The well-known mathematical model SEIR of the epidemic process is considered. The work is devoted to solving the optimisation problem in the scenario of countering the spread of the infectious disease. The purpose of the study: to find the cost-optimal control effect in a scenario of three applied measures: mobility restrictions, vaccination and preventive prophylactic measures, provided that the proportion of infected persons does not exceed the established value. The SEIR model was used to simulate the spread of infection. The decision was to solve the model approximately, not numerically, to make optimisation easier. The relevant propositions were taken: zero mortality and the models for considered factors (mobility restrictions, vaccination and preventive prophylactic influences) on the predicted state. The task of optimising the introduced measures is the task of finding such a set of model parameters that depend on the control actions, in which the minimum cost of measures is achieved while observing the condition of limiting the proportion of infected persons. The solution was carried out by the internal point method, the implementation of which turned out to be computationally efficient after a piecewise approximate solution for the zero-mortality SEIR model was found. Using the found approximate solution, an algorithm for searching for the optimal combination of infection containment measures with a limit on the number of infected is constructed. The algorithm found is a general way to optimise infection containment measures, provided that it develops according to the SEIR model with no mortality.