title: Optimal control analysis of malaria-schistosomiasis co-infection dynamics.
abstract: This paper presents a mathematical model for malaria--schistosomiasis co-infection in order to investigate their synergistic relationship in the presence of treatment. We first analyse the single infection steady states, then investigate the existence and stability of equilibria and then calculate the basic reproduction numbers. Both the single-infection models and the co-infection model exhibit backward bifurcations. We carrying out a sensitivity analysis of the co-infection model and show that schistosomiasis infection may not be associated with an increased risk of malaria. Conversely, malaria infection may be associated with an increased risk of schistosomiasis. Furthermore, we found that effective treatment and prevention of schistosomiasis infection would also assist in the effective control and eradication of malaria. Finally, we apply Pontryagin's Maximum Principle to the model in order to determine optimal strategies for control of both diseases.
authors.affiliation: Department of Mathematics, Vaal University of Technology, Andries Potgieter Boulevard, Vanderbijlpark, 1911, South Africa. email: kazeemoare@gmail.com.
authors.forename: Kazeem Oare
authors.initials: KO
authors.lastname: Okosun
authors.forename: Robert
authors.initials: R
authors.lastname: Smith
mesh_terms: D050936:Basic Reproduction Number; D060085:Coinfection; D006801:Humans; D008288:Malaria / Q000150:complications* / Q000188:drug therapy / Q000453:epidemiology / Q000517:prevention & control*; D008962:Models, Theoretical; D012552:Schistosomiasis / Q000150:complications* / Q000188:drug therapy / Q000453:epidemiology / Q000517:prevention & control*