title: A Mathematical Study to Control Visceral Leishmaniasis: An Application to South Sudan.
abstract: In this manuscript, we propose and analyze a compartmental model of visceral leishmaniasis (VL). We model the human population with six compartments including asymptomatic, symptomatic and PKDL-infected, animal population as second host and sandfly population as the vector. Furthermore, the non-adult stage of the sandfly population is introduced in the system, which was not considered before in the literature. We show that the increase in the number of host of sandfly population generates a backward bifurcation. Thus, multiple hosts will cause disease persistence even if the basic reproduction number ([Formula: see text]) is below unity. We perform a sensitivity analysis of important model parameters with respect to some epidemiologically significant responses. We validate our model by calibrating it to weekly VL incidence data from South Sudan for the year 2013. We perform cost-effectiveness analysis on different interventions: treatment, non-adult control, adult control and their different layered combinations based on their implementation cost (in USD) and case reduction. We also use a global sensitivity analysis technique to understand the effect of important parameters of our model on the implementation cost of different controls. This cost-effectiveness study and cost-sensitivity analysis are relatively new in existing literature of this disease.
authors.affiliation: Agricultural and Ecological Research Unit, Indian Statistical Institute, 203, B. T. Road, Kolkata, West Bengal, 700108, India.
authors.forename: Indrajit
authors.initials: I
authors.lastname: Ghosh
authors.affiliation: Department of Mathematics, Dinabandhu Andrews College, Baishnabghata, P.O. Garia, Dist. 24 Paraganas (S), Kolkata, West Bengal, 700084, India.
authors.forename: Tridip
authors.initials: T
authors.lastname: Sardar
authors.affiliation: Agricultural and Ecological Research Unit, Indian Statistical Institute, 203, B. T. Road, Kolkata, West Bengal, 700108, India. joydev@isical.ac.in.
authors.forename: Joydev
authors.initials: J
authors.lastname: Chattopadhyay
mesh_terms: D000818:Animals; D003362:Cost-Benefit Analysis; D006790:Host-Parasite Interactions; D006801:Humans; D015994:Incidence; D007300:Insect Control / Q000191:economics; D007303:Insect Vectors / Q000469:parasitology; D007898:Leishmaniasis, Visceral / Q000453:epidemiology / Q000517:prevention & control* / Q000635:transmission; D055641:Mathematical Concepts; D008954:Models, Biological; D011576:Psychodidae / Q000469:parasitology; D000068037:South Sudan / Q000453:epidemiology
keywords: Backward bifurcation; Compartmental model; Cost-effectiveness analysis; Global sensitivity methods; Parameter estimation; Visceral Leishmaniasis