Bull Math Biol
DOI 10.1007/s11538-017-0276-3
ORIGINAL ARTICLE
A Malaria Transmission Model with
Temperature-Dependent Incubation Period
Xiunan Wang
1
· Xiao-Qiang Zhao
1
Received: 20 December 2016 / Accepted: 29 March 2017
© Society for Mathematical Biology 2017
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 para-
sites, we formulate a delay differential equations model with a periodic time delay.
We derive the basic reproduction ratio R
0
and establish a threshold type result on
the global dynamics in terms of R
0
, that is, the unique disease-free periodic solution
is globally asymptotically stable if R
0
< 1; and the model system admits a unique
positive periodic solution which is globally asymptotically stable if R
0
> 1. Numeri-
cally, 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.
Keywords Vector-borne disease · Periodic delay · Basic reproduction ratio ·
Periodic solution · Global attractivity
This work is supported in part by the NSERC of Canada.
B Xiunan Wang
xiunan.wang@mun.ca
Xiao-Qiang Zhao
zhao@mun.ca
1
Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s,
NL A1C 5S7, Canada
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