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A delay fractional order model for the co-infection of malaria and HIV/AIDS

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Abstract

We propose a delay fractional order model for the co-infection of malaria and the human immunodeficiency virus, where personal protection and vaccination against malaria are considered. We compute the reproduction number of the model and study the stability of the disease free equilibrium. The numerical simulations of the model are performed for distinct values of the order of the fractional derivative, \(\alpha \in (0,1]\). We have also varied relevant parameters, such as the susceptibility to malaria of individuals showing symptoms of acquired immunodeficiency syndrome, \(\nu _2\), the degree of sexual activity due to malaria, \(\epsilon _2\), the human immunodeficiency virus related mortality due to co-infection, \(\psi \), and the level of personal protection against malaria, b. The outputs of the model are biologically meaningful.

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Acknowledgments

Authors wish to thank the Polytechnic of Porto, through the PAPRE Programa de Apoio à Publicação em Revistas Científicas de Elevada Qualidade for financial support. The first author was partially supported by CMUP (UID/MAT/00144/2013), which is funded by FCT (Portugal) with national (MEC) and European structural funds through the programs FEDER, under the partnership agreement PT2020. The research of AC was partially supported by a FCT Grant with reference SFRH/BD/96816/2013.

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Authors and Affiliations

  1. Faculdade de Ciências da Universidade do Porto, Rua do Campo Alegre s/n, 4440-452, Porto, Portugal

    Ana Carvalho

  2. School of Engineering, Polytechnic of Porto, Center of Mathematics of the University of Porto, Rua Dr António Bernardino de Almeida, 431, 4200-072, Porto, Portugal

    Carla M. A. Pinto

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  1. Ana Carvalho
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Correspondence to Carla M. A. Pinto.

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Carvalho, A., Pinto, C.M.A. A delay fractional order model for the co-infection of malaria and HIV/AIDS. Int. J. Dynam. Control 5, 168–186 (2017). https://doi.org/10.1007/s40435-016-0224-3

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  • DOI: https://doi.org/10.1007/s40435-016-0224-3

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