model.clairon {REMixed} | R Documentation |
Model from Clairon and al.,2023
Description
Generates the dynamics of antibodies secreting cells -S
- that produces antibodies -AB
- over time, with two injection of vaccine at time t_0=0
and t_{inj}
, using Clairon and al., 2023, model.
Usage
model.clairon(t, y, parms, tinj = 21)
Arguments
t |
vector of timepoint. |
y |
initial condition, named vector of form c(S=S0,Ab=A0). |
parms |
named vector of model parameter (should contain " |
tinj |
time of injection (default to 21). |
Details
Model is defined as
\displaystyle\left\{\begin{matrix} \frac{d}{dt} S(t) &=& f_{\overline M_k} e^{-\delta_V(t-t_k)}-\delta_S S(t) \\ \frac{d}{dt} Ab(t) &=& \theta S(t) - \delta_{Ab} Ab(t)\end{matrix}\right.
on each interval I_1=[0;t_{inj}[
and I_2=[t_{inj};+\infty[
. For each interval I_k
, we have t_k
corresponding to the last injection date of vaccine, such that t_1=0
and t_2=t_{inj}
. By definition, f_{\overline M_1}=1
(Clairon and al., 2023).
Value
Matrix of time and observation of antibody secreting cells S
and antibody titer Ab
.
References
Quentin Clairon, Melanie Prague, Delphine Planas, Timothee Bruel, Laurent Hocqueloux, et al. Modeling the evolution of the neutralizing antibody response against SARS-CoV-2 variants after several administrations of Bnt162b2. 2023. hal-03946556
See Also
Examples
y = c(S=1,Ab=0)
parms = c(fM2 = 4.5,
theta = 18.7,
delta_S = 0.01,
delta_Ab = 0.23,
delta_V = 2.7)
t = seq(0,35,1)
res <- model.clairon(t,y,parms)
plot(res)