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A stochastic analysis of the impact of fluctuations in the environment on pre-exposure prophylaxis for HIV infection

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Abstract

We propose a stochastic model for HIV/AIDS transmission where pre-exposure prophylaxis is considered as a prevention measure for new HIV infections. A white noise is introduced into the model, representing fluctuations in the environment that manifest themselves on the transmission coefficient rate. We prove the existence and uniqueness of a global positive solution of the stochastic model and establish conditions under which extinction and persistence in mean hold. Numerical simulations are provided which illustrate the theoretical results, and conclusions are derived on the impact of the fluctuations in the environment on the number of the susceptible individuals that are under pre-exposure prophylaxis.

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Acknowledgements

The authors are very grateful to the anonymous reviewers whose comments greatly improved the presentation of the paper. Silva was supported by the Portuguese Foundation for Science and Technology (FCT) within projects UID/MAT/04106/2019 (CIDMA) and PTDC/EEI-AUT/2933/2014 (TOCCATA), funded by Project 3599 - Promover a Produção Científica e Desenvolvimento Tecnológico e a Constituição de Redes Temáticas and FEDER funds through COMPETE 2020, Programa Operacional Competitividade e Internacionalização (POCI). Silva was also supported by national funds (OE), through FCT, I.P., in the scope of the framework contract foreseen in the numbers 4, 5 and 6 of the article 23, of the Decree-Law 57/2016, of August 29, changed by Law 57/2017, of July 19. Djordjevic was supported by Grant No 174007 of MNTRS. The authors are also grateful to the support of the COST Action CA16227 - Investigation and Mathematx ical Analysis of Avant-garde Disease Control via Mosquito Nano-Tech-Repellents (WG2 on “Structured Models & Optimal Control”).

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Authors and Affiliations

  1. Faculty of Science and Mathematics, University of Niš, Višegradska 33, Niš, 18000, Serbia

    Jasmina Djordević

  2. Department of Mathematics, Center for Research and Development in Mathematics and Applications (CIDMA), University of Aveiro, 3810-193, Aveiro, Portugal

    Cristiana J. Silva

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  1. Jasmina Djordević
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  2. Cristiana J. Silva
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Correspondence to Cristiana J. Silva.

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Communicated by T. Veloz.

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Djordević, J., Silva, C.J. A stochastic analysis of the impact of fluctuations in the environment on pre-exposure prophylaxis for HIV infection. Soft Comput 25, 6731–6743 (2021). https://doi.org/10.1007/s00500-019-04611-1

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  • DOI: https://doi.org/10.1007/s00500-019-04611-1

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