The paper is devoted to the study of a new class of optimal control problems\ud
governed by the classical Moreau sweeping process with the new feature that the polyhe-\ud
dral moving set is not fixed while controlled by time-dependent functions. The dynamics of\ud
such problems is described by dissipative non-Lipschitzian differential inclusions with state\ud
constraints of equality and inequality types. It makes challenging and difficult their anal-\ud
ysis and optimization. In this paper we establish some existence results for the sweeping\ud
process under consideration and develop the method of discrete approximations that allows\ud
us to strongly approximate, in the W^{1,2} topology, optimal solutions of the continuous-type\ud
sweeping process by their discrete counterparts
Background: The wMel strain of Wolbachia has been successfully introduced into Aedes aegypti mosquitoes and subsequently shown to reduce transmission of dengue and other pathogens, under both laboratory and field conditions. Here we describe the entomological outcomes of wMel Wolbachia mosquito releases in two small communities in Nha Trang City in central Vietnam. Methods: The wMel strain of Wolbachia was backcrossed into local Aedes aegypti genotype and mosquito releases were undertaken by community members or by staff. Field monitoring was undertaken to track Wolbachia establishment in local Ae. aegypti mosquito populations. Ecological studies were undertaken to assess relationships between environmental factors and the spatial and temporal variability in Wolbachia infection prevalence in mosquitoes. Results: Releases of wMel Wolbachia Ae. aegypti mosquitoes in two small communities in Nha Trang City resulted in the initial establishment of Wolbachia in the local Ae. aegypti mosquito populations, followed by seasonal fluctuations in Wolbachia prevalence. There was significant small-scale spatial heterogeneity in Wolbachia infection prevalence in the Tri Nguyen Village site, resulting in the loss of wMel Wolbachia infection in mosquitoes in north and center areas, despite Wolbachia prevalence remaining high in mosquitoes in the south area. In the second site, Vinh Luong Ward, Wolbachia has persisted at a high level in mosquitoes throughout this site despite similar seasonal fluctuations in wMel Wolbachia prevalence. Conclusion: Seasonal variation in Wolbachia infection prevalence in mosquitoes was associated with elevated temperature conditions, and was possibly due to imperfect maternal transmission of Wolbachia. Heterogeneity in Wolbachia infection prevalence was found throughout one site, and indicates additional factors may influence Wolbachia establishment.
Background: The wMel strain of Wolbachia has been successfully introduced into Aedes aegypti mosquitoes and subsequently shown to reduce transmission of dengue and other pathogens, under both laboratory and field conditions. Here we describe the entomological outcomes of wMel Wolbachia mosquito releases in two small communities in Nha Trang City in central Vietnam. Methods: The wMel strain of Wolbachia was backcrossed into local Aedes aegypti genotype and mosquito releases were undertaken by community members or by staff. Field monitoring was undertaken to track Wolbachia establishment in local Ae. aegypti mosquito populations. Ecological studies were undertaken to assess relationships between environmental factors and the spatial and temporal variability in Wolbachia infection prevalence in mosquitoes. Results: Releases of wMel Wolbachia Ae. aegypti mosquitoes in two small communities in Nha Trang City resulted in the initial establishment of Wolbachia in the local Ae. aegypti mosquito populations, followed by seasonal fluctuations in Wolbachia prevalence. There was significant small-scale spatial heterogeneity in Wolbachia infection prevalence in the Tri Nguyen Village site, resulting in the loss of wMel Wolbachia infection in mosquitoes in north and center areas, despite Wolbachia prevalence remaining high in mosquitoes in the south area. In the second site, Vinh Luong Ward, Wolbachia has persisted at a high level in mosquitoes throughout this site despite similar seasonal fluctuations in wMel Wolbachia prevalence. Conclusion: Seasonal variation in Wolbachia infection prevalence in mosquitoes was associated with elevated temperature conditions, and was possibly due to imperfect maternal transmission of Wolbachia. Heterogeneity in Wolbachia infection prevalence was found throughout one site, and indicates additional factors may influence Wolbachia establishment.
This paper concerns optimal control problems for a class of sweeping processes governed by discontinuous unbounded differential inclusions that are described via normal cone mappings to controlled moving sets. Largely motivated by applications to hysteresis, we consider a general setting where moving sets are given as inverse images of closed subsets of finite-dimensional spaces under nonlinear differentiable mappings dependent on both state and control variables. Developing the method of discrete approximations and employing generalized differential tools of first-order and second-order variational analysis allow us to derive nondegenerated necessary optimality conditions for such problems in extended Euler-Lagrange and Hamiltonian forms involving the Hamiltonian maximization. The latter conditions of the Pontryagin Maximum Principle type are the first in the literature for optimal control of sweeping processes with control-dependent moving sets.
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