Coupling the Within-Host Process and Between-Host Transmission of COVID-19 Suggests Vaccination and School Closures are Critical.

Most models of COVID-19 are implemented at a single micro or macro scale, ignoring the interplay between immune response, viral dynamics, individual infectiousness and epidemiological contact networks. Here we develop a data-driven model linking the within-host viral dynamics to the between-host transmission dynamics on a multilayer contact network to investigate the potential factors driving transmission dynamics and to inform how school closures and antiviral treatment can influence the epidemic. Using multi-source data, we initially determine the viral dynamics and estimate the relationship between viral load and infectiousness. Then, we embed the viral dynamics model into a four-layer contact network and formulate an agent-based model to simulate between-host transmission. The results illustrate that the heterogeneity of immune response between children and adults and between vaccinated and unvaccinated infections can produce different transmission patterns. We find that school closures play a significant effect on mitigating the pandemic as more adults get vaccinated and the virus mutates. If enough infected individuals are diagnosed by testing before symptom onset and then treated quickly, the transmission can be effectively curbed. Our multiscale model reveals the critical role played by younger individuals and antiviral treatment with testing in controlling the epidemic.

Optimal Learning Control Scheme for Discrete-Time Systems With Nonuniform Trials.

In reality such as a rehabilitation training, a repetitive control is necessary but the operational lengths may be iteration varying due to health condition. For the issue, this article investigates an intermittent optimal learning control scheme that considers the partially available information for the learning processing. The performance index is to minimize the summation of the quadratic timewise tracking error and the amplified adjacent-iteration timewise inputs drift while the argument is assigned as the iteration-time-varying learning gain. By adopting the latest captured historical timewise input and the tracking error, the optimal learning gain is achieved. Theoretical analysis conveys that the timewise tracking error is asymptotically convergent along the iteration direction. In particular, the tracking error may vanish at some finite iteration if the amplifier is null. Numerical simulations for a permanent magnet linear motor model testify the validity and effectiveness of the proposed scheme.

Iterative Learning Control for Discrete-Time Systems With Full Learnability.

This article considers iterative learning control (ILC) for a class of discrete-time systems with full learnability and unknown system dynamics. First, we give a framework to analyze the learnability of the control system and build the relationship between the learnability of the control system and the input-output coupling matrix (IOCM). The control system has full learnability if and only if the IOCM is full-row rank and the control system has no learnability almost everywhere if and only if the rank of the IOCM is less than the dimension of system output. Second, by using the repetitiveness of the control system, some data-based learning schemes are developed. It is shown that we can obtain all the needed information on system dynamics through the developed learning schemes if the control system is controllable. Third, by the dynamic characteristics of system outputs of the ILC system along the iteration direction, we show how to use the available information of system dynamics to design the iterative learning gain matrix and the current state feedback gain matrix. And we strictly prove that the iterative learning scheme with the current state feedback mechanism can guarantee the monotone convergence of the ILC process if the IOCM is full-row rank. Finally, a numerical example is provided to validate the effectiveness of the proposed iterative learning scheme with the current state feedback mechanism.

Measles dynamics on network models with optimal control strategies.

To investigate the influences of heterogeneity and waning immunity on measles transmission, we formulate a network model with periodic transmission rate, and theoretically examine the threshold dynamics. We numerically find that the waning of immunity can lead to an increase in the basic reproduction number R 0 and the density of infected individuals. Moreover, there exists a critical level for average degree above which R 0 increases quicker in the scale-free network than in the random network. To design the effective control strategies for the subpopulations with different activities, we examine the optimal control problem of the heterogeneous model. Numerical studies suggest us no matter what the network is, we should implement control measures as soon as possible once the outbreak takes off, and particularly, the subpopulation with high connectivity should require high intensity of interventions. However, with delayed initiation of controls, relatively strong control measures should be given to groups with medium degrees. Furthermore, the allocation of costs (or resources) should coincide with their contact patterns.