Control of the immune response by a threshold automata model on a lattice

The KUT mean-field model for the immune response is generalized on a lattice, using boolcan and threshold automata. It is shown that the lattice model can exhibit properties that the mean-field model cannot, even if the biological meaning of the lattice geometry is dubious. The attractors of the mean-field model become unstable under mixing of populations and the system may reach the paralysis state instead of the memory, vaccinated. The probability of vaccination is calculated analytically and checked numerically. A threshold automata model, which includes interactions with the antigen and uses random neighbours and random time delays, is proposed, allowing control of the immune response by the concentration of antigen. Finally, quantitative results of the dynamics are given using the model itself, unlike previous works that used differential equations. The numerical results show low- and high-dose paralysis versus medium-dose vaccination.