Optimal control-based vaccination and testing strategies for COVID-19

Optimal control of vaccination for an epidemic model with standard incidence rate

A critical challenge for diseases spread is the development of effective prevention and control measures while minimizing costs, representing the foremost priority. Unfortunately, research in this crucial area remains inadequately explored. Consequently, this paper addresses the issue by leveraging an SI reaction-diffusion epidemic model incorporating a logistic birth rate and standard incidence rate. Employing vaccination as a control variable and integrating sparse optimal control theory, the study elucidates the achievement of epidemic prevention and control through the optimization of resource allocation, emphasizing a perspective rooted in pattern structure transformation. On the one hand, we theoretically prove the existence of the optimal solutions, first-order necessary optimality conditions, and the sparsity properties. On the other hand, we use numerical simulations to verify the rationality of the control method and the effectiveness of the control strategy from three aspects of control effect, control error and control cost. In addition, tailored targeting options are proposed based on the economic status of each region, specifying the required inoculum amount for each moment. Ultimately, the study demonstrates the effectiveness of input vaccination in controlling epidemics in a majority of areas. In summary, this work offers crucial insights into the prevention and control of a non-quasimonotonic reaction-diffusion epidemic model.

Chance-constrained stochastic optimal control of epidemic models: A fourth moment method-based reformulation

This work proposes a methodology for the reformulation of chance-constrained stochastic optimal control problems that ensures reliable uncertainty management of epidemic outbreaks. Specifically, the chance constraints are reformulated in terms of the first four moments of the stochastic state variables through the so-called fourth moment method for reliability. Moreover, a spectral technique is employed to obtain surrogate models of the stochastic state variables, which enables the efficient computation of the required statistics. The practical implementation of the proposed approach is demonstrated via the optimal control of two different stochastic mathematical models of the COVID-19 transmission. The numerical experiments confirm that, unlike those reformulations based on the Chebyshev-Cantelli's inequality, the proposed method does not exhibit the undesired outcomes that are typically observed when a higher precision is required for the risk level associated to the given chance constraints.

Learning from the COVID-19 pandemic: A systematic review of mathematical vaccine prioritization models

As the world becomes ever more connected, the chance of pandemics increases as well. The recent COVID-19 pandemic and the concurrent global mass vaccine roll-out provides an ideal setting to learn from and refine our understanding of infectious disease models for better future preparedness. In this review, we systematically analyze and categorize mathematical models that have been developed to design optimal vaccine prioritization strategies of an initially limited vaccine. As older individuals are disproportionately affected by COVID-19, the focus is on models that take age explicitly into account. The lower mobility and activity level of older individuals gives rise to non-trivial trade-offs. Secondary research questions concern the optimal time interval between vaccine doses and spatial vaccine distribution. This review showcases the effect of various modeling assumptions on model outcomes. A solid understanding of these relationships yields better infectious disease models and thus public health decisions during the next pandemic.

Impact of immunity loss on the optimal vaccination strategy for an age-structured epidemiological model

The pursuit of effective vaccination strategies against COVID-19 remains a critical endeavour in global public health, particularly amidst challenges posed by immunity loss and evolving epidemiological dynamics. This study investigated optimal vaccination strategies by considering age structure, immunity dynamics, and varying maximal vaccination rates. To this end, we formulated an SEIR model stratified into $ n $ age classes, with the vaccination rate as an age-dependent control variable in an optimal control problem. We developed an objective function aimed at minimising critical infections while optimising vaccination efforts and then conducted rigorous mathematical analyses to ensure the existence and characterization of the optimal control. Using data from three countries with diverse age distributions, in expansive, constrictive, and stationary pyramids, we performed numerical simulations to evaluate the optimal age-dependent vaccination strategy, number of critical infections, and vaccination frequency. Our findings highlight the significant influence of maximal vaccination rates on shaping optimal vaccination strategies. Under constant maximal vaccination rates, prioritising age groups based on population demographics proves effective, with higher rates resulting in fewer critically infected individuals across all age distributions. Conversely, adopting age-dependent maximal vaccination rates, akin to the WHO strategy, may not always lead to the lowest critical infection peaks but offers a viable alternative in resource-constrained settings.

Predicting the transmission trends of COVID-19: an interpretable machine learning approach based on daily, death, and imported cases

COVID-19 is caused by the SARS-CoV-2 virus, which has produced variants and increasing concerns about a potential resurgence since the pandemic outbreak in 2019. Predicting infectious disease outbreaks is crucial for effective prevention and control. This study aims to predict the transmission patterns of COVID-19 using machine learning, such as support vector machine, random forest, and XGBoost, using confirmed cases, death cases, and imported cases, respectively. The study categorizes the transmission trends into the three groups: L0 (decrease), L1 (maintain), and L2 (increase). We develop the risk index function to quantify changes in the transmission trends, which is applied to the classification of machine learning. A high accuracy is achieved when estimating the transmission trends for the confirmed cases (91.5-95.5%), death cases (85.6-91.8%), and imported cases (77.7-89.4%). Notably, the confirmed cases exhibit a higher level of accuracy compared to the data on the deaths and imported cases. L2 predictions outperformed L0 and L1 in all cases. Predicting L2 is important because it can lead to new outbreaks. Thus, this robust L2 prediction is crucial for the timely implementation of control policies for the management of transmission dynamics.

Learning from the COVID-19 pandemic: a systematic review of mathematical vaccine prioritization models

As the world becomes ever more connected, the chance of pandemics increases as well. The recent COVID-19 pandemic and the concurrent global mass vaccine roll-out provides an ideal setting to learn from and refine our understanding of infectious disease models for better future preparedness. In this review, we systematically analyze and categorize mathematical models that have been developed to design optimal vaccine prioritization strategies of an initially limited vaccine. As older individuals are disproportionately affected by COVID-19, the focus is on models that take age explicitly into account. The lower mobility and activity level of older individuals gives rise to non-trivial trade-offs. Secondary research questions concern the optimal time interval between vaccine doses and spatial vaccine distribution. This review showcases the effect of various modeling assumptions on model outcomes. A solid understanding of these relationships yields better infectious disease models and thus public health decisions during the next pandemic.

A model-based strategy for the COVID-19 vaccine roll-out in the Philippines

COVID-19 has affected millions of people worldwide, causing illness and death, and disrupting daily life while imposing a significant social and economic burden. Vaccination is an important control measure that significantly reduces mortality if properly and efficiently distributed. In this work, an age-structured model of COVID-19 transmission, incorporating an unreported infectious compartment, is developed. Three age groups are considered: young (0-19 years), adult (20-64 years), and elderly (65+ years). The transmission rate and reporting rate are determined for each group by utilizing the number of COVID-19 cases in the National Capital Region in the Philippines. Optimal control theory is employed to identify the best vaccine allocation to different age groups. Further, three different vaccination periods are considered to reflect phases of vaccination priority groups: the first, second, and third account for the inoculation of the elderly, adult and elderly, and all three age groups, respectively. This study could guide in making informed decisions in mitigating a population-structured disease transmission under limited resources.

The relationship between controllability, optimal testing resource allocation, and incubation-latent period mismatch as revealed by COVID-19

The severe shortfall in testing supplies during the initial COVID-19 outbreak and ensuing struggle to manage the pandemic have affirmed the critical importance of optimal supply-constrained resource allocation strategies for controlling novel disease epidemics. To address the challenge of constrained resource optimization for managing diseases with complications like pre- and asymptomatic transmission, we develop an integro partial differential equation compartmental disease model which incorporates realistic latent, incubation, and infectious period distributions along with limited testing supplies for identifying and quarantining infected individuals. Our model overcomes the limitations of typical ordinary differential equation compartmental models by decoupling symptom status from model compartments to allow a more realistic representation of symptom onset and presymptomatic transmission. To analyze the influence of these realistic features on disease controllability, we find optimal strategies for reducing total infection sizes that allocate limited testing resources between 'clinical' testing, which targets symptomatic individuals, and 'non-clinical' testing, which targets non-symptomatic individuals. We apply our model not only to the original, delta, and omicron COVID-19 variants, but also to generically parameterized disease systems with varying mismatches between latent and incubation period distributions, which permit varying degrees of presymptomatic transmission or symptom onset before infectiousness. We find that factors that decrease controllability generally call for reduced levels of non-clinical testing in optimal strategies, while the relationship between incubation-latent mismatch, controllability, and optimal strategies is complicated. In particular, though greater degrees of presymptomatic transmission reduce disease controllability, they may increase or decrease the role of non-clinical testing in optimal strategies depending on other disease factors like transmissibility and latent period length. Importantly, our model allows a spectrum of diseases to be compared within a consistent framework such that lessons learned from COVID-19 can be transferred to resource constrained scenarios in future emerging epidemics and analyzed for optimality.

Interval type-2 Fuzzy control and stochastic modeling of COVID-19 spread based on vaccination and social distancing rates

BACKGROUND AND OBJECTIVE

Besides efforts on vaccine discovery, robust and intuitive government policies could also significantly influence the pandemic state. However, such policies require realistic virus spread models, and the major works on COVID-19 to date have been only case-specific and use deterministic models. Additionally, when a disease affects large portions of the population, countries develop extensive infrastructures to contain the condition that should adapt continuously and extend the healthcare system's capabilities. An accurate mathematical model that reasonably addresses these complex treatment/population dynamics and their corresponding environmental uncertainties is necessary for making appropriate and robust strategic decisions.

METHODS

Here, we propose an interval type-2 fuzzy stochastic modeling and control strategy to deal with the realistic uncertainties of pandemics and manage the size of the infected population. For this purpose, we first modify a previously established COVID-19 model with definite parameters to a Stochastic SEIAR (S2EIAR) approach with uncertain parameters and variables. Next, we propose to use normalized inputs, rather than the usual parameter settings in the previous case-specific studies, hence offering a more generalized control structure. Furthermore, we examine the proposed genetic algorithm-optimized fuzzy system in two scenarios. The first scenario aims to keep infected cases below a certain threshold, while the second addresses the changing healthcare capacities. Finally, we examine the proposed controller on stochasticity and disturbance in parameters, population sizes, social distance, and vaccination rate.

RESULTS

The results show the robustness and efficiency of the proposed method in the presence of up to 1% noise and 50% disturbance in tracking the desired size of the infected population. The proposed method is compared to Proportional Derivative (PD), Proportional Integral Derivative (PID), and type-1 fuzzy controllers. In the first scenario, both fuzzy controllers perform more smoothly despite PD and PID controllers reaching a lower mean squared error (MSE). Meanwhile, the proposed controller outperforms PD, PID, and the type-1 fuzzy controller for the MSE and decision policies for the second scenario.

CONCLUSIONS

The proposed approach explains how we should decide on social distancing and vaccination rate policies during pandemics against the prevalent uncertainties in disease detection and reporting.

Modeling the Impact of the Imperfect Vaccination of the COVID-19 with Optimal Containment Strategy

Since the beginning of the COVID-19 pandemic, vaccination has been the main strategy to contain the spread of the coronavirus. However, with the administration of many types of vaccines and the constant mutation of viruses, the issue of how effective these vaccines are in protecting the population is raised. This work aimed to present a mathematical model that investigates the imperfect vaccine and finds the additional measures needed to help reduce the burden of disease. We determine the R0 threshold of disease spread and use stability analysis to determine the condition that will result in disease eradication. We also fitted our model to COVID-19 data from Morocco to estimate the parameters of the model. The sensitivity analysis of the basic reproduction number, with respect to the parameters of the model, is simulated for the four possible scenarios of the disease progress. Finally, we investigate the optimal containment measures that could be implemented with vaccination. To illustrate our results, we perform the numerical simulations of optimal control.