Dr. Wandi Ding, Middle Tennessee State University
Abstract: We present some optimal control work on mosquito-borne diseases: Malaria and West Nile Virus. First, a malaria transmission model with SEIR (susceptible-exposed-infected-recovered) classes for the human population, SEI (susceptible-exposed-infected) classes for the wild mosquitoes and an additional class for sterile mosquitoes is formulated. We derive the basic reproduction number of the infection. We formulate an optimal control problem in which the goal is to minimize both the infected human populations and the cost to implement two control strategies: the release of sterile mosquitoes and the usage of insecticide-treated nets to reduce the malaria transmission. Adjoint equations are derived, and the characterization of the optimal controls are established. Finally, we quantify the effectiveness of the two interventions aimed at limiting the spread of Malaria. A combination of both strategies leads to a more rapid elimination of the wild mosquito population that can suppress Malaria transmission.
Secondly, we consider a West-Nile Virus transmission model that describes the interaction between bird and mosquito populations (eggs, larvae, adults) and the dynamics for larvicide and adulticide, with impulse controls. We derive the basic reproduction number of the infection. We reformulate the impulse control problems as nonlinear optimization problems to derive adjoint equations and establish optimality conditions. We formulate three optimal control problems which seek to balance the cost of insecticide applications (both the timing and application level) with (1) the benefit of reducing the number of mosquitoes, (2) the benefit of reducing the disease burden, or (3) the benefit of preserving the healthy bird population. Numerical simulations are provided to illustrate the results of both models.
Bio: Dr. Ding is a professor in the Department of Mathematical Sciences at Middle Tennessee State University. She serves as faculty for the Interdisciplinary Ph.D. in Computational and Data Science Program, as well as the Honors College. She is an active learner and user of SIMIODE, which is a Community of Practice dedicated to using modeling to teach differential equations, and she serves as Board of Contributing Advisors for SIMIODE (2017 – current). She serves as co-president for Association for Women in Science (AWIS) Tennessee Chapter (2021-current). Dr. Ding's research interests include mathematical biology, computational biology, optimal control, mathematical modeling, ordinary and partial differential equations, difference equations, agent/individual-based modeling, and hybrid systems with applications to population dynamics, disease modeling and control, natural resource management, and systems biology. She is also interested in deep learning. Dr. Ding's research focuses on understanding the spatial and temporal patterns that arise in dynamic biological systems and, when possible, finding the best way to control the system. She served as the editor for Society for Mathematical Biology (SMB) Digest, 2013 – 2019, and has been the editor and guest editor for multiple journals.