Hamiltonian Monte Carlo -- Unknown Posterior

I was using Hamiltonian Monte Carlo (HMC) to perform a model simulation. The model is for the timecourse fitting of two metabolites, and it has 6 parameters for a set of ODEs (see code). I assume they follow a multivariate normal distribution, but with unknown mean and covariance matrix. I also assume that the residual error follows a normal distribution. The problem is that HMC requires taking the derivative of the log posterior density. How can I derive the gradient analytically without knowing the mean and covariance? Many thanks!

function PLmat = model_ode(x,timevec,tofit)
 kpl=x(1);
 rho=x(2);
 Z=x(3);
 alpha=x(4);
 beta=x(5);
 t0=x(6);
 P0  = tofit(1,1);   %initial value 1
 L0  = tofit(1,2);   %initial value 2
 f=Z*gampdf(timevec-t0,alpha,beta)/sum(f);    %input function
 [~,PLmat] = ode15s(@(t,y)ODE(t,y,timevec,f,Z,rho,kpl),timevec,[P0;L0]);  
end

function dydt = ODE(t,y,ft,f,Z,rho,kpl)
 fin=interp1(ft,f,t);
 dydt = zeros(2,1);
 dydt(1)=-rho*y(1)-kpl*y(1)+fa;
 dydt(2)=-rho*y(2)+kpl*y(1);
end