Recovery of compartment model parameters of dynamical systems for the epidemiological SIR model

Background and Objectives: In problems where the model of dynamical system is known and the parameters need to be determined, researchers most often encounter the problem of "getting stuck" in local minima of the cost function. Most known methods do not guarantee finding the global minimum, although they increase the probability of finding it. A known method of avoiding local maxima, which consists of simultaneously using several cost functions that behave differently in the vicinity of local minima, detecting the minimum as local, in some cases does not find a way to leave the region of the local minimum of the cost function. In this paper, we propose an improvement in the latter method, which allows finding the global minimum with a higher probability. Materials and Methods: In this paper, 4 different error values were calculated at each iteration of the parameter selection algorithm. The parameter values were saved when at least one of the cost functions reaches a new minimum value. Both the parameters were varied, and the random choice between the saved sets of parameters corresponding to the smallest value of at least one of the cost functions was made, when the procedure is “getting stuck” in local minima. Results: An improved algorithm for estimating the values of control parameters of ordinary differential equation models has been presented. The method demonstrates good results in restoring the parameters of the considered dynamical system both in the case of steady-state solutions different from the equilibrium state and in the case of transient processes. Conclusion: As the results of numerical modeling using the described algorithm have shown, preserving several sets of parameters that correspond to the best values of error values allows us to avoid local minima of cost functions with a higher probability in the presence of noise.