https://doi.org/10.1140/epjp/i2017-11625-3
Regular Article
On the dynamics of HIV-AIDS and cryptosporidiosis
1
Department of Mathematics, Vaal University of Technology, Vanderbijlpark, South Africa
2
Department of Mathematics, City University of Science and Information Technology, 2500, Khyber Pakhtunkhwa, Pakistan
3
Department of Mathematics and Statistics, Kumasi Technical University, Kumasi, Ghana
4
Department of Mathematical Sciences, Federal University of Technology, Akure, Nigeria
* e-mail: altafdir@gmail.com
Received:
10
June
2017
Accepted:
30
June
2017
Published online:
25
August
2017
This paper seeks to examine a mathematical model for cryptosporidiosis-HIV co-infection, in order to explore their synergistic relationship in the presence of prevention and treatment. Firstly, we investigate the sub-models and their steady states properties. They are found to be locally and globally stable. Thereafter, the steady states of the co-infected model waswere studied and itthey proved to exhibit backward bifurcation phenomena. Furthermore, we incorporate time-dependent controls in the model and apply Pontryagin’s maximum principle, so that we can determine the best optimal strategy to control the co-infected diseases. Finally, we present the numerical results, which show that the best strategy to control co-infection is to combine all the five controls at the same time.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, 2017