title: Zoonotic visceral leishmaniasis transmission: modeling, backward bifurcation, and optimal control.
abstract: Visceral leishmaniasis (VL), a vector-borne disease caused by protozoan flagellates of the genus Leishmania, is transmitted by sand flies. After malaria, VL is the second-largest parasitic killer, responsible for an estimated 500,000 infections and 51,000 deaths annually worldwide. Mathematical models proposed for VL have included the impact of dogs versus wild canids in disease dissemination and models developed to assist in control approaches. However, quantitative conditions that are required to control or eradicate VL transmission are not provided and there are no mathematical methods proposed to quantitatively calculate optimal control strategies for VL transmission. The research objective of this work was to model VL disease transmission system (specifically Zoonotic VL), perform bifurcation analysis to discuss control conditions, and calculate optimal control strategies. Three time-dependent control strategies involving dog populations, sand fly population, and humans are mainly discussed. Another strategy sometimes used in attempts to control zoonotic VL transmission, dog culling, is also evaluated in this paper.
authors.affiliation: Department of Industrial and Manufacturing Systems Engineering, Kansas State University, 2022 Durland Hall, Manhattan, KS, 66506, USA.
authors.forename: Songnian
authors.initials: S
authors.lastname: Zhao
authors.affiliation: Department of Industrial and Manufacturing Systems Engineering, Kansas State University, 2010 Durland Hall, Manhattan, KS, 66506, USA.
authors.forename: Yan
authors.initials: Y
authors.lastname: Kuang
authors.affiliation: Department of Industrial and Manufacturing Systems Engineering, Kansas State University, 2018 Durland Hall, Manhattan, KS, 66506, USA. chw@ksu.edu.
authors.forename: Chih-Hang
authors.initials: CH
authors.lastname: Wu
authors.affiliation: Department of Industrial and Manufacturing Systems Engineering, Kansas State University, 2016 Durland Hall, Manhattan, KS, 66506, USA.
authors.forename: David
authors.initials: D
authors.lastname: Ben-Arieh
authors.affiliation: Department of Entomology, Kansas State University, 106 Waters Annex, Manhattan, KS, 66506, USA.
authors.forename: Marcelo
authors.initials: M
authors.lastname: Ramalho-Ortigao
authors.affiliation: Department of Industrial and Manufacturing Systems Engineering, Kansas State University, 2032 Durland Hall, Manhattan, Kansas, 66506, USA.
authors.forename: Kaiming
authors.initials: K
authors.lastname: Bi
mesh_terms: D000818:Animals; D004285:Dogs; D004812:Epidemiologic Methods; D006801:Humans; D007898:Leishmaniasis, Visceral / Q000517:prevention & control* / Q000635:transmission*; D008954:Models, Biological; D011576:Psychodidae
keywords: Backward bifurcation; Optimal control; Visceral leishmaniasis; Zoonotic disease transmission