Determination of an optimal control strategy for vaccine administration in COVID-19 pandemic treatment

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 Modeling Study on the Effect of Interstate Mobility Restrictions on the SARS-CoV-2 Pandemic

Mobility is a crucial element in comprehending the possible expansion of the transmission chain in an epidemic. In the initial phases, strategies for containing cases can be directly linked to population mobility restrictions, especially when only non-pharmaceutical measures are available. During the pandemic of COVID-19 in Brazil, mobility limitation measures were strongly opposed by a large portion of the population. Hypothetically, if the population had supported such measures, the sharp rise in the number of cases could have been suppressed. In this context, computational modeling offers systematic methods for analyzing scenarios about the development of the epidemiological situation taking into account specific conditions. In this study, we examine the impacts of interstate mobility in Brazil. To do so, we develop a metapopulational model that considers both intra and intercompartmental dynamics, utilizing graph theory. We use a parameter estimation technique that allows us to infer the effective reproduction number in each state and estimate the time-varying transmission rate. This makes it possible to investigate scenarios related to mobility and quantify the effect of people moving between states and how certain measures to limit movement might reduce the impact of the pandemic. Our results demonstrate a clear association between the number of cases and mobility, which is heightened when states are closer to each other. This serves as a proof of concept and shows how reducing mobility in more heavily trafficked areas can be more effective.

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.

An Epidemic Model with Infection Age and Vaccination Age Structure

A model of epidemic dynamics is developed that incorporates continuous variables for infection age and vaccination age. The model analyzes pre-symptomatic and symptomatic periods of an infected individual in terms of infection age. This property is shown to be of major importance in the severity of the epidemic, when the infectious period of an infected individual precedes the symptomatic period. The model also analyzes the efficacy of vaccination in terms of vaccination age. The immunity to infection of vaccinated individuals varies with vaccination age and is also of major significance in the severity of the epidemic. Application of the model to the 2003 SARS epidemic in Taiwan and the COVID-19 epidemic in New York provides insights into the dynamics of these diseases. It is shown that the SARS outbreak was effectively contained due to the complete overlap of infectious and symptomatic periods, allowing for the timely isolation of affected individuals. In contrast, the pre-symptomatic spread of COVID-19 in New York led to a rapid, uncontrolled epidemic. These findings underscore the critical importance of the pre-symptomatic infectious period and the vaccination strategies in influencing the dynamics of an epidemic.

Introduction to Computational Biomedicine

The domain of computational biomedicine is a new and burgeoning one. Its areas of concern cover all scales of human biology, physiology, and pathology, commonly referred to as medicine, from the genomic to the whole human and beyond, including epidemiology and population health. Computational biomedicine aims to provide high-fidelity descriptions and predictions of the behavior of biomedical systems of both fundamental scientific and clinical importance. Digital twins and virtual humans aim to reproduce the extremely accurate duplicate of real-world human beings in cyberspace, which can be used to make highly accurate predictions that take complicated conditions into account. When that can be done reliably enough for the predictions to be actionable, such an approach will make an impact in the pharmaceutical industry by reducing or even replacing the extremely laboratory-intensive preclinical process of making and testing compounds in laboratories, and in clinical applications by assisting clinicians to make diagnostic and treatment decisions.

The hammer and the jab: Are COVID-19 lockdowns and vaccinations complements or substitutes?

The COVID-19 pandemic has devastated lives and economies around the world. Initially a primary response was locking down parts of the economy to reduce social interactions and, hence, the virus' spread. After vaccines have been developed and produced in sufficient quantity, they can largely replace broad lock downs. This paper explores how lockdown policies should be varied during the year or so gap between when a vaccine is approved and when all who wish have been vaccinated. Are vaccines and lockdowns substitutes during that crucial time, in the sense that lockdowns should be reduced as vaccination rates rise? Or might they be complementary with the prospect of imminent vaccination increasing the value of stricter lockdowns, since hospitalization and death averted then may be permanently prevented, not just delayed? We investigate this question with a simple dynamic optimization model that captures both epidemiological and economic considerations. In this model, increasing the rate of vaccine deployment may increase or reduce the optimal total lockdown intensity and duration, depending on the values of other model parameters. That vaccines and lockdowns can act as either substitutes or complements even in a relatively simple model casts doubt on whether in more complicated models or the real world one should expect them to always be just one or the other. Within our model, for parameter values reflecting conditions in developed countries, the typical finding is to ease lockdown intensity gradually after substantial shares of the population have been vaccinated, but other strategies can be optimal for other parameter values. Reserving vaccines for those who have not yet been infected barely outperforms simpler strategies that ignore prior infection status. For certain parameter combinations, there are instances in which two quite different policies can perform equally well, and sometimes very small increases in vaccine capacity can tip the optimal solution to one that involves much longer and more intense lockdowns.

Impact of vaccination and non-pharmacological interventions on COVID-19: a review of simulation modeling studies in Asia

Introduction

Epidemiological modeling is widely used to offer insights into the COVID-19 pandemic situation in Asia. We reviewed published computational (mathematical/simulation) models conducted in Asia that assessed impacts of pharmacological and non-pharmacological interventions against COVID-19 and their implications for vaccination strategy.

Methods

A search of the PubMed database for peer-reviewed, published, and accessible articles in English was performed up to November 2022 to capture studies in Asian populations based on computational modeling of outcomes in the COVID-19 pandemic. Extracted data included model type (mechanistic compartmental/agent-based, statistical, both), intervention type (pharmacological, non-pharmacological), and procedures for parameterizing age. Findings are summarized with descriptive statistics and discussed in terms of the evolving COVID-19 situation.

Results

The literature search identified 378 results, of which 59 met criteria for data extraction. China, Japan, and South Korea accounted for approximately half of studies, with fewer from South and South-East Asia. Mechanistic models were most common, either compartmental (61.0%), agent-based (1.7%), or combination (18.6%) models. Statistical modeling was applied less frequently (11.9%). Pharmacological interventions were examined in 59.3% of studies, and most considered vaccination, except one study of an antiviral treatment. Non-pharmacological interventions were also considered in 84.7% of studies. Infection, hospitalization, and mortality were outcomes in 91.5%, 30.5%, and 30.5% of studies, respectively. Approximately a third of studies accounted for age, including 10 that also examined mortality. Four of these studies emphasized benefits in terms of mortality from prioritizing older adults for vaccination under conditions of a limited supply; however, one study noted potential benefits to infection rates from early vaccination of younger adults. Few studies (5.1%) considered the impact of vaccination among children.

Conclusion

Early in the COVID-19 pandemic, non-pharmacological interventions helped to mitigate the health burden of COVID-19; however, modeling indicates that high population coverage of effective vaccines will complement and reduce reliance on such interventions. Thus, increasing and maintaining immunity levels in populations through regular booster shots, particularly among at-risk and vulnerable groups, including older adults, might help to protect public health. Future modeling efforts should consider new vaccines and alternative therapies alongside an evolving virus in populations with varied vaccination histories.

Optimized numerical solutions of SIRDVW multiage model controlling SARS-CoV-2 vaccine roll out: An application to the Italian scenario

In the context of SARS-CoV-2 pandemic, mathematical modelling has played a fundamental role for making forecasts, simulating scenarios and evaluating the impact of preventive political, social and pharmaceutical measures. Optimal control theory represents a useful mathematical tool to plan the vaccination campaign aimed at eradicating the pandemic as fast as possible. The aim of this work is to explore the optimal prioritisation order for planning vaccination campaigns able to achieve specific goals, as the reduction of the amount of infected, deceased and hospitalized in a given time frame, among age classes. For this purpose, we introduce an age stratified SIR-like epidemic compartmental model settled in an abstract framework for modelling two-doses vaccination campaigns and conceived with the description of COVID19 disease. Compared to other recent works, our model incorporates all stages of the COVID-19 disease, including death or recovery, without accounting for additional specific compartments that would increase computational complexity and that are not relevant for our purposes. Moreover, we introduce an optimal control framework where the model is the state problem while the vaccine doses administered are the control variables. An extensive campaign of numerical tests, featured in the Italian scenario and calibrated on available data from Dipartimento di Protezione Civile Italiana, proves that the presented framework can be a valuable tool to support the planning of vaccination campaigns. Indeed, in each considered scenario, our optimization framework guarantees noticeable improvements in terms of reducing deceased, infected or hospitalized individuals with respect to the baseline vaccination policy.

City-scale model for COVID-19 epidemiology with mobility and social activities represented by a set of hidden Markov models

BACKGROUND AND OBJECTIVE

SARS-CoV-2 emerged by the end of 2019 and became a global pandemic due to its rapid spread. Various outbreaks of the disease in different parts of the world have been studied, and epidemiological analyses of these outbreaks have been useful for developing models with the aim of tracking and predicting the spread of epidemics. In this paper, an agent-based model that predicts the local daily evolution of the number of people hospitalized in intensive care due to COVID-19 is presented.

METHODS

An agent-based model has been developed, taking into consideration the most relevant characteristics of the geography and climate of a mid-size city, its population and pathology statistics, and its social customs and mobility, including the state of public transportation. In addition to these inputs, the different phases of isolation and social distancing are also taken into account. By means of a set of hidden Markov models, the system captures and reproduces virus transmission associated with the stochastic nature of people's mobility and activities in the city. The spread of the virus in the host is also simulated by following the stages of the disease and by considering the existence of comorbidities and the proportion of asymptomatic carriers.

RESULTS

As a case study, the model was applied to Paraná city (Entre Ríos, Argentina) in the second half of 2020. The model adequately predicts the daily evolution of people hospitalized in intensive care due to COVID-19. This adequacy is reflected by the fact that the prediction of the model (including its dispersion), as with the data reported in the field, never exceeded 90% of the capacity of beds installed in the city. In addition, other epidemiological variables of interest, with discrimination by age range, were also adequately reproduced, such as the number of deaths, reported cases, and asymptomatic individuals.

CONCLUSIONS

The model can be used to predict the most likely evolution of the number of cases and hospital bed occupancy in the short term. By adjusting the model to match the data on hospitalizations in intensive care units and deaths due to COVID-19, it is possible to analyze the impact of isolation and social distancing measures on the disease spread dynamics. In addition, it allows for simulating combinations of characteristics that would lead to a potential collapse in the health system due to lack of infrastructure as well as predicting the impact of social events or increases in people's mobility.

Optimal vaccine allocation for the control of sexually transmitted infections

The burden of sexually transmitted infections (STIs) poses a challenge due to its large negative impact on sexual and reproductive health worldwide. Besides simple prevention measures and available treatment efforts, prophylactic vaccination is a powerful tool for controlling some viral STIs and their associated diseases. Here, we investigate how prophylactic vaccines are best distributed to prevent and control STIs. We consider sex-specific differences in susceptibility to infection, as well as disease severity outcomes. Different vaccination strategies are compared assuming distinct budget constraints that mimic a scarce vaccine stockpile. Vaccination strategies are obtained as solutions to an optimal control problem subject to a two-sex Kermack-McKendrick-type model, where the control variables are the daily vaccination rates for females and males. One important aspect of our approach relies on conceptualizing a limited but specific vaccine stockpile via an isoperimetric constraint. We solve the optimal control problem via Pontryagin's Maximum Principle and obtain a numerical approximation for the solution using a modified version of the forward-backward sweep method that handles the isoperimetric budget constraint in our formulation. The results suggest that for a limited vaccine supply ([Formula: see text]-[Formula: see text] vaccination coverage), one-sex vaccination, prioritizing females, appears to be more beneficial than the inclusion of both sexes into the vaccination program. Whereas, if the vaccine supply is relatively large (enough to reach at least [Formula: see text] coverage), vaccinating both sexes, with a slightly higher rate for females, is optimal and provides an effective and faster approach to reducing the prevalence of the infection.

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 combined use of COVID Alert SA app and vaccination to curb COVID-19 infections in South Africa

The unanticipated continued deep-rooted trend of the Severe Acute Respiratory Syndrome Corona-virus-2 the originator pathogen of the COVID-19 persists posing concurrent anxiety globally. More effort is affixed in the scientific arena via continuous investigations in a prolific effort to understand the transmission dynamics and control measures in eradication of the epidemic. Both pharmaceutical and non-pharmaceutical containment measure protocols have been assimilated in this effort. In this study, we develop a modified SEIR deterministic model that factors in alternative-amalgamation of use of COVID Alert SA app and vaccination against the COVID-19 to the Republic of South Africa's general public in an endeavor to discontinue the chain of spread for the pandemic. We analyze the key properties of the model not limited to positivity, boundedness, and stability. We authenticate the model by fitting it to the Republic of South Africa's cumulative COVID-19 cases reported data utilizing the Maximum Likelihood Estimation algorithm implemented in fitR package. Sensitivity analysis and simulations for the model reveal that simultaneously-gradually increased implementation of the COVID Alert SA app use and vaccination against COVID-19 to the public substantially accelerate reduction in the plateau number of COVID-19 infections across all the observed vaccine efficacy scenarios. More fundamentally, it is discovered that implementing at least 12% app use (mainly for the susceptible population not vaccinated) with simultaneous vaccination of over 12% of the susceptible population majorly not using the app using a vaccine of at least 50% efficacy would be sufficient in eradicating the pandemic over relatively shorter time span.

Effects of vaccination on mitigating COVID-19 outbreaks: a conceptual modeling approach

This paper is devoted to investigating the impact of vaccination on mitigating COVID-19 outbreaks. In this work, we propose a compartmental epidemic ordinary differential equation model, which extends the previous so-called SEIRD model ^[1,2,3,4] by incorporating the birth and death of the population, disease-induced mortality and waning immunity, and adding a vaccinated compartment to account for vaccination. Firstly, we perform a mathematical analysis for this model in a special case where the disease transmission is homogeneous and vaccination program is periodic in time. In particular, we define the basic reproduction number $ \mathcal{R}_0 $ for this system and establish a threshold type of result on the global dynamics in terms of $ \mathcal{R}_0 $. Secondly, we fit our model into multiple COVID-19 waves in four locations including Hong Kong, Singapore, Japan, and South Korea and then forecast the trend of COVID-19 by the end of 2022. Finally, we study the effects of vaccination again the ongoing pandemic by numerically computing the basic reproduction number $ \mathcal{R}_0 $ under different vaccination programs. Our findings indicate that the fourth dose among the high-risk group is likely needed by the end of the year.

A computational supervised neural network procedure for the fractional SIQ mathematical model

The purpose of the current work is to provide the numerical solutions of the fractional mathematical system of the susceptible, infected and quarantine (SIQ) system based on the lockdown effects of the coronavirus disease. These investigations provide more accurateness by using the fractional SIQ system. The investigations based on the nonlinear, integer and mathematical form of the SIQ model together with the effects of lockdown are also presented in this work. The impact of the lockdown is classified into the susceptible/infection/quarantine categories, which is based on the system of differential models. The fractional study is provided to find the accurate as well as realistic solutions of the SIQ model using the artificial intelligence (AI) performances along with the scale conjugate gradient (SCG) design, i.e., AI-SCG. The fractional-order derivatives have been used to solve three different cases of the nonlinear SIQ differential model. The statics to perform the numerical results of the fractional SIQ dynamical system are 7% for validation, 82% for training and 11% for testing. To observe the exactness of the AI-SCG procedure, the comparison of the numerical attained performances of the results is presented with the reference Adam solutions. For the validation, authentication, aptitude, consistency and validity of the AI-SCG solver, the computing numerical results have been provided based on the error histograms, state transition measures, correlation/regression values and mean square error.

Supplementary Information

The online version contains supplementary material available at 10.1140/epjs/s11734-022-00738-9.

Comparison of health-oriented cross-regional allocation strategies for the COVID-19 vaccine: a mathematical modelling study

BACKGROUND

Controlling the epidemic spread and establishing the immune barrier in a short time through accurate vaccine demand prediction and optimised vaccine allocation strategy are still urgent problems to be solved under the condition of frequent virus mutations.

METHODS

A cross-regional Susceptible-Exposed-Infected-Removed dynamic model was used for scenario simulation to systematically elaborate and compare the effects of different cross-regional vaccine allocation strategies on the future development of the epidemic in regions with different population sizes, prevention and control capabilities, and initial risk levels. Furthermore, the trajectory of the cross-regional vaccine allocation strategy, calculated using a particle swarm optimisation algorithm, was compared with the trajectories of other strategies.

RESULTS

By visualising the final effect of the particle swarm optimisation vaccine allocation strategy, this study revealed the important role of prevention and control (including the level of social distancing control, the speed of tracking and isolating exposed and infected individuals, and the initial frequency of mask-wearing) in determining the allocation of vaccine resources. Most importantly, it supported the idea of prioritising control in regions with a large population and low initial risk level, which broke the general view that high initial risk needs to be given priority and proposed that outbreak risk should be firstly considered instead.

CONCLUSIONS

This is the first study to use a particle swarm optimisation algorithm to study the cross-regional allocation of COVID-19 vaccines. These data provide a theoretical basis for countries and regions to develop more targeted and sustainable vaccination strategies.KEY MESSAGEThe innovative combination of particle swarm optimisation and cross-regional SEIR model to simulate the pandemic trajectory and predict the vaccine demand helped to speed up and stabilise the construction of the immune barrier, especially faced with new virus mutations.We proposed that priority should be given to regions where it is possible to prevent more infections rather than regions where it is at high initial risk, thus regional outbreak risk should be considered when making vaccine allocation decisions.An optimal health-oriented strategy for vaccine allocation in the COVID-19 pandemic is determined considering both pharmaceutical and non-pharmaceutical policy interventions, including speed of isolation, degree of social distancing control, and frequency of mask-wearing.

A data-driven spatially-specific vaccine allocation framework for COVID-19

Although coronavirus disease 2019 (COVID-19) vaccines have been introduced, their allocation is a challenging problem. We propose a data-driven, spatially-specific vaccine allocation framework that aims to minimize the number of COVID-19-related deaths or infections. The framework combines a regional risk-level classification model solved by a self-organizing map neural network, a spatially-specific disease progression model, and a vaccine allocation model that considers vaccine production capacity. We use data obtained from Wuhan and 35 other cities in China from January 26 to February 11, 2020, to avoid the effects of intervention. Our results suggest that, in region-wise distribution of vaccines, they should be allocated first to the source region of the outbreak and then to the other regions in order of decreasing risk whether the outcome measure is the number of deaths or infections. This spatially-specific vaccine allocation policy significantly outperforms some current allocation policies.

A mathematical model analysis of the human melioidosis transmission dynamics with an asymptomatic case

In this paper, we develop and examine a mathematical model of human melioidosis transmission with asymptomatic cases to describe the dynamics of the epidemic. The basic reproduction number ( R 0 ) of the model is obtained. Disease-free equilibrium of the model is proven to be globally asymptotically stable whenR 0 is less than the unity, while the endemic equilibrium of the model is shown to be locally asymptotically stable ifR 0 is greater than unity. Sensitivity analysis is performed to illustrate the effect of the model parameters influencing on the disease dynamics. Furthermore, numerical experiments of the model are conducted to validate the theoretical findings.

Community structured model for vaccine strategies to control COVID19 spread: A mathematical study

Initial efforts to mitigate the COVID-19 pandemic have relied heavily on non-pharmaceutical interventions (NPIs), including physical distancing, hand hygiene, and mask-wearing. However, an effective vaccine is essential to containing the spread of the virus. We developed a compartmental model to examine different vaccine strategies for controlling the spread of COVID-19. Our framework accounts for testing rates, test-turnaround times, and vaccination waning immunity. Using reported case data from the city of Toronto, Canada between Mar-Dec, 2020 we defined epidemic phases of infection using contact rates as well as the probability of transmission upon contact. We investigated the impact of vaccine distribution by comparing different permutations of waning immunity, vaccine coverage and efficacy throughout various stages of NPI's relaxation in terms of cases and deaths. The basic reproduction number is also studied. We observed that widespread vaccine coverage substantially reduced the number of cases and deaths. Under phases with high transmission, an early or late reopening will result in new resurgence of the infection, even with the highest coverage. On the other hand, under phases with lower transmission, 60% of coverage is enough to prevent new infections. Our analysis of R0 showed that the basic reproduction number is reduced by decreasing the tests turnaround time and transmission in the household. While we found that household transmission can decrease following the introduction of a vaccine, public health efforts to reduce test turnaround times remain important for virus containment.

Detection of multiple waves for COVID-19 and its optimal control through media awareness and vaccination: study based on some Indian states

COVID-19 is a highly infectious disease, and in very recent times, it has shown a massive impact throughout the globe. Several countries faced the COVID-19 infection waves multiple times. These later waves are more aggressive than the first wave and drastically impact social and economic factors. We developed a mechanistic model with imperfect lockdown effect, reinfection, transmission variability between symptomatic & asymptomatic, and media awareness to focus on the early detection of multiple waves and their control measures. Using daily COVID-19 cases data from six states of India, we estimated several important model parameters. Moreover, we estimated the home quarantine, community, and basic reproduction numbers. We developed an algorithm to carry out global sensitivity analysis (Sobol) of the parameters that influence the number of COVID-19 waves ( W C ) and the average number of COVID-19 cases in a wave ( A W ). We have identified some critical controlling parameters that mainly influenced W C and A W . Our study also revealed the best COVID-19 control strategy/strategies among vaccination, media awareness, and their combination using an optimal cost-effective study. The detailed analysis suggests that the severity of asymptomatic transmission is around 10% to 29% of that of symptomatic transmission in all six locations. About 1% to 4% of the total population under lockdown may contribute to new COVID-19 infection in all six locations. Optimal cost-effective analysis based on interventions, namely only vaccination (VA), only media awareness (ME), and a combination of vaccination & media (VA+ME), are projected for the period March 14, 2020, to August 31, 2021, for all the six locations. We have found that a large percentage of the population (26% to 45%) must be vaccinated from February 13 to August 31, 2021, to avert an optimal number of COVID-19 cases in these six locations.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s11071-022-07887-5.

A Mathematical Model Analysis for the Transmission Dynamics of Leptospirosis Disease in Human and Rodent Populations

This work is aimed at formulating and analyzing a compartmental mathematical model to investigate the impact of rodent-born leptospirosis on the human population by considering a load of pathogenic agents of the disease in an environment and the incidence rate of human infection due to the interaction between infected rodents and the environment. Firstly, the basic properties of the model, the equilibria points, and their stability analysis are studied. We also found the basic reproduction number (R₀) of the model using the next-generation matrix approach. From the stability analysis, we obtained that the disease-free equilibrium (DFE) is globally asymptotically stable if R₀ < 1 and unstable otherwise. The local stability of endemic equilibrium is performed using the phenomenon of the center manifold theory, and the model exhibits forward bifurcation. The most sensitive parameters on the model outcome are also identified using the normalized forward sensitivity index. Finally, numerical simulations of the model are performed to show the stability behavior of endemic equilibrium and the varying effect of the human transmission rates, human recovery rate, and the mortality rate rodents on the model dynamics. The model is simulated using the forward fourth-order Runge-Kutta method, and the results are presented graphically. From graphical stability analysis, we observed that all trajectories of the model solutions evolve towards the unique endemic equilibrium over time when R₀ > 1. Our numerical results revealed that decreasing the transmission rates and increasing the rate of recovery and reduction of the rodent population using appropriate intervention mechanisms have a significant role in reducing the spread of disease infection in the population.

An agent-based model to assess large-scale COVID-19 vaccination campaigns for the Italian territory: The case study of Lombardy region

BACKGROUND

In Italy, the administration of COVID-19 vaccines began in late 2020. In the early stages, the number of available doses was limited. To maximize the effectiveness of the vaccine campaign, the national health agency assigned priority access to at-risk individuals, such as health care workers and the elderly. Current vaccination campaign strategies do not take full advantage of the latest mathematical models, which capture many subtle nuances, allowing different territorial situations to be analyzed aiming to make context-specific decisions.

OBJECTIVES

The main objective is the definition of an agent-based model using open data and scientific literature to assess and optimize the impact of vaccine campaigns for an Italian region. Specifically, the aim is twofold: (i) estimate the reduction in the number of infections and deaths attributable to vaccines, and (ii) assess the performances of alternative vaccine allocation strategies.

METHODS

The COVID-19 Agent-based simulator Covasim has been employed to build an agent-based model by considering the Lombardy region as case study. The model has been tailored by leveraging open data and knowledge from the scientific literature. Dynamic mobility restrictions and the presence of Variant of Concern have been explicitly represented. Free parameters have been calibrated using the grid search methodology.

RESULTS

The model mimics the COVID-19 wave that hit Lombardy from September 2020 to April 2021. It suggests that 168,492 cumulative infections 2,990 cumulative deaths have been avoided due to the vaccination campaign in Lombardy from January 1 to April 30, 2021. Without vaccines, the number of deaths would have been 66% greater in the 80-89 age group and 114% greater for those over 90. The best vaccine allocation strategy depends on the goal. To minimize infections, the best policy is related to dose availability. If at least 1/3 of the population can be covered in 4 months, targeting at-risk individuals and the elderly first is recommended; otherwise, the youngest people should be vaccinated first. To minimize overall deaths, priority is best given to at-risk groups and the elderly in all scenarios.

CONCLUSIONS

This work proposes a methodological approach that leverages open data and scientific literature to build a model of COVID-19 capable of assessing and optimizing the impact of vaccine campaigns. This methodology can help national institutions to design regional mathematical models that can support pandemic-related decision-making processes.

Using simulation modelling and systems science to help contain COVID-19: A systematic review

This study systematically reviews applications of three simulation approaches, that is, system dynamics model (SDM), agent-based model (ABM) and discrete event simulation (DES), and their hybrids in COVID-19 research and identifies theoretical and application innovations in public health. Among the 372 eligible papers, 72 focused on COVID-19 transmission dynamics, 204 evaluated both pharmaceutical and non-pharmaceutical interventions, 29 focused on the prediction of the pandemic and 67 investigated the impacts of COVID-19. ABM was used in 275 papers, followed by 54 SDM papers, 32 DES papers and 11 hybrid model papers. Evaluation and design of intervention scenarios are the most widely addressed area accounting for 55% of the four main categories, that is, the transmission of COVID-19, prediction of the pandemic, evaluation and design of intervention scenarios and societal impact assessment. The complexities in impact evaluation and intervention design demand hybrid simulation models that can simultaneously capture micro and macro aspects of the socio-economic systems involved.

An assessment of transmission dynamics via time-varying reproduction number of the second wave of the COVID-19 epidemic in Fiji

This study involves the estimation of a key epidemiological parameter for evaluating and monitoring the transmissibility of a disease. The time-varying reproduction number is the index for quantifying the transmissibility of infectious diseases. Accurate and timely estimation of the time-varying reproduction number is essential for optimizing non-pharmacological interventions and movement control orders during epidemics. The time-varying reproduction number for the second wave of the pandemic in Fiji is estimated using the popular EpiEstim R package and the publicly available COVID-19 data from 19 April 2021 to 1 December 2021. Our findings show that the non-pharmacological interventions and movement control orders introduced and enforced by the Fijian Government had a significant impact in preventing the spread of COVID-19. Moreover, the results show that many restrictions were either relaxed or eased when the time-varying reproduction number was below the threshold value of 1. The results have provided some information on the second wave of the COVID-19 pandemic that could be used in the future as a guide for public health policymakers in Fiji. Estimation of time-varying reproduction numbers would be helpful for continuous monitoring of the effectiveness of the current public health policies that are being implemented in Fiji.

Optimising the impact of COVID-19 vaccination on mortality and hospitalisations using an individual additive risk measuring approach based on a risk adjustment scheme

In this population-based cohort study, billing data from German statutory health insurance (BARMER, 10% of population) are used to develop a prioritisation model for COVID-19 vaccinations based on cumulative underlying conditions. Using a morbidity-based classification system, prevalence and risks for COVID-19-related hospitalisations, ventilations and deaths are estimated. Trisomies, behavioural and developmental disorders (relative risk: 2.09), dementia and organic psychoorganic syndromes (POS) (2.23) and (metastasised) malignant neoplasms (1.99) were identified as the most important conditions for escalations of COVID-19 infection. Moreover, optimal vaccination priority schedules for participants are established on the basis of individual cumulative escalation risk and are compared to the prioritisation scheme chosen by the German Government. We estimate how many people would have already received a vaccination prior to escalation. Vaccination schedules based on individual cumulative risk are shown to be 85% faster than random schedules in preventing deaths, and as much as 57% faster than the German approach, which was based primarily on age and specific diseases. In terms of hospitalisation avoidance, the individual cumulative risk approach was 51% and 28% faster. On this basis, it is concluded that using individual cumulative risk-based vaccination schedules, healthcare systems can be relieved and escalations more optimally avoided.

Mean field control problems for vaccine distribution

With the invention of the COVID-19 vaccine, shipping and distributing are crucial in controlling the pandemic. In this paper, we build a mean-field variational problem in a spatial domain, which controls the propagation of pandemics by the optimal transportation strategy of vaccine distribution. Here, we integrate the vaccine distribution into the mean-field SIR model designed in Lee W, Liu S, Tembine H, Li W, Osher S (2020) Controlling propagation of epidemics via mean-field games. arXiv preprint arXiv:2006.01249. Numerical examples demonstrate that the proposed model provides practical strategies for vaccine distribution in a spatial domain.

Accurate Numerical Treatment on a Stochastic SIR Epidemic Model with Optimal Control Strategy

In this paper, a numerical study has been undertaken on the susceptible-infected-recovered (SIR) epidemic model that encompasses the mechanisms of the evolution of disease transmission; a prophylactic vaccination strategy in the susceptible populations, depending on the infective individuals. We furnish numerical and graphical simulation combined with explicit series solutions of the proposed model using the New Iterative Method (NIM) and Modified New Iterative Method (MNIM). The analytic-numeric New Iterative Method failed to deliver accurate solution for the large time domain. A new reliable algorithm based on NIM, the coupling of the Laplace transforms, and the New Iterative method is called Modified New Iterative Method (MNIM) which is presented to enhance the validity domain of NIM techniques. The convergence analysis of the MNIM has also been illustrated. The simulation results show that the vaccination strategy can slow down the spread of the epidemic rapidly. Numerical results illustrate the excellent performance of the MNIM and show that the modified method is much more accurate than the NIM.

An efficient nonstandard computer method to solve a compartmental epidemiological model for COVID-19 with vaccination and population migration

BACKGROUND AND OBJECTIVE

In this manuscript, we consider a compartmental model to describe the dynamics of propagation of an infectious disease in a human population. The population considers the presence of susceptible, exposed, asymptomatic and symptomatic infected, quarantined, recovered and vaccinated individuals. In turn, the mathematical model considers various mechanisms of interaction between the sub-populations in addition to population migration.

METHODS

The steady-state solutions for the disease-free and endemic scenarios are calculated, and the local stability of the equilibium solutions is determined using linear analysis, Descartes' rule of signs and the Routh-Hurwitz criterion. We demonstrate rigorously the existence and uniqueness of non-negative solutions for the mathematical model, and we prove that the system has no periodic solutions using Dulac's criterion. To solve this system, a nonstandard finite-difference method is proposed.

RESULTS

As the main results, we show that the computer method presented in this work is uniquely solvable, and that it preserves the non-negativity of initial approximations. Moreover, the steady-state solutions of the continuous model are also constant solutions of the numerical scheme, and the stability properties of those solutions are likewise preserved in the discrete scenario. Furthermore, we establish the consistency of the scheme and, using a discrete form of Gronwall's inequality, we prove theoretically the stability and the convergence properties of the scheme. For convenience, a Matlab program of our method is provided in the appendix.

CONCLUSIONS

The computer method presented in this work is a nonstandard scheme with multiple dynamical and numerical properties. Most of those properties are thoroughly confirmed using computer simulations. Its easy implementation make this numerical approach a useful tool in the investigation on the propagation of infectious diseases. From the theoretical point of view, the present work is one of the few papers in which a nonstandard scheme is fully and rigorously analyzed not only for the dynamical properties, but also for consistently, stability and convergence.

Global Stability of a Humoral Immunity COVID-19 Model with Logistic Growth and Delays

The mathematical modeling and analysis of within-host or between-host coronavirus disease 2019 (COVID-19) dynamics are considered robust tools to support scientific research. Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the cause of COVID-19. This paper proposes and investigates a within-host COVID-19 dynamics model with latent infection, the logistic growth of healthy epithelial cells and the humoral (antibody) immune response. Time delays can affect the dynamics of SARS-CoV-2 infection predicted by mathematical models. Therefore, we incorporate four time delays into the model: (i) delay in the formation of latent infected epithelial cells, (ii) delay in the formation of active infected epithelial cells, (iii) delay in the activation of latent infected epithelial cells, and (iv) maturation delay of new SARS-CoV-2 particles. We establish that the model’s solutions are non-negative and ultimately bounded. This confirms that the concentrations of the virus and cells should not become negative or unbounded. We deduce that the model has three steady states and their existence and stability are perfectly determined by two threshold parameters. We use Lyapunov functionals to confirm the global stability of the model’s steady states. The analytical results are enhanced by numerical simulations. The effect of time delays on the SARS-CoV-2 dynamics is investigated. We observe that increasing time delay values can have the same impact as drug therapies in suppressing viral progression. This offers some insight useful to develop a new class of treatment that causes an increase in the delay periods and then may control SARS-CoV-2 replication.

Optimal Drug Regimen and Combined Drug Therapy and Its Efficacy in the Treatment of COVID-19: A Within-Host Modeling Study

The COVID-19 pandemic has resulted in more than 524 million cases and 6 million deaths worldwide. Various drug interventions targeting multiple stages of COVID-19 pathogenesis can significantly reduce infection-related mortality. The current within-host mathematical modeling study addresses the optimal drug regimen and efficacy of combination therapies in the treatment of COVID-19. The drugs/interventions considered include Arbidol, Remdesivir, Interferon (INF) and Lopinavir/Ritonavir. It is concluded that these drugs, when administered singly or in combination, reduce the number of infected cells and viral load. Four scenarios dealing with the administration of a single drug, two drugs, three drugs and all four are discussed. In all these scenarios, the optimal drug regimen is proposed based on two methods. In the first method, these medical interventions are modeled as control interventions and a corresponding objective function and optimal control problem are formulated. In this framework, the optimal drug regimen is derived. Later, using the comparative effectiveness method, the optimal drug regimen is derived based on the basic reproduction number and viral load. The average number of infected cells and viral load decreased the most when all four drugs were used together. On the other hand, the average number of susceptible cells decreased the most when Arbidol was administered alone. The basic reproduction number and viral load decreased the most when all four interventions were used together, confirming the previously obtained finding of the optimal control problem. The results of this study can help physicians make decisions about the treatment of the life-threatening COVID-19 infection.

COVID-19 epidemic in New York City: development of an age group-specific mathematical model to predict the outcome of various vaccination strategies

BACKGROUND

Since December 14, 2020, New York City (NYC) has started the first batch of COVID-19 vaccines. However, the shortage of vaccines is currently an inevitable problem. Therefore, optimizing the age-specific COVID-19 vaccination is an important issue that needs to be addressed as a priority.

OBJECTIVE

Combined with the reported COVID-19 data in NYC, this study aimed to construct a mathematical model with five age groups to estimate the impact of age-specific vaccination on reducing the prevalence of COVID-19.

METHODS

We proposed an age-structured mathematical model and estimated the unknown parameters based on the method of Markov Chain Monte Carlo (MCMC). We also calibrated our model by using three different types of reported COVID-19 data in NYC. Moreover, we evaluated the reduced cumulative number of deaths and new infections with different vaccine allocation strategies.

RESULTS

Compared with the current vaccination strategy in NYC, if we gradually increased the vaccination coverage rate for only one age groups from March 1, 2021 such that the vaccination coverage rate would reach to 40% by June 1, 2021, then as of June 1, 2021, the cumulative deaths in the 75-100 age group would be reduced the most, about 72 fewer deaths per increased 100,000 vaccinated individuals, and the cumulative new infections in the 0-17 age group would be reduced the most, about 21,591 fewer new infections per increased 100,000 vaccinated individuals. If we gradually increased the vaccination coverage rate for two age groups from March 1, 2021 such that the vaccination coverage rate would reach to 40% by June 1, 2021, then as of June 1, 2021, the cumulative deaths in the 65-100 age group would be reduced the most, about 36 fewer deaths per increased 100,000 vaccinated individuals, and the cumulative new infections in the 0-44 age group would be reduced the most, about 17,515 fewer new infections per increased 100,000 vaccinated individuals. In addition, if we had an additional 100,000 doses of vaccine for 0-17 and 75-100 age groups as of June 1, 2021, then the allocation of 80% to the 0-17 age group and 20% to the 75-100 age group would reduce the maximum numbers of new infections and deaths simultaneously in NYC.

CONCLUSIONS

The COVID-19 burden including deaths and new infections would decrease with increasing vaccination coverage rate. Priority vaccination to the elderly and adolescents would minimize both deaths and new infections.

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.

Best Practices for COVID-19 Mass Vaccination Clinics

PURPOSE

The coronavirus disease 2019 (COVID-19) pandemic is an unprecedented global public health crisis. Mass vaccination is the safest and fastest pandemic exit strategy. Mass vaccination clinics are a particularly important tool in quickly achieving herd immunity. Primary care physicians have played a crucial role in organizing and running vaccination clinics. In this special report, we synthesize existing guidelines and peer-reviewed studies to provide physicians with practical guidance on planning and implementing COVID-19 mass vaccination clinics.

METHODS

PubMed, Ovid MEDLINE and Embase were used to search for relevant literature using search terms that included COVID-19, mass vaccination, and best practice. We also identified and analyzed national and international guidelines.

RESULTS

Forty-six relevant articles, reports, and guidelines were identified and synthesized. Articles included mass vaccination clinic guidelines and studies before and during the COVID-19 pandemic. Key considerations for COVID-19 mass vaccination clinics include leadership and role designation, site selection, clinic layout and workflow, day-to-day operations, infection prevention, and communication strategies.

CONCLUSIONS

Planning and implementing a successful COVID-19 mass vaccination clinic requires several key considerations. Primary care plays an important role in organizing clinics and ensuring populations made vulnerable by social and economic policies are being reached. Ongoing data collection is required to evaluate and continuously improve COVID-19 mass vaccination efforts. As the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) vaccine rollout occurs in various countries, research will be required to identify the main factors for success to inform future pandemic responses.VISUAL ABSTRACT.

A Numerical Study of the Fractional Order Dynamical Nonlinear Susceptible Infected and Quarantine Differential Model Using the Stochastic Numerical Approach

The theme of this study is to present the impacts and importance of the fractional order derivatives of the susceptible, infected and quarantine (SIQ) model based on the coronavirus with the lockdown effects. The purpose of these investigations is to achieve more accuracy with the use of fractional derivatives in the SIQ model. The integer, nonlinear mathematical SIQ system with the lockdown effects is also provided in this study. The lockdown effects are categorized into the dynamics of the susceptible, infective and quarantine, generally known as SIQ mathematical system. The fractional order SIQ mathematical system has never been presented before, nor solved by using the strength of the stochastic solvers. The stochastic solvers based on the Levenberg-Marquardt backpropagation scheme (LMBS) along with the neural networks (NNs), i.e., LMBS-NNs have been implemented to solve the fractional order SIQ mathematical system. Three cases using different values of the fractional order have been provided to solve the fractional order SIQ mathematical model. The data to present the numerical solutions of the fractional order SIQ mathematical model is selected as 80% for training and 10% for both testing and validation. For the correctness of the LMBS-NNs, the obtained numerical results have been compared with the reference solutions through the Adams–Bashforth–Moulton based numerical solver. In order to authenticate the competence, consistency, validity, capability and exactness of the LMB-NNs, the numerical performances using the state transitions (STs), regression, correlation, mean square error (MSE) and error histograms (EHs) are also provided.

A new threshold reveals the uncertainty about the effect of school opening on diffusion of Covid-19

Studies on the effects of school openings or closures during the Covid-19 pandemic seem to reach contrasting conclusions even in similar contexts. We aim at clarifying this controversy. A mathematical analysis of compartmental models with subpopulations has been conducted, starting from the SIR model, and progressively adding features modeling outbreaks or upsurge of variants, lockdowns, and vaccinations. We find that in all cases, the in-school transmission rates only affect the overall course of the pandemic above a certain context dependent threshold. We provide rigorous proofs and computations of the thresdhold through linearization. We then confirm our theoretical findings through simulations and the review of data-driven studies that exhibit an often unnoticed phase transition. Specific implications are: awareness about the threshold could inform choice of data collection, analysis and release, such as in-school transmission rates, and clarify the reason for divergent conclusions in similar studies; schools may remain open at any stage of the Covid-19 pandemic, including variants upsurge, given suitable containment rules; these rules would be extremely strict and hardly sustainable if only adults are vaccinated, making a compelling argument for vaccinating children whenever possible.

Optimal Control Studies on Age Structured Modeling of COVID-19 in Presence of Saturated Medical Treatment of Holling Type III

COVID-19 pandemic has caused the most severe health problems to adults over 60 years of age, with particularly fatal consequences for those over 80. In this case, age-structured mathematical modeling could be useful to determine the spread of the disease and to develop a better control strategy for different age groups. In this study, we first propose an age-structured model considering two different age groups, the first group with population age below 30 years and the second with population age above 30 years, and discuss the stability of the equilibrium points and the sensitivity of the model parameters. In the second part of the study, we propose an optimal control problem to understand the age-specific role of treatment in controlling the spread of COVID -19 infection. From the stability analysis of the equilibrium points, it was found that the infection-free equilibrium point remains locally asymptotically stable whenR 0 < 1 , and when R 0 is greater than one, the infected equilibrium point remains locally asymptotically stable. The results of the optimal control study show that infection decreases with the implementation of an optimal treatment strategy, and that a combined treatment strategy considering treatment for both age groups is effective in keeping cumulative infection low in severe epidemics. Cumulative infection was found to increase with increasing saturation in medical treatment.

Mathematical modeling and optimal intervention strategies of the COVID-19 outbreak

34,354,966 active cases and 460,787 deaths because of COVID-19 pandemic were recorded on November 06, 2021, in India. To end this ongoing global COVID-19 pandemic, there is an urgent need to implement multiple population-wide policies like social distancing, testing more people and contact tracing. To predict the course of the pandemic and come up with a strategy to control it effectively, a compartmental model has been established. The following six stages of infection are taken into consideration: susceptible (S), asymptomatic infected (A), clinically ill or symptomatic infected (I), quarantine (Q), isolation (J) and recovered (R), collectively termed as SAIQJR. The qualitative behavior of the model and the stability of biologically realistic equilibrium points are investigated in terms of the basic reproduction number. We performed sensitivity analysis with respect to the basic reproduction number and obtained that the disease transmission rate has an impact in mitigating the spread of diseases. Moreover, considering the non-pharmaceutical and pharmaceutical intervention strategies as control functions, an optimal control problem is implemented to mitigate the disease fatality. To reduce the infected individuals and to minimize the cost of the controls, an objective functional has been constructed and solved with the aid of Pontryagin's maximum principle. The implementation of optimal control strategy at the start of a pandemic tends to decrease the intensity of epidemic peaks, spreading the maximal impact of an epidemic over an extended time period. Extensive numerical simulations show that the implementation of intervention strategy has an impact in controlling the transmission dynamics of COVID-19 epidemic. Further, our numerical solutions exhibit that the combination of three controls are more influential when compared with the combination of two controls as well as single control. Therefore, the implementation of all the three control strategies may help to mitigate novel coronavirus disease transmission at this present epidemic scenario.

Supplementary Information

The online version supplementary material available at 10.1007/s11071-022-07235-7.

Age Structured Mathematical Modeling Studies on COVID-19 with respect to Combined Vaccination and Medical Treatment Strategies

In this study, we develop a mathematical model incorporating age-specific transmission dynamics of COVID-19 to evaluate the role of vaccination and treatment strategies in reducing the size of COVID-19 burden. Initially, we establish the positivity and boundedness of the solutions of the non controlled model and calculate the basic reproduction number and do the stability analysis. We then formulate an optimal control problem with vaccination and treatment as control variables and study the same. Pontryagin’s Minimum Principle is used to obtain the optimal vaccination and treatment rates. Optimal vaccination and treatment policies are analysed for different values of the weight constant associated with the cost of vaccination and different efficacy levels of vaccine. Findings from these suggested that the combined strategies (vaccination and treatment) worked best in minimizing the infection and disease induced mortality. In order to reduce COVID-19 infection and COVID-19 induced deaths to maximum, it was observed that optimal control strategy should be prioritized to the population with age greater than 40 years. Varying the cost of vaccination it was found that sufficient implementation of vaccines (more than 77 %) reduces the size of COVID-19 infections and number of deaths. The infection curves varying the efficacies of the vaccines against infection were also analysed and it was found that higher efficacy of the vaccine resulted in lesser number of infections and COVID induced deaths. The findings would help policymakers to plan effective strategies to contain the size of the COVID-19 pandemic.

Time Optimal Control Studies on COVID-19 Incorporating Adverse Events of the Antiviral Drugs

COVID -19 pandemic has resulted in more than 257 million infections and 5.15 million deaths worldwide. Several drug interventions targeting multiple stages of the pathogenesis of COVID -19 can significantly reduce induced infection and thus mortality. In this study, we first develop SIV model at within-host level by incorporating the intercellular time delay and analyzing the stability of equilibrium points. The model dynamics admits a disease-free equilibrium and an infected equilibrium with their stability based on the value of the basic reproduction number R 0. We then formulate an optimal control problem with antiviral drugs and second-line drugs as control measures and study their roles in reducing the number of infected cells and viral load. The comparative study conducted in the optimal control problem suggests that if the first-line antiviral drugs show adverse effects, considering these drugs in reduced amounts along with the second-line drugs would be very effective in reducing the number of infected cells and viral load in a COVID-19 infected patient. Later, we formulate a time-optimal control problem with the goal of driving the system from any initial state to the desired infection-free equilibrium state in finite minimal time. Using Pontryagin’s Minimum Principle, it is shown that the optimal control strategy is of the bang-bang type, with the possibility of switching between two extreme values of the optimal controls. Numerically, it is shown that the desired infection-free state is achieved in a shorter time when the higher values of the optimal controls. The results of this study may be very helpful to researchers, epidemiologists, clinicians and physicians working in this field.

Mathematical analysis for the effect of voluntary vaccination on the propagation of Corona virus pandemic

In this manuscript, a new nonlinear model for the rapidly spreading Corona virus disease (COVID-19) is developed. We incorporate an additional class of vaccinated humans which ascertains the impact of vaccination strategy for susceptible humans. A complete mathematical analysis of this model is conducted to predict the dynamics of Corona virus in the population. The analysis proves the effectiveness of vaccination strategy employed and helps public health services to control or to reduce the burden of corona virus pandemic. We first prove the existence and uniqueness and then boundedness and positivity of solutions. Threshold parameter for the vaccination model is computed analytically. Stability of the proposed model at fixed points is investigated analytically with the help of threshold parameter to examine epidemiological relevance of the pandemic. We apply LaSalle's invariance principle from the theory of Lyapunov function to prove the global stability of both the equilibria. Two well known numerical techniques namely Runge-Kutta method of order 4 (RK4), and the Non-Standard Finite Difference (NSFD) method are employed to solve the system of ODE's and to validate our obtained theoretical results. For different coverage levels of voluntary vaccination, we explored a complete quantitative analysis of the model. To draw our conclusions, the effect of proposed vaccination on threshold parameter is studied numerically. It is claimed that Corona virus disease could be eradicated faster if a human community selfishly adopts mandatory vaccination measures at various coverage levels with proper awareness. Finally, we have executed the joint variability of all classes to understand the effect of vaccination strategy on a disease dynamics.

Mathematical modeling and impact analysis of the use of COVID Alert SA app

The human life-threatening novel Severe Acute Respiratory Syndrome Corona-virus-2 (SARS-CoV-2) has lasted for over a year escalating and posing simultaneous anxiety day-by-day globally since its first report in the late December 2019. The scientific arena has been kept animated via continuous investigations in an effort to understand the spread dynamics and the impact of various mitigation measures to keep this pandemic diminished. Despite a lot of research works having been accomplished this far, the pandemic is still deep-rooted in many regions worldwide signaling for more scientific investigations. This study joins the field by developing a modified SEIR (Susceptible-Exposed-Infectious-Removed) compartmental deterministic model whose key distinct feature is the incorporation of the COVID Alert SA app use by the general public in prolific intention to control the spread of the epidemic. Validation of the model is performed by fitting the model to the Republic of South Africa's COVID-19 cases reported data using the Maximum Likelihood Estimation algorithm implemented in fitR package. The model's sensitivity analysis and simulations stipulate that gradual to complete use of the app would be perfect in contact tracing and substantially reduce the plateau number of COVID-19 infections. This would consequentially contribute remarkably to the eradication of the SARS-CoV-2 over time. Proportional amalgamation of the app use and test for COVID-19 on individuals not using the app would also reduce the peak number of infections apart from the 50 - 50% ratio which spikes the plateau number beyond any other proportion. The study establishes that at least 30% implementation of the app use with gradual increase in tests conducted for individuals not using the app would suffice to stabilize the disease free equilibrium resulting to gradual eradication of the pandemic.

What We Are Learning from COVID-19 for Respiratory Protection: Contemporary and Emerging Issues

Infectious respiratory diseases such as the current COVID-19 have caused public health crises and interfered with social activity. Given the complexity of these novel infectious diseases, their dynamic nature, along with rapid changes in social and occupational environments, technology, and means of interpersonal interaction, respiratory protective devices (RPDs) play a crucial role in controlling infection, particularly for viruses like SARS-CoV-2 that have a high transmission rate, strong viability, multiple infection routes and mechanisms, and emerging new variants that could reduce the efficacy of existing vaccines. Evidence of asymptomatic and pre-symptomatic transmissions further highlights the importance of a universal adoption of RPDs. RPDs have substantially improved over the past 100 years due to advances in technology, materials, and medical knowledge. However, several issues still need to be addressed such as engineering performance, comfort, testing standards, compliance monitoring, and regulations, especially considering the recent emergence of pathogens with novel transmission characteristics. In this review, we summarize existing knowledge and understanding on respiratory infectious diseases and their protection, discuss the emerging issues that influence the resulting protective and comfort performance of the RPDs, and provide insights in the identified knowledge gaps and future directions with diverse perspectives.

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

BACKGROUND AND OBJECTIVE

Assuming the availability of a limited amount of effective COVID-19 rapid tests, the effects of various vaccination strategies on SARS-CoV-2 virus transmission are compared for different vaccination scenarios characterized by distinct limitations associated with vaccine supply and administration.

METHODS

The vaccination strategies are defined by solving optimal control problems of a compartmental epidemic model in which the daily vaccination rate and the daily testing rate for the identification and isolation of asymptomatic subjects are the control variables. Different kinds of algebraic constraints are considered, representing different vaccination scenarios in which the total amount of vaccines available during the time period under consideration is limited or the number of daily available vaccines is limited. These optimal control problems are numerically solved by means of a direct transcription technique, which allows both equality and inequality constraints to be straightforwardly included in the formulation of the optimal control problems.

RESULTS

Several numerical experiments are conducted, in which the objective functional to be minimized is a combination of the number of symptomatic and asymptomatic infectious subjects with the cost of vaccination of susceptible subjects and testing of asymptomatic infectious subjects. The results confirm the hypothesis that the implementation of early control measures significantly reduces the number of symptomatic infected subjects, which is a key aspect for the resilience of the healthcare system. The sensitivity analysis of the solutions to the weighting parameters of the objective functional reveals that it is possible to obtain a vaccination strategy that allows vaccination supplies to be saved while keeping the same number of symptomatic infected subjects. Furthermore, it indicates that if the vaccination plan is not supported by a sufficient rate of testing, the number of symptomatic infected subjects could increase. Finally, the sensitivity analysis shows that a significant reduction in the efficacy of the vaccines could also lead to a relevant increase in the number of symptomatic infected subjects.

CONCLUSIONS

The numerical experiments show that the proposed approach, which is based on optimal control of compartmental epidemic models, provides healthcare systems with a suitable method for scheduling vaccination plans and testing policies to control the spread of the SARS-CoV-2 virus.

Optimization in the Context of COVID-19 Prediction and Control: A Literature Review

This paper presents an overview of some key results from a body of optimization studies that are specifically related to COVID-19, as reported in the literature during 2020-2021. As shown in this paper, optimization studies in the context of COVID-19 have been used for many aspects of the pandemic. From these studies, it is observed that since COVID-19 is a multifaceted problem, it cannot be studied from a single perspective or framework, and neither can the related optimization models. Four new and different frameworks are proposed that capture the essence of analyzing COVID-19 (or any pandemic for that matter) and the relevant optimization models. These are: (i) microscale vs. macroscale perspective; (ii) early stages vs. later stages perspective; (iii) aspects with direct vs. indirect relationship to COVID-19; and (iv) compartmentalized perspective. To limit the scope of the review, only optimization studies related to the prediction and control of COVID-19 are considered (public health focused), and which utilize formal optimization techniques or machine learning approaches. In this context and to the best of our knowledge, this survey paper is the first in the literature with a focus on the prediction and control related optimization studies. These studies include optimization of screening testing strategies, prediction, prevention and control, resource management, vaccination prioritization, and decision support tools. Upon reviewing the literature, this paper identifies current gaps and major challenges that hinder the closure of these gaps and provides some insights into future research directions.

Differential evolution and particle swarm optimization against COVID-19

COVID-19 disease, which highly affected global life in 2020, led to a rapid scientific response. Versatile optimization methods found their application in scientific studies related to COVID-19 pandemic. Differential Evolution (DE) and Particle Swarm Optimization (PSO) are two metaheuristics that for over two decades have been widely researched and used in various fields of science. In this paper a survey of DE and PSO applications for problems related with COVID-19 pandemic that were rapidly published in 2020 is presented from two different points of view: 1. practitioners seeking the appropriate method to solve particular problem, 2. experts in metaheuristics that are interested in methodological details, inter comparisons between different methods, and the ways for improvement. The effectiveness and popularity of DE and PSO is analyzed in the context of other metaheuristics used against COVID-19. It is found that in COVID-19 related studies: 1. DE and PSO are most frequently used for calibration of epidemiological models and image-based classification of patients or symptoms, but applications are versatile, even interconnecting the pandemic and humanities; 2. reporting on DE or PSO methodological details is often scarce, and the choices made are not necessarily appropriate for the particular algorithm or problem; 3. mainly the basic variants of DE and PSO that were proposed in the late XX century are applied, and research performed in recent two decades is rather ignored; 4. the number of citations and the availability of codes in various programming languages seems to be the main factors for choosing metaheuristics that are finally used.

An application of the ensemble Kalman filter in epidemiological modelling

Since the novel coronavirus (COVID-19) outbreak in China, and due to the open accessibility of COVID-19 data, several researchers and modellers revisited the classical epidemiological models to evaluate their practical applicability. While mathematical compartmental models can predict various contagious viruses' dynamics, their efficiency depends on the model parameters. Recently, several parameter estimation methods have been proposed for different models. In this study, we evaluated the Ensemble Kalman filter's performance (EnKF) in the estimation of time-varying model parameters with synthetic data and the real COVID-19 data of Hubei province, China. Contrary to the previous works, in the current study, the effect of damping factors on an augmented EnKF is studied. An augmented EnKF algorithm is provided, and we present how the filter performs in estimating models using uncertain observational (reported) data. Results obtained confirm that the augumented-EnKF approach can provide reliable model parameter estimates. Additionally, there was a good fit of profiles between model simulation and the reported COVID-19 data confirming the possibility of using the augmented-EnKF approach for reliable model parameter estimation.

Impact of vaccine supplies and delays on optimal control of the COVID-19 pandemic: mapping interventions for the Philippines

BACKGROUND

Around the world, controlling the COVID-19 pandemic requires national coordination of multiple intervention strategies. As vaccinations are globally introduced into the repertoire of available interventions, it is important to consider how changes in the local supply of vaccines, including delays in administration, may be addressed through existing policy levers. This study aims to identify the optimal level of interventions for COVID-19 from 2021 to 2022 in the Philippines, which as a developing country is particularly vulnerable to shifting assumptions around vaccine availability. Furthermore, we explore optimal strategies in scenarios featuring delays in vaccine administration, expansions of vaccine supply, and limited combinations of interventions.

METHODS

Embedding our work within the local policy landscape, we apply optimal control theory to the compartmental model of COVID-19 used by the Philippine government's pandemic surveillance platform and introduce four controls: (a) precautionary measures like community quarantines, (b) detection of asymptomatic cases, (c) detection of symptomatic cases, and (d) vaccinations. The model is fitted to local data using an L-BFGS minimization procedure. Optimality conditions are identified using Pontryagin's minimum principle and numerically solved using the forward-backward sweep method.

RESULTS

Simulation results indicate that early and effective implementation of both precautionary measures and symptomatic case detection is vital for averting the most infections at an efficient cost, resulting in [Formula: see text] reduction of infections compared to the no-control scenario. Expanding vaccine administration capacity to 440,000 full immunizations daily will reduce the overall cost of optimal strategy by [Formula: see text], while allowing for a faster relaxation of more resource-intensive interventions. Furthermore, delays in vaccine administration require compensatory increases in the remaining policy levers to maintain a minimal number of infections. For example, delaying the vaccines by 180 days (6 months) will result in an [Formula: see text] increase in the cost of the optimal strategy.

CONCLUSION

We conclude with practical insights regarding policy priorities particularly attuned to the Philippine context, but also applicable more broadly in similar resource-constrained settings. We emphasize three key takeaways of (a) sustaining efficient case detection, isolation, and treatment strategies; (b) expanding not only vaccine supply but also the capacity to administer them, and; (c) timeliness and consistency in adopting policy measures.

A COVID-19 Epidemic Model Predicting the Effectiveness of Vaccination in the US

A model of a COVID-19 epidemic is used to predict the effectiveness of vaccination in the US. The model incorporates key features of COVID-19 epidemics: asymptomatic and symptomatic infectiousness, reported and unreported cases data, and social measures implemented to decrease infection transmission. The model analyzes the effectiveness of vaccination in terms of vaccination efficiency, vaccination scheduling, and relaxation of social measures that decrease disease transmission. The model demonstrates that the subsiding of the epidemic as vaccination is implemented depends critically on the scale of relaxation of social measures that reduce disease transmission.