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In this article, we focus on solving a sequence of linear systems that have identical (or similar) coefficient matrices. For this type of problem, we investigate subspace correction (SC) and deflation methods, which use an auxiliary matrix (subspace) to accelerate the convergence of the iterative method. In practical simulations, these acceleration methods typically work well when the range of the auxiliary matrix contains eigenspaces corresponding to small eigenvalues of the coefficient matrix. We develop a new algebraic auxiliary matrix construction method based on error vector sampling in which eigenvectors with small eigenvalues are efficiently identified in the solution process. We use the generated auxiliary matrix for convergence acceleration in the following solution step. Numerical tests confirm that both SC and deflation methods with the auxiliary matrix can accelerate the solution process of the iterative solver. Furthermore, we examine the applicability of our technique to the estimation of the condition number of the coefficient matrix. We also present the algorithm of the preconditioned conjugate gradient method with condition number estimation. [ABSTRACT FROM AUTHOR]

Most vector control activities in urban areas are focused on household environments; however, information relating to infection risks in spaces other than households is poor, and the relative risk that these spaces represent has not yet been fully understood. We used data-driven simulations to investigate the importance of household and non-household environments for dengue entomological risk in two Kenyan cities where dengue circulation has been reported. Fieldwork was performed using four strategies that targeted different stages of mosquitoes: ovitraps, larval collections, Prokopack aspiration, and BG-sentinel traps. Data were analyzed separately between household and non-household environments to assess mosquito presence, the number of vectors collected, and the risk factors for vector presence. With these data, we simulated vector and human populations to estimate the parameter m and mosquito-to-human density in both household and non-household environments. Among the analyzed variables, the main difference was found in mosquito abundance, which was consistently higher in non-household environments in Kisumu but was similar in Ukunda. Risk factor analysis suggests that small, clean water-related containers serve as mosquito breeding places in households as opposed to the trash- and rainfall-related containers found in non-household structures. We found that the density of vectors (m) was higher in non-household than household environments in Kisumu and was also similar or slightly lower between both environments in Ukunda. These results suggest that because vectors are abundant, there is a potential risk of transmission in non-household environments; hence, vector control activities should take these spaces into account. [ABSTRACT FROM AUTHOR]

Most vector control activities in urban areas are focused on household environments; however, information relating to infection risks in spaces other than households is poor, and the relative risk that these spaces represent has not yet been fully understood. We used data-driven simulations to investigate the importance of household and non-household environments for dengue entomological risk in two Kenyan cities where dengue circulation has been reported. Fieldwork was performed using four strategies that targeted different stages of mosquitoes: ovitraps, larval collections, Prokopack aspiration, and BG-sentinel traps. Data were analyzed separately between household and non-household environments to assess mosquito presence, the number of vectors collected, and the risk factors for vector presence. With these data, we simulated vector and human populations to estimate the parameter m and mosquito-to-human density in both household and non-household environments. Among the analyzed variables, the main difference was found in mosquito abundance, which was consistently higher in non-household environments in Kisumu but was similar in Ukunda. Risk factor analysis suggests that small, clean water-related containers serve as mosquito breeding places in households as opposed to the trash- and rainfall-related containers found in non-household structures. We found that the density of vectors (m) was higher in non-household than household environments in Kisumu and was also similar or slightly lower between both environments in Ukunda. These results suggest that because vectors are abundant, there is a potential risk of transmission in non-household environments; hence, vector control activities should take these spaces into account.