathogen for 21 days on average (γP = 21−1), the transferable vaccine is groomed off individuals after 6 days on average (α = 1/15000, and the pathogen is non-virulent (ν = 0).
Fig 7.
Pathogen reduction across different host lifespans.
Level of pathogen reduction achieved across various times of vaccination with different average host lifespans indicated by the different colors. Solid lines represent the level of pathogen reduction achieved for a given date of vaccine introduction. Dashed lines and the grey region beneath them represent the birthing season. Day 1 corresponds to the first day of the birthing season as well as the first possible day of vaccine introduction. The remaining parameters are: an average population size of 2000 individuals (), s = 3, R0,V = 1.5, R0,P = 2, 250 vaccines are distributed each year (NV = 250), individuals can disseminate vaccine for 21 days on average (γV and γg = 21−1), individuals remain infectious with the pathogen for 21 days on average (γP = 21−1), the transferable vaccine is groomed off individuals after 6 days on average (α = 1/15000, and the pathogen is non-virulent (ν = 0).
Fig 8.
Pathogen reduction across differing levels of host seasonality.
Level of pathogen reduction achieved across various times of vaccination for varying levels of synchronous births (s). Low s or low synchrony implies births occur over a large amount of time whereas high s or high synchrony implies all births occur over a very short time frame. Solid lines represent the level of pathogen reduction achieved for a given date of vaccine introduction. The grey region outlined by the dashed colored lines represent the birthing season for the respective parameter regime shared with the solid lines. Day 1 corresponds to the first day of the birthing season as well as the first possible day of vaccine introduction. The remaining parameters are: an average population size of 2000 individuals (), an average lifespan of 1 year (d = 1/365), R0,V = 1.5, R0,P = 2, 250 vaccines are distributed each year (NV = 250), individuals can disseminate vaccine for 21 days on average (γV and γg = 21−1), individuals remain infectious with the pathogen for 21 days on average (γP = 21−1), the transferable vaccine is groomed off individuals after 6 days on average (α = 1/15000, and the pathogen is non-virulent (ν = 0).
Fig 9.
Specific example for M. natalensis that describes the level of pathogen reduction achieved across various times of vaccination with different vaccine R0 values indicated by the different colors. Solid lines represent the level of pathogen reduction achieved for a given date of vaccine introduction. The grey region outlined by the dashed line represents the birthing season where day 1 corresponds to the first day of the birthing season. The remaining parameters used were: an average population size of 2000 individuals (), s = 13.078, an average lifespan of 1 year (d = 1/365), R0,P = 1.5, 200 vaccines are distributed each year (NV = 200), individuals can disseminate the transferable vaccine for 2 days on average (γg = 2−1), individuals remain infectious with the transmissible vaccine for their entire life (γV = 0), individuals remain infectious with the pathogen for 21 days on average (γP = 21−1), the transferable vaccine is groomed off individuals after 6 days on average (α = 1/15000, and the pathogen is non-virulent (ν = 0).
Fig 10.
Specific example for D. rotundus on the level of pathogen reduction achieved across various times of vaccination with different vaccine R0 values indicated by the different colors. Solid lines represent the level of pathogen reduction achieved for a given date of vaccine introduction. The grey region outlined by the dashed lined represents the birthing season where day 1 corresponds to the first day of the birthing season. The remaining parameters used were: an average population size of 240 individuals (), s = 2.59, an average lifespan of 3.5 years (d = 1/(365 × 3.5), R0,P = 1.5, 24 vaccines are distributed each year (NV = 24), individuals can disseminate the transferable vaccine for 7 days on average (γg = 2−1), individuals remain infectious with the transmissible vaccine for their entire life (γV = 0), individuals remain infectious with the pathogen for 21 days on average (γP = 21−1), the transferable vaccine is groomed off individuals after 6 days on average (α = 1/15000, and the pathogen is virulent (ν = 0.005).