Abstract
A model of an immunosensor is proposed based on a system of differential equations with time delay on a hexagonal lattice. The presented main result consists of conditions of local asymptotic stability of an endemic state. To obtain this result, the method of Lyapunov functionals is used. It combines the general approach to constructing Lyapunov functionals for predator-prey models and differential equations with time delay on a hexagonal lattice. A numerical example shows the influence of time delays on stability, namely, the transition from a stable focus to a limit cycle through a Hopf bifurcation occurs.
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