REMixed (version 1.1.2)

model.clairon: 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)

Value

Matrix of time and observation of antibody secreting cells \(S\) and antibody titer \(Ab\).

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 "fM2","theta","delta_S","delta_Ab","delta_V").

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).

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

indParm

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)