REMixed (version 1.1.2)

dynFUN_demo: Dynamic functions demo

Description

Example of solver for remix and cv.remix algorithm. It is perfectly adapted for the Monolix demo project (see getMLXdir).

Usage

dynFUN_demo

Format

dynFUN_demo function of t, y, parms :

t

vector of timepoint.

y

initial condition, named vector of form c(AB=<...>,S=<...>).

parms

named vector of model parameter ; should contain phi_S,delta_AB,delta_S.

Details

Suppose you have antibodies secreting cells -\(S\)- that produces antibodies -\(AB\)- at rate \(\varphi_S\). These two biological entities decay respectively at rate \(\delta_S\) and \(\delta_{AB}\). The biological mechanism behind is : $$ \left\{\begin{matrix} \frac{d}{dt}S(t) &=& -\delta_S S(t) \\ \frac{d}{dt} AB(t) &=& \varphi_S S(t) - \delta_{AB} AB(t) \\ (S(0),AB(0)) &=& (S_0,AB_0) \end{matrix}\right. $$

References

Pasin C, Balelli I, Van Effelterre T, Bockstal V, Solforosi L, Prague M, Douoguih M, Thiébaut R, for the EBOVAC1 Consortium. 2019. Dynamics of the humoral immune response to a prime-boost Ebola vaccine: quantification and sources of variation. J Virol 93 : e00579-19. https://doi.org/10.1128/JVI.00579-19

See Also

model.pasin, getMLXdir.

Examples

t = seq(0,300,1)
y =c(AB=1000,S=5)
parms = c(phi_S = 611, delta_AB = 0.03, delta_S=0.01)

res <- dynFUN_demo(t,y,parms)

plot(res[,"time"],
     log10(res[,"AB"]),
     ylab="log10(AB(t))",
     xlab="time (days)",
     main="Antibody titer over the time",
     type="l")

plot(res[,"time"],
     res[,"S"],
     ylab="S(t)",
     xlab="time (days)",
     main="Antibody secreting cells quantity over time",
     type="l")