title: Modeling schistosomiasis and HIV/AIDS codynamics.
abstract: We formulate a mathematical model for the cointeraction of schistosomiasis and HIV/AIDS in order to assess their synergistic relationship in the presence of therapeutic measures. Comprehensive mathematical techniques are used to analyze the model steady states. The disease-free equilibrium is shown to be locally asymptotically stable when the associated disease threshold parameter known as the basic reproduction number for the model is less than unity. Centre manifold theory is used to show that the schistosomiasis-only and HIV/AIDS-only endemic equilibria are locally asymptotically stable when the associated reproduction numbers are greater than unity. The impact of schistosomiasis and its treatment on the dynamics of HIV/AIDS is also investigated. To illustrate the analytical results, numerical simulations using a set of reasonable parameter values are provided, and the results suggest that schistosomiasis treatment will always have a positive impact on the control of HIV/AIDS.
authors.affiliation: Modelling Biomedical Systems Research Group, Department of Applied Mathematics, National University of Science and Technology, P.O. Box 939 Ascot, Bulawayo, Zimbabwe. steadymushaya@gmail.com
authors.forename: S
authors.initials: S
authors.lastname: Mushayabasa
authors.forename: C P
authors.initials: CP
authors.lastname: Bhunu
mesh_terms: D000465:Algorithms; D050936:Basic Reproduction Number; D003198:Computer Simulation; D018562:Disease Transmission, Infectious / Q000517:prevention & control; D015658:HIV Infections / Q000150:complications* / Q000188:drug therapy / Q000517:prevention & control / Q000635:transmission / Q000821:virology*; D006801:Humans; D008954:Models, Biological; D015995:Prevalence; D012552:Schistosomiasis / Q000150:complications* / Q000188:drug therapy / Q000469:parasitology* / Q000635:transmission