A Poisson Kalman Filter to Control the Dynamics of Neonatal Sepsis and Postinfectious Hydrocephalus
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Neonatal sepsis (NS) and resulting complications, such as postinfectious hydrocephalus (PIH), are a significant cause of neonatal and infant mortality throughout the developing world. Addressing this problem requires dynamical modeling and estimation of the true state of the disease using realistic data collection schemes, followed by optimal allocation of resources to control the disease with a combination of prevention and treatment. To address these issues, we first develop a compartmental model for non-communicable infections, which are especially common with NS. Then, we develop a novel optimal linear filter for Poisson observations, characteristic of infectious diseases, which model the number of patients recorded as presenting each day at hospitals. The classical Linear Quadratic Regulator is generalized to nonautonomous linear dynamics with mixed linear and quadratic cost functions, which better model real world costs. At each step we apply our methods to a case study of NS and PIH, using parameters estimated from publicly available data for Uganda. We demonstrate the effectiveness of our filter in numerical experiments and study the effect of the economic cost of NS and PIH on the optimal allocation of resources between prevention and treatment. Our approach is applicable to a broad range of disease dynamics, and can be extended to the inherent nonlinearities of communicable infectious diseases.
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