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 [20−25] • 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).

Mosquito vectors survey reveals new record of Culiseta subochrea in Al-Ahsa Oasis, Saudi Arabia

“…Aedes aegypti larval abundance also showed significant temporal variation, being usually more abundant in wet season compared to dry one [26]. Recently, mathematical assessment of the role of temperature and rainfall on mosquito population dynamics revealed positive correlation [39].…”

Mathematical analysis of a spatio‐temporal model for the population ecology of anopheles mosquito

“…We point out that the model extends some of the existing models in many respects. Unlike, it incorporates the gonotrophic cycle of adult female mosquito population. It further extends the model in by incorporating the more general egg oviposition function (a new birth rate function for modeling mosquito oviposition is proposed).…”

“…Remark From the ecological point of view, it is well known that the Maynard‐Smith‐Slatkin oviposition function is more suitable to model the mosquito oviposition rate, compared with the Malthus and Verhulst‐Pearl logistic functions . Therefore, the latter function will be our focus throughout the theoretical and numerical investigations in this work, with one of the main target of solving the opened problem in regarding the global asymptotic stability of the MPE. However, our results can readily apply to the Hassell oviposition function, whereas for Malthus and Verhulst‐Pearl functions, we refer the reader to …”

“…Therefore, the latter function will be our focus throughout the theoretical and numerical investigations in this work, with one of the main target of solving the opened problem in regarding the global asymptotic stability of the MPE. However, our results can readily apply to the Hassell oviposition function, whereas for Malthus and Verhulst‐Pearl functions, we refer the reader to …”

“…Thus, it is necessary to take into account all stages in the gonotrophic cycle (questing, resting, and breeding females) for the adult female mosquitoes in order to get insights into the behavior and dynamics of mosquitoes. The ultimate purpose of this paper is to extend the works, as well as the temporal models in into an advection‐reaction‐diffusion system in which spatial heterogeneity is taken into consideration explicitly. Heterogeneity in the behaviour of anopheles mosquitoes is present in all malaria endemic regions.…”