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

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...

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Bibliographic Details
Published inRussian journal of numerical analysis and mathematical modelling Vol. 31; no. 5; pp. 281 - 291
Main Author Pertsev, Nikolay V.
Format Journal Article
LanguageEnglish
Published De Gruyter 01.10.2016
Subjects
34E10
92C60
93D20
asymptotic behaviour of model solution
exponential estimates
HIV-infection
Mathematical model
nonsingular M-matrix
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Summary: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.
ISSN:0927-6467
1569-3988
DOI:10.1515/rnam-2016-0027