title: Mathematical assessment of the role of temperature and rainfall on mosquito population dynamics.
abstract: A new stage-structured model for the population dynamics of the mosquito (a major vector for numerous vector-borne diseases), which takes the form of a deterministic system of non-autonomous nonlinear differential equations, is designed and used to study the effect of variability in temperature and rainfall on mosquito abundance in a community. Two functional forms of eggs oviposition rate, namely the Verhulst-Pearl logistic and Maynard-Smith-Slatkin functions, are used. Rigorous analysis of the autonomous version of the model shows that, for any of the oviposition functions considered, the trivial equilibrium of the model is locally- and globally-asymptotically stable if a certain vectorial threshold quantity is less than unity. Conditions for the existence and global asymptotic stability of the non-trivial equilibrium solutions of the model are also derived. The model is shown to undergo a Hopf bifurcation under certain conditions (and that increased density-dependent competition in larval mortality reduces the likelihood of such bifurcation). The analyses reveal that the Maynard-Smith-Slatkin oviposition function sustains more oscillations than the Verhulst-Pearl logistic function (hence, it is more suited, from ecological viewpoint, for modeling the egg oviposition process). The non-autonomous model is shown to have a globally-asymptotically stable trivial periodic solution, for each of the oviposition functions, when the associated reproduction threshold is less than unity. Furthermore, this model, in the absence of density-dependent mortality rate for larvae, has a unique and globally-asymptotically stable periodic solution under certain conditions. Numerical simulations of the non-autonomous model, using mosquito surveillance and weather data from the Peel region of Ontario, Canada, show a peak mosquito abundance for temperature and rainfall values in the range [Formula: see text]C and [15-35] mm, respectively. These ranges are recorded in the Peel region between July and August (hence, this study suggests that anti-mosquito control effects should be intensified during this period).
authors.affiliation: School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona, 85287-1804, USA.|Mathematics and Statistics Department, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Kingdom of Saudi Arabia.
authors.forename: Ahmed
authors.initials: A
authors.lastname: Abdelrazec
authors.affiliation: School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona, 85287-1804, USA. agumel@asu.edu.
authors.forename: Abba B
authors.identifier: 0000-0002-8413-1248
authors.initials: AB
authors.lastname: Gumel
mesh_terms: D000818:Animals; D003198:Computer Simulation; D009033:Culicidae / Q000502:physiology; D005260:Female; D055641:Mathematical Concepts; D008954:Models, Biological; D000072138:Mosquito Vectors / Q000502:physiology; D017711:Nonlinear Dynamics; D009864:Ontario; D010058:Oviposition; D011157:Population Dynamics / Q000706:statistics & numerical data; D011891:Rain; D013696:Temperature
keywords: Autonomous and non-autonomous model; Climate change; Culex; Hopf bifurcation; Mosquitoes