Impulsive Neural Control to Schedule Antivirals and Immunomodulators for COVID-19.

New SARS-CoV-2 variants escaping the effect of vaccines are an eminent threat. The use of antivirals to inhibit the viral replication cycle or immunomodulators to regulate host immune responses can help to tackle the viral infection at the host level. To evaluate the potential use of these therapies, we propose the application of an inverse optimal neural controller to a mathematical model that represents SARS-CoV-2 dynamics in the host. Antiviral effects and immune responses are considered as the control actions. The variability between infected hosts can be large, thus, the host infection dynamics are identified based on a Recurrent High-Order Neural Network (RHONN) trained with the Extended Kalman Filter (EKF). The performance of the control strategies is tested by employing a Monte Carlo analysis. Simulation results present different scenarios where potential antivirals and immunomodulators could reduce the viral load.

Optimal control strategies to tailor antivirals for acute infectious diseases in the host: a study case of COVID-19

Several mathematical models in SARS-CoV-2 have shown how the target cell model can help to understand the spread of the virus in the host and how potential antiviral treatments can help to control the virus. Concepts as equilibrium and stability have shown to be crucial to qualitatively determine the best alternatives to schedule drugs, based on their effectiveness in reducing the viral infection and replication rates. Important biological events such as rebounds of the infections (when antivirals are incorrectly interrupted) can also be explained by means of a dynamic study of the target cell model. In this work a full characterization of the dynamical behavior of the target cell models under control actions is given and, based on this characterization, the optimal fixed-dose antiviral schedule that produces the smallest amount of dead cells (without viral load rebounds) is computed. The results of several simulations – performed by considering real patient data – show the potential benefits of both the model characterization and the control strategy. © 2022 Elsevier Inc. All rights reserved.

Switching Logistic Maps to Design Cycling Approaches Against Antimicrobial Resistance

Antimicrobial resistance is a major threat to global health, in particular, new SARS-CoV-2 variants during the COVID-19 pandemic. Scheduling cycling therapies by targeting phenotypic states associated with specific mutations can help us to eradicate pathogenic variants. In this paper, we introduce a logistic switching model to mutation networks of collateral resistance. We found conditions for which the unstable zero-equilibrium of the logistic maps can be stabilized through a switching signal. That is, persistent populations can be eradicated through tailored switching regimes. Starting from an optimal-control formulation, the switching policies show their potential in the stabilization of the zero-equilibrium for dynamics governed by logistic maps. Simulation results show the applicability of Parrondo's Paradox to design cycling therapies against drug resistance.

Inverse optimal control for positive impulsive systems toward personalized therapeutic regimens

Infectious diseases are latent threats to humankind. Control theoretical approaches can help practitioners to advance the scheduling of drugs. For the case of infectious diseases, it is not possible to keep continuous flow of drug administration over all time-steps, thus the action of the control input has to be restricted at some of the kth instants. This paper presents the adaptation of inverse optimal control to positive impulsive systems in discrete-time to schedule therapies. The properties of positive systems are used to simplify the control design. Thus, the problem of scheduling therapies in infectious diseases is illustrated with influenza and COVID-19. Numerical results show the applicability of the control algorithms. © 2022 John Wiley & Sons Ltd.

Neural inverse optimal control applied to design therapeutic options for patients with COVID-19

In this paper we apply an inverse optimal controller (IOC) based on a control Lyapunov function (CLF) to schedule theoretical therapies for the novel coronavirus disease (COVID-19). This controller can represent the viral dynamics of Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) in the host. The virus dynamics consider the antiviral effects and immune responses as control inputs. The proposed controller is based on a Recurrent High Order Neural Network (RHONN) used as an identifier trained with Extended Kalman Filter (EKF). Simulations show that applying treatment 2 days post symptoms would not significantly alter the viral load. The proposed controller to stimulate the immune response displays a better effectiveness compared to the effectiveness displayed by the antiviral effects.

Model predictive control for optimal social distancing in a type SIR-switched model

Social distancing strategies have been adopted by governments to manage the COVID-19 pandemic, since the first outbreak began. However, further epidemic waves keep out the return of economic and social activities to their standard levels of intensity. Social distancing interventions based on control theory are needed to consider a formal dynamic characterization of the implemented SIR-type model to avoid unrealistic objectives and prevent further outbreaks. The objective of this work is twofold: to fully understand some dynamical aspects of SIR-type models under control actions (associated with second waves) and, based on it, to propose a switching non-linear model predictive control that optimize the non-pharmaceutical measures strategy. Opposite to other strategies, the objective here is not just to minimize the number of infected individuals at any time, but to minimize the final size of the epidemic while minimizing the time of social restrictions and avoiding the infected prevalence peak to overpass a maximum established by the healthcare system capacity. Simulations illustrate the benefits of the aforementioned proposal. Copyright (C) 2021 The Authors.

Modeling SARS-CoV-2: Mitigation Interventions and Increased Mobility Events

From the beginning of the SARS-CoV-2 pandemic, mathematical models have been developed to describe, predict, and control its evolution. This chapter presents a set of useful mathematical tools to understand the epidemic dynamics. First, to obtain a rough approximation to the magnitude of the epidemic, the basic and effective reproduction numbers are estimated. Then, several growth models are applied to estimate the peak and final size of the epidemic. The results show that mitigation measures were able to flatten the epidemic curve, at the cost of extending it more than expected. Nonetheless, these heuristic models have limitations. Thus a mechanistic Kermack-McKendrick model is used to explore transmission and superspreading events. Our results show that these events can delay the peak incidence or drive the epidemic into a long plateau with relatively constant but high incidence. This highlights the need to monitor and anticipate atypical mobility events. Also, our projections of the pandemic trend for the last part of 2020 and the beginning of 2021, show that temporary immunity and an increase in the effective contact rate may generate an epidemic rebound by the end of 2020. Data from Mexico is used to exemplify the estimation and limitations of all the models. Although Mexico is our case study, the methodology can be extended to other regions. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Neural Control for Epidemic Model of Covid-19 with a Complex Network Approach

This paper presents the mathematical model Susceptible-Infected-Recovered SIR with parameters that describe the COVID-19 dynamics. This model is based on a system of ordinary differential equations in which appropriate conditions and starting parameter values such as transmission rates and recovery rates are considered known. These parameters are utilized to obtain a simulation of COVID-19 behavior, in order to establish a possible solution to avoid a greater chance of disease transmission. On the proposed scheme, we use a neural impulsive inverse optimal control for a complex network in which the dynamic of each node is a discrete version of SIR model that describe the dynamics of COVID-19. The neural network is trained with an extended Kalmans filter and is used as a neural identifier for the selected nodes of the system. The control law used represents a hypothetical treatment for COVID-19. This work aims to simulate the interaction of different populations during an epidemic outbreak in which populations are represented by the complex network nodes

Epidemiological Characteristics of COVID-19 in Mexico and the Potential Impact of Lifting Confinement Across Regions

The novel coronavirus SARS-CoV-2 has paralyzed our societies, leading to self-isolation and quarantine for several days. As the 10th most populated country in the world, Mexico is on a major threat by COVID-19 due to the limitations of intensive care capacities, about 1.5 hospital beds for every 1,000 citizens. In this paper, we characterize the COVID-19 pandemic in Mexico and projected different scenarios to evaluate sharp or gradual quarantine lifting strategies. Mexican government relaxed strict social distancing regulations on June 1, 2020, deriving to pandemic data with large fluctuations and uncertainties of the tendency of the pandemic in Mexico. Our results suggest that lifting social confinement must be gradually sparse while maintaining a decentralized region strategy among the Mexican states. To substantially lower the number of infections, simulations highlight that a fraction of the population that represents the elderly should remain in social confinement (approximately 11.3% of the population);a fraction of the population that represents the confined working class (roughly 27% of the population) must gradually return in at least four parts in consecutive months;and to the last a fraction of the population that assumes the return of students to schools (about 21.7%). As the epidemic progresses, deconfinement strategies need to be continuously re-adjusting with the new pandemic data. All mathematical models, including ours, are only a possibility of many of the future, however, the different scenarios that were developed here highlight that a gradual decentralized region deconfinement with a significant increase in healthcare capacities is paramount to avoid a high death toll in Mexico. ©, Copyright © Azanza Ricardo and Hernandez-Vargas.