Integrating Risk Assessment and Decision-Making Methods in Analyzing the Dynamics of COVID-19 Epidemics in Davao City, Mindanao Island, Philippines

The COVID-19 pandemic has become a public health crisis in the Philippines and the attention of national and local health authorities is focused on managing the fluctuating COVID-19 cases. This study presents a method that integrates risk management tools into health care decision-making processes to enhance the understanding and utilization of risk-based thinking in public health decision making. The risk assessment consists of the identification of the key risk factors of the COVID-19 contagion via bow-tie diagrams. Second, the safety controls for each risk factor relevant to the Davao City context are taken into account and are identified as barriers in the bow-tie. After which, the prioritization of the identified COVID-19 risks, as well as the effectiveness of the proposed interventions, is performed using the analytic hierarchy process. Consequently, the dynamics of COVID-19 management initiatives were explored using these priorities and a system of ordinary differential equations. Our results show that reducing the number of COVID-19 fatalities should be the top priority of the health authorities. In turn, we predict that the COVID-19 contagion can be controlled and eliminated in Davao city in three-month time after prioritizing the fatalities. In order to reduce the COVID-19 fatalities, health authorities should ensure an adequate number of COVID-ready ICU facilities. The general public, on the other hand, should follow medical and science-based advice and suspected and confirmed COVID-19 patients should strictly follow isolation protocols. Overall, an informed decision-making is necessary to avoid the unwanted consequences of an uncontrolled contagion.

Random fluctuations around a stable limit cycle in a stochastic system with parametric forcing

Many real populations exhibit stochastic behaviour that appears to have some periodicity. In terms of populations, these time series can occur as limit cycles that arise through seasonal variation of parameters such as, e.g., disease transmission rate. The general mathematical context is that of a stochastic differential system with periodic parametric forcing whose solution is a stochastically perturbed limit cycle. Earlier work identified the power spectral density (PSD) features of these fluctuations by computation of the autocorrelation function of the stochastic process and its transform. Here, we present an alternative analysis which shows that the structure of the fluctuations around the limit cycle is analogous to that of fluctuations about a fixed point. Furthermore, we show that these fluctuations can be expressed, approximately, as a factorization which reveals the combined frequencies of the limit cycle and the stochastic perturbation. This result, based on a new limit theorem near a Hopf point, yields an understanding of the previously found features of the PSD. Further insights are obtained from the corresponding stochastic equations for phase and amplitude.

Local perturbation analysis: a computational tool for biophysical reaction-diffusion models

Diffusion and interaction of molecular regulators in cells is often modeled using reaction-diffusion partial differential equations. Analysis of such models and exploration of their parameter space is challenging, particularly for systems of high dimensionality. Here, we present a relatively simple and straightforward analysis, the local perturbation analysis, that reveals how parameter variations affect model behavior. This computational tool, which greatly aids exploration of the behavior of a model, exploits a structural feature common to many cellular regulatory systems: regulators are typically either bound to a membrane or freely diffusing in the interior of the cell. Using well-documented, readily available bifurcation software, the local perturbation analysis tracks the approximate early evolution of an arbitrarily large perturbation of a homogeneous steady state. In doing so, it provides a bifurcation diagram that concisely describes various regimes of the model's behavior, reducing the need for exhaustive simulations to explore parameter space. We explain the method and provide detailed step-by-step guides to its use and application.

A model for intracellular actin waves explored by nonlinear local perturbation analysis

Waves and dynamic patterns in chemical and physical systems have long interested experimentalists and theoreticians alike. Here we investigate a recent example within the context of cell biology, where waves of actin (a major component of the cytoskeleton) and its regulators (nucleation promoting factors, NPFs) are observed experimentally. We describe and analyze a minimal reaction diffusion model depicting the feedback between signalling proteins and filamentous actin (F-actin). Using numerical simulation, we show that this model displays a rich variety of patterning regimes. A relatively recent nonlinear stability method, the Local Perturbation Analysis (LPA), is used to map the parameter space of this model and explain the genesis of patterns in various linear and nonlinear patterning regimes. We compare our model for actin waves to others in the literature, and focus on transitions between static polarization, transient waves, periodic wave trains, and reflecting waves. We show, using LPA, that the spatially distributed model gives rise to dynamics that are absent in the kinetics alone. Finally, we show that the width and speed of the waves depend counter-intuitively on parameters such as rates of NPF activation, negative feedback, and the F-actin time scale.