Implicit vector equilibrium problems with applications

Let X and Y be Hausdorff topological vector spaces, K a nonempty, closed, and convex subset of X, C: K--> 2(Y) a point-to-set mapping such that for any x is an element of K, C(x) is a pointed, closed, and convex cone in Y and int C(x) not equal 0. Given a mapping g : K --> K and a vector valued bifunction f : K x K - Y, we consider the implicit vector equilibrium problem (IVEP) of finding x* is an element of K such that f (g(x*), y) is not an element of - int C(x) for all y is an element of K. This problem generalizes the (scalar) implicit equilibrium problem and implicit variational inequality problem. We propose the dual of the implicit vector equilibrium problem (DIVEP) and establish the equivalence between (IVEP) and (DIVEP) under certain assumptions. Also, we give characterizations of the set of solutions for (IVP) in case of nonmonotonicity, weak C-pseudomonotonicity, C-pseudomonotonicity, and strict C-pseudomonotonicity, respectively. Under these assumptions, we conclude that the sets of solutions are nonempty, closed, and convex. Finally, we give some applications of (IVEP) to vector variational inequality problems and vector optimization problems. (C) 2003 Elsevier Science Ltd. All rights reserved.

Enhanced vector competence of Aedes aegypti (Diptera : Culicidae) from the torres strait compared with mainland Australia for dengue 2 and 4 viruses

Australian Aedes aegypti (L.) mosquitoes colonized from the Torres Strait and three mainland localities (Charters Towers, Townsville, and Cairns) were fed on blood suspensions containing dengue virus type 2 (DEN-2) or dengue virus type 4 (DEN-4). Variation was found in oral susceptibility to DEN-2 (59-99% infection) and DEN-4 (28-79% infection) among Ae. aegypti assayed for virus at 8, 12, 16, or 20 d after ingestion of infected blood. Torres Strait Ae. aegypti were the most susceptible to DEN-2 and were significantly more efficient in transmission to capillary tube at 16 d (76% transmission) than mainland Ae. aegypti populations (20-28% transmission). Torres Strait Ae. aegypti were also the most susceptible to DEN-4, although transmission did not vary significantly from mainland populations at 16 d (12% compared with 0-4%) or 20 d (16% compared with 4-16%). Disseminated infection (i.e., leg infection) with either DEN-2 or DEN-4 was not an accurate predictor of transmission potential. This study demonstrates differences among Australian Ae. aegypti populations in vector competence for DEN-2 and DEN-4. Torres Strait Ae. aegypti were more frequently infected and able to transmit DEN-2 at higher rates than mainland populations. These data indicate that the Torres Strait region is potentially more receptive to dengue transmission than mainland localities, a finding discussed with respect to past outbreaks.

Vector competence of Australian mosquitoes (Diptera : Culicidae) for Japanese encephalitis virus

Australian mosquitoes were evaluated for their ability to become infected with and transmit a Torres Strait strain of Japanese encephalitis virus. Mosquitoes, which were obtained from either laboratory colonies and collected using Centers for Disease Control and Prevention light traps baited with CO2 and octenol or reared from larvae, were infected by feeding on a blood/sucrose solution containing 10(4.5+/-0.1) porcine stable-equine kidney (PS-EK) tissue culture infectious dose(50)/ mosquito of the TS3306 virus strain. After 14 d, infection and transmission rates of 100% and 81%, respectively, were obtained for a southeast Queensland strain of Culex annulirostris Skuse, and 93% and 61%, respectively, for a far north Queensland strain. After 13 or more days, infection and transmission rates of > 90% and greater than or equal to 50%, respectively, were obtained for southeast Queensland strains of Culex sitiens Wiedemann and Culex quinquefasciatus Say, and a far north Queensland strain of Culex gelidus Theobald. Although infection rates were > 55%, only 17% of Ochlerotatus vigilax (Skuse) and no Cx. quinquefasciatus, collected from far north Queensland, transmitted virus. North Queensland strains of Aedes aegypti L., Ochlerotatus kochi (Donitz), and Verrallina funerea (Theobald) were relatively refractory to infection. Vertical transmission was not detected among 673 F, progeny of Oc. vigilax. Results of the current vector competence study, coupled with high field isolation rates, host feeding patterns and widespread distribution, confirm the status of Cx. annulirostris as the major vector of Japanese encephalitis virus in northern Australia. The relative roles of other species in potential Japanese encephalitis virus transmission cycles in northern Australia are discussed.