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Equations of a continuous-discrete mathematical model describing the propagation of HIV infection among the population of several regions are presented. The model equations take into account the reproduction and migration of the population, the risk of infection of individuals from different social groups, an impulse change in the number of individuals at discrete time moments under the action of various factors. The results of the study of the model solutions are also presented. We obtain conditions for the model parameters and initial data that provide the existence of solutions interpreted as full eradication of HIV infection in all considered regions or maintenance of sizes of groups of infected individuals at some acceptable level. The solutions analysis uses the monotone operators method and properties of nonsingular M-matrices.

Study of solutions of a continuous-discrete model of HIV infection spread