ABSTRACT
A new deterministic model for the population biology of immature and mature mosquitoes is designed and used to assess the impact of temperature and rainfall on the abundance of mosquitoes in a community. The trivial equilibrium of the model is globally-asymptotically stable when the associated vectorial reproduction number (R0) is less than unity. In the absence of density-dependence mortality in the larval stage, the autonomous version of the model has a unique and globally-asymptotically stable non-trivial equilibrium whenever 1 andlt;R0 andlt;RC0 (this equilibrium bifurcates into a limit cycle, via a Hopf bifurcation at R0=RC0). Numerical simulations of the weather-driven model, using temperature and rainfall data from three cities in Sub-Saharan Africa (Kwazulu Natal, South Africa; Lagos, Nigeria; and Nairobi, Kenya), show peak mosquito abundance occurring in the cities when the mean monthly temperature and rainfall values lie in the ranges [22-25]0C, [98-121] mm; [24-27]0C, [113-255] mm and [20.5-21.5]0C, [70-120] mm, respectively (thus, mosquito control efforts should be intensified in these cities during the periods when the respective suitable weather ranges are recorded).
Subject(s)
Culicidae/physiology , Malaria/epidemiology , Malaria/transmission , Weather , Aedes , Africa South of the Sahara , Algorithms , Animals , Computer Simulation , Culex , Disease Vectors , Ecology , Female , Humans , Kenya , Male , Models, Statistical , Nigeria , Population Dynamics , South Africa , TemperatureABSTRACT
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).
Subject(s)
Culicidae , Models, Biological , Animals , Computer Simulation , Culicidae/physiology , Female , Mathematical Concepts , Mosquito Vectors/physiology , Nonlinear Dynamics , Ontario , Oviposition , Population Dynamics/statistics & numerical data , Rain , TemperatureABSTRACT
A deterministic model for the transmission dynamics of dengue fever is formulated to study, with a nonlinear recovery rate, the impact of available resources of the health system on the spread and control of the disease. Model results indicate the existence of multiple endemic equilibria, as well as coexistence of an endemic equilibrium with a periodic solution. Additionally, our model exhibits the phenomenon of backward bifurcation. The results of this study could be helpful for public health authorities in their planning of a proper resource allocation for the control of dengue transmission.
Subject(s)
Dengue/transmission , Health Resources , Models, Theoretical , Public Health , Dengue/prevention & control , HumansABSTRACT
There are more than 300 avian species that can transmit West Nile virus (WNv). In general, the corvid and non-corvid families of birds have different responses to the virus, with corvids suffering a higher disease-induced mortality rate. By taking both corvids and non-corvids as the primary reservoir hosts and mosquitoes as vectors; we formulate and study a system of ordinary differential equations to model a single season of the transmission dynamics of WNv in the mosquito-bird cycle. We calculate the basic reproduction number and analyze the existence and stability of the equilibria. The existence of a backward bifurcation gives a further sub-threshold condition beyond the basic reproduction number for the spread of the virus. We also discuss the role of corvids and non-corvids in spreading the virus. We conclude that knowledge of the relative abundance of corvid bird species and other mammals assist us in accurate estimation of the epidemic of WNv.
