title: A Malaria Transmission Model with Temperature-Dependent Incubation Period.
abstract: Malaria is an infectious disease caused by Plasmodium parasites and is transmitted among humans by female Anopheles mosquitoes. Climate factors have significant impact on both mosquito life cycle and parasite development. To consider the temperature sensitivity of the extrinsic incubation period (EIP) of malaria parasites, we formulate a delay differential equations model with a periodic time delay. We derive the basic reproduction ratio [Formula: see text] and establish a threshold type result on the global dynamics in terms of [Formula: see text], that is, the unique disease-free periodic solution is globally asymptotically stable if [Formula: see text]; and the model system admits a unique positive periodic solution which is globally asymptotically stable if [Formula: see text]. Numerically, we parameterize the model with data from Maputo Province, Mozambique, and simulate the long-term behavior of solutions. The simulation result is consistent with the obtained analytic result. In addition, we find that using the time-averaged EIP may underestimate the basic reproduction ratio.
authors.affiliation: Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL, A1C 5S7, Canada. xiunan.wang@mun.ca.
authors.forename: Xiunan
authors.identifier: 0000-0002-3822-6334
authors.initials: X
authors.lastname: Wang
authors.affiliation: Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL, A1C 5S7, Canada.
authors.forename: Xiao-Qiang
authors.initials: XQ
authors.lastname: Zhao
mesh_terms: D000818:Animals; D000852:Anopheles / Q000469:parasitology; D050936:Basic Reproduction Number; D003198:Computer Simulation; D005260:Female; D006801:Humans; D055256:Infectious Disease Incubation Period; D008288:Malaria / Q000453:epidemiology / Q000469:parasitology / Q000635:transmission*; D055641:Mathematical Concepts; D008954:Models, Biological; D000072138:Mosquito Vectors / Q000469:parasitology; D009073:Mozambique / Q000453:epidemiology; D010961:Plasmodium / Q000254:growth & development; D013696:Temperature
keywords: Basic reproduction ratio; Global attractivity; Periodic delay; Periodic solution; Vector-borne disease