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

• Published in: International journal of dynamics and control Vol. 5; no. 1; pp. 168 - 186
• Main Authors: Carvalho, Ana, Pinto, Carla M. A.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2017; Springer Nature B.V
• Subjects: Acquired immune deficiency syndrome; AIDS; Complexity; Computer simulation; Control; Control and Systems Theory; Delay; Dynamical Systems; Engineering; HIV; Human immunodeficiency virus; Infections; Malaria; Mathematical models; Vibration; Viruses; Malaria; FHIV; Fractional order model
• ISSN: 2195-268X; 2195-2698
• DOI: 10.1007/s40435-016-0224-3

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, α ∈ ( 0 , 1 ] . We have also varied relevant parameters, such as the susceptibility to malaria of individuals showing symptoms of acquired immunodeficiency syndrome, ν 2 , the degree of sexual activity due to malaria, ϵ 2 , the human immunodeficiency virus related mortality due to co-infection, ψ , and the level of personal protection against malaria, b . The outputs of the model are biologically meaningful.