Mathematical model of COVID-19 with comorbidity and controlling using non-pharmaceutical interventions and vaccination

A multilayer network model of interaction between rumor propagation and media influence

Rumors spread among the crowd have an impact on media influence, while media influence also has an impact on rumor dissemination. This article constructs a two-layer rumor media interaction network model, in which the rumors spread in the crowd are described using the susceptibility-apathy-propagation-recovery model, and the media influence is described using the corresponding flow model. The rationality of the model is studied, and then a detailed analysis of the model is conducted. In the simulation section, we undertake a sensitivity analysis of the crucial parameters within our model, focusing particularly on their impact on the basic reproduction number. According to data simulation analysis, the following conclusion can be drawn: First, when the media unilaterally influences the crowd and does not accept feedback from the crowd, the influence of the media will decrease to zero over time, which has a negative effect on the spread of rumors among the crowd (the degree of rumor dissemination decreases). Second, when the media does not affect the audience and accepts feedback from the audience, this state is similar to the media collecting information stage, which is to accept rumors from the audience but temporarily not disclose their thoughts. At this time, both the media influence and the spread of rumors in the audience will decrease. Finally, the model is validated using an actual dataset of rumors. The simulation results show an R-squared value of 0.9606, indicating that the proposed model can accurately simulate rumor propagation in real social networks.

The impact of comorbidities and economic inequality on COVID-19 mortality in Mexico: a machine learning approach

Introduction

Studies from different parts of the world have shown that some comorbidities are associated with fatal cases of COVID-19. However, the prevalence rates of comorbidities are different around the world, therefore, their contribution to COVID-19 mortality is different. Socioeconomic factors may influence the prevalence of comorbidities; therefore, they may also influence COVID-19 mortality.

Methods

This study conducted feature analysis using two supervised machine learning classification algorithms, Random Forest and XGBoost, to examine the comorbidities and level of economic inequalities associated with fatal cases of COVID-19 in Mexico. The dataset used was collected by the National Epidemiology Center from February 2020 to November 2022, and includes more than 20 million observations and 40 variables describing the characteristics of the individuals who underwent COVID-19 testing or treatment. In addition, socioeconomic inequalities were measured using the normalized marginalization index calculated by the National Population Council and the deprivation index calculated by NASA.

Results

The analysis shows that diabetes and hypertension were the main comorbidities defining the mortality of COVID-19, furthermore, socioeconomic inequalities were also important characteristics defining the mortality. Similar features were found with Random Forest and XGBoost.

Discussion

It is imperative to implement programs aimed at reducing inequalities as well as preventable comorbidities to make the population more resilient to future pandemics. The results apply to regions or countries with similar levels of inequality or comorbidity prevalence.

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.

Policy Disparities Between Singapore and Israel in Response to the First Omicron Wave

Purpose

The purpose of this study is to evaluate public health measures during the first Omicron wave in Singapore and Israel to inform other countries confronted by COVID-19 outbreaks.

Methods

A comparative analysis was conducted using epidemiological data from Singapore and Israel between November 25th, 2021 and May 2nd, 2022 and policy information to examine the effects of public health measures in the two countries during the COVID-19 pandemic.

Results

Public health measures implemented by Singapore and Israel in response to the first Omicron wave were primarily intended to mitigate the effects of the COVID-19 pandemic. In Singapore, the pandemic led to more than 910,000 confirmed cases, a mortality rate of approximately 0.047%, a hospitalization rate of approximately 10.95%, and a severe illness rate of approximately 0.48%, without a second peak. In Israel, the pandemic not only resulted in over 2.74 million confirmed cases, a mortality rate of 0.095%, a hospitalization rate of about 7.39%, and a severe illness rate of approximately 2.30% but also returned after the significant relaxation of prevention regulations from March 1st, 2022.

Conclusion

Early and strict border control measures and surveillance measures are more effective in preventing and controlling the rapid spread of new strains of COVID-19 in the early stage. Furthermore, to prevent and control this highly infectious disease, COVID-19 vaccinations and booster shots must be promoted as soon as possible, medical service capacity must be enhanced, the hierarchical medical system must be improved, and non-pharmacological interventions must be implemented.

Allocation of hospital beds on the emergence of new infectious disease: A mathematical model

This paper is concerned to a mathematical model for the management of hospital beds when a new infection emerges in the population with the existing infections. The study of this joint dynamics presents formidable mathematical challenges due to a limited number of hospital beds. We have derived the invasion reproduction number, which investigates the potential of a newly emerged infectious disease to persist when some infectious diseases are already invaded the host population. We have shown that the proposed system exhibits transcritical, saddle-node, Hopf, and Bogdanov-Takens bifurcations under certain conditions. We have also shown that the total number of infected individuals may increase if the fraction of the total number of hospital beds is not properly allotted to the existing and a newly emerged infectious disease. The analytically obtained results are verified with the help of numerical simulations.

Symptomatic COVID-19 in Pregnancy: Hospital Cohort Data between May 2020 and April 2021, Risk Factors and Medicolegal Implications

Pregnancy does not appear to increase susceptibility to SARS-CoV-2 infection, but some physiological changes, such as the reduction of residual functional volumes, elevation of the diaphragm, and impaired cellular immunity, may increase the risk of severe disease and result in a higher risk of complications. The article’s primary objective is to evaluate the factors associated with symptomatic COVID-19 disease in pregnancy. The secondary objective is to describe maternal and neonatal outcomes and cases of vertical transmission of the infection. All pregnant women hospitalized with SARS-CoV2 infection were included in a prospective study in the UOC of Obstetrics and Gynecology, AOOR Villa Sofia—Cervello, Palermo, between May 2020 and April 2021. The patients who requested the termination of the pregnancy according to Law 194/78 were excluded. We included 165 pregnancies with a total number of 134 deliveries. Overall, 88.5% of the patients were asymptomatic at the time of admission and 11.5% were symptomatic. Of them, 1.8% of the patients required hospital admission in the intensive care unit. Symptoms occurrences were positively associated with the increase in maternal BMI (OR 1.17; p = 0.002), the prematurity (OR 4.71; p = 0.022), and at a lower birth weight (OR 0.99; p = 0.007). One infant tested positive for SARS-CoV2 nasopharyngeal swab; 11.4% of newborns had IgG anti SARS-CoV2 at birth; IgM was positive in 2.4% of newborns. There was no difference statistically significant difference in the vertical transmission of the infection among the group of symptomatic pregnant women and that of asymptomatic pregnant women.

Using a real-world network to model the trade-off between stay-at-home restriction, vaccination, social distancing and working hours on COVID-19 dynamics

Background

Human behaviour, economic activity, vaccination, and social distancing are inseparably entangled in epidemic management. This study aims to investigate the effects of various parameters such as stay-at-home restrictions, work hours, vaccination, and social distance on the containment of pandemics such as COVID-19.

Methods

To achieve this, we have developed an agent based model based on a time-dynamic graph with stochastic transmission events. The graph is constructed from a real-world social network. The edges of graph have been categorized into three categories: home, workplaces, and social environment. The conditions needed to mitigate the spread of wild-type COVID-19 and the delta variant have been analyzed. Our purposeful agent based model has carefully executed tens of thousands of individual-based simulations. We propose simple relationships for the trade-offs between effective reproduction number (R _e), transmission rate, working hours, vaccination, and stay-at-home restrictions.

Results

We have found that the effect of a 13.6% increase in vaccination for wild-type (WT) COVID-19 is equivalent to reducing four hours of work or a one-day stay-at-home restriction. For the delta, 20.2% vaccination has the same effect. Also, since we can keep track of household and non-household infections, we observed that the change in household transmission rate does not significantly alter the R _e. Household infections are not limited by transmission rate due to the high frequency of connections. For the specifications of COVID-19, the R _e depends on the non-household transmissions rate.

Conclusions

Our findings highlight that decreasing working hours is the least effective among the non-pharmaceutical interventions. Our results suggest that policymakers decrease work-related activities as a last resort and should probably not do so when the effects are minimal, as shown. Furthermore, the enforcement of stay-at-home restrictions is moderately effective and can be used in conjunction with other measures if absolutely necessary.

Optimal control and cost-effectiveness analysis for a COVID-19 model with individual protection awareness

This paper is focused on the design of optimal control strategies for COVID-19 and the model containing susceptible individuals with awareness of protection and susceptible individuals without awareness of protection is established. The goal of this paper is to minimize the number of infected people and susceptible individuals without protection awareness, and to increase the willingness of susceptible individuals to take protection measures. We conduct a qualitative analysis of this mathematical model. Based on the sensitivity analysis, the optimal control method is proposed, namely personal protective measures, vaccination and awareness raising programs. It is found that combining the three methods can minimize the number of infected people. Moreover, the introduction of awareness raising program in society will greatly reduce the existence of susceptible individuals without protection awareness. To evaluate the most cost-effective strategy we performed a cost-effectiveness analysis using the ICER method.

Investigation of vaccination game approach in spreading covid-19 epidemic model with considering the birth and death rates

In this study, an epidemic model for spreading COVID-19 is presented. This model considers the birth and death rates in the dynamics of spreading COVID-19. The birth and death rates are assumed to be the same, so the population remains constant. The dynamics of the model are explained in two phases. The first is the epidemic phase, which spreads during a season based on the proposed SIR/V model and reaches a stable state at the end of the season. The other one is the "vaccination campaign", which takes place between two seasons based on the rules of the vaccination game. In this stage, each individual in the population decides whether to be vaccinated or not. Investigating the dynamics of the studied model during a single epidemic season without consideration of the vaccination game shows waves in the model as experimental knowledge. In addition, the impact of the parameters is studied via the rules of the vaccination game using three update strategies. The result shows that the pandemic speeding can be changed by varying parameters such as efficiency and cost of vaccination, defense against contagious, and birth and death rates. The final epidemic size decreases when the vaccination coverage increases and the average social payoff is modified.

A stochastically perturbed co-infection epidemic model for COVID-19 and hepatitis B virus

A new co-infection model for the transmission dynamics of two virus hepatitis B (HBV) and coronavirus (COVID-19) is formulated to study the effect of white noise intensities. First, we present the model equilibria and basic reproduction number. The local stability of the equilibria points is proved. Moreover, the proposed stochastic model has been investigated for a non-negative solution and positively invariant region. With the help of Lyapunov function, analysis was performed and conditions for extinction and persistence of the disease based on the stochastic co-infection model were derived. Particularly, we discuss the dynamics of the stochastic model around the disease-free state. Similarly, we obtain the conditions that fluctuate at the disease endemic state holds if min ( R H s , R C s , R HC s ) > 1 . Based on extinction as well as persistence some conditions are established in form of expression containing white noise intensities as well as model parameters. The numerical results have also been used to illustrate our analytical results.

The heterogeneous mixing model of COVID-19 with interventions

The emergence of mutant strains of COVID-19 reduces the effectiveness of vaccines in preventing infection, but remains effective in preventing severe illness and death. This paper established a heterogeneous mixing model of age groups with pharmaceutical and non-pharmaceutical interventions by analyzing the transmission mechanism of breakthrough infection caused by the heterogeneity of protection period under the action of vaccine-preventable infection with the original strain. The control reproduction number Rc of the system is analyzed, and the existence and stability of equilibrium are given by the comparison principle. Numerical simulation was conducted to evaluate the vaccination program and intervention measures in the customized scenario, demonstrating that the group-3 coverage rate p3 plays a key role in Rc. It is proposed that accelerating the rate of admission and testing is conducive to epidemic control by further fitting data of COVID-19 transmission in real scenarios. The findings provide a general modeling idea for the emergence of new vaccines to prevent infection by mutant strains, as well as a solid theoretical foundation for mainland China to formulate future vaccination strategies for new vaccines. This manuscript was submitted as part of a theme issue on “Modelling COVID-19 and Preparedness for Future Pandemics”.

Modeling the effect of time delay in the increment of number of hospital beds to control an infectious disease

One of the key factors to control the spread of any infectious disease is the health care facilities, especially the number of hospital beds. To assess the impact of number of hospital beds and control of an emerged infectious disease, we have formulated a mathematical model by considering population (susceptible, infected, hospitalized) and newly created hospital beds as dynamic variables. In formulating the model, we have assumed that the number of hospital beds increases proportionally to the number of infected individuals. It is shown that on a slight change in parameter values, the model enters to different kinds of bifurcations, e.g., saddle-node, transcritical (backward and forward), and Hopf bifurcation. Also, the explicit conditions for these bifurcations are obtained. We have also shown the occurrence of Bogdanov-Takens (BT) bifurcation using the Normal form. To set up a new hospital bed takes time, and so we have also analyzed our proposed model by incorporating time delay in the increment of newly created hospital beds. It is observed that the incorporation of time delay destabilizes the system, and multiple stability switches arise through Hopf-bifurcation. To validate the results of the analytical analysis, we have carried out some numerical simulations.

Isolation in the control of epidemic

Among many epidemic prevention measures, isolation is an important method to control the spread of infectious disease. Scholars rarely study the impact of isolation on disease dissemination from a quantitative perspective. In this paper, we introduce an isolation ratio and establish the corresponding model. The basic reproductive number and its biological explanation are given. The stability conditions of the disease-free and endemic equilibria are obtained by analyzing its distribution of characteristic values. It is shown that the isolation ratio has an important influence on the basic reproductive number and the stability conditions. Taking the COVID-19 in Wuhan as an example, isolating more than 68% of the population can control the spread of the epidemic. This method can provide precise epidemic prevention strategies for government departments. Numerical simulations verify the effectiveness of the results.

A multicompartment mathematical model to study the dynamic behaviour of COVID-19 using vaccination as control parameter

To analyse novel coronavirus disease (COVID-19) transmission in India, this article provides an extended SEIR multicompartment model using vaccination as a control parameter. The model considers eight classes of infection: susceptible ( S ), vaccinated ( V ), exposed ( E ), asymptomatic infected ( A ), symptomatic infected ( I ), isolated ( J ), hospitalised ( H ), recovered ( R ). To begin, a mathematical study is performed to demonstrate the suggested model's uniform boundedness, epidemic equilibrium, and basic reproduction number. The findings indicate that if, R 0 < 1 , the disease-free equilibrium is locally asymptotically stable; but, if, R 0 > 1 the equilibrium is unstable. Secondly, we examine the effect on those who have received vaccinations with what are deemed optimal values. The suggested model is numerically simulated using MATLAB 14.0, and the results confirm the capacity of the proposed model to provide an accurate forecast of the progress of the epidemic in India. Finally, we examine the impact of immunisation on COVID-19 dissemination.

Study of COVID-19 epidemiological evolution in India with a multi-wave SIR model

The global pandemic due to the outbreak of COVID-19 ravages the whole world for more than two years in which all the countries are suffering a lot since December 2019. In this article characteristics of a multi-wave SIR model have been studied which successfully explains the features of this pandemic waves in India. Origin of the multi-wave pattern in the solution of this model is explained. Stability of this model has been studied by identifying the equilibrium points as well as by finding the eigenvalues of the corresponding Jacobian matrices. In this model, a finite probability of the recovered people for becoming susceptible again is introduced which is found crucial for obtaining the oscillatory solution in other words. Which on the other hand incorporates the effect of new variants, like delta, omicron, etc in addition to the SARS-CoV-2 virus. The set of differential equations has been solved numerically in order to obtain the variation of susceptible, infected and removed populations with time. In this phenomenological study, some specific sets of parameters are chosen in order to explain the nonperiodic variation of infected population which is found necessary to capture the feature of epidemiological wave prevailing in India. The numerical estimations are compared with the actual cases along with the analytic results.

A method for forecasting the number of hospitalized and deceased based on the number of newly infected during a pandemic

In this paper we propose a phenomenological model for forecasting the numbers of deaths and of hospitalized persons in a pandemic wave, assuming that these numbers linearly depend, with certain delays $$\tau >0$$ τ > 0 for deaths and $$\delta >0$$ δ > 0 for hospitalized, on the number of new cases. We illustrate the application of our method using data from the third wave of the COVID-19 pandemic in Croatia, but the method can be applied to any new wave of the COVID-19 pandemic, as well as to any other possible pandemic. We also supply freely available Mathematica modules to implement the method.

Modelling policy combinations of vaccination and transmission suppression of SARS-CoV-2 in Rio de Janeiro, Brazil

COVID-19 vaccination in Brazil required a phased program, with priorities for age groups, health workers, and vulnerable people. Social distancing and isolation interventions have been essential to mitigate the advance of the pandemic in several countries. We developed a mathematical model capable of capturing the dynamics of the SARS-CoV-2 dissemination aligned with social distancing, isolation measures, and vaccination. Surveillance data from the city of Rio de Janeiro provided a case study to analyze possible scenarios, including non-pharmaceutical interventions and vaccination in the epidemic scenario. Our results demonstrate that the combination of vaccination and policies of transmission suppression potentially lowered the number of hospitalized cases by 380+ and 66+ thousand cases, respectively, compared to an absence of such policies. On top of transmission suppression-only policies, vaccination impacted more than 230+ thousand averted hospitalized cases and 43+ thousand averted deaths. Therefore, health surveillance activities should be maintained along with vaccination planning in scheduled groups until a large vaccinated coverage is reached. Furthermore, this analytical framework enables evaluation of such scenarios.

Is Peracetic Acid Fumigation Effective in Public Transportation?

The COVID-19 pandemic made more people aware of the danger of viruses and bacteria, which is why disinfection began to be used more and more often. Epidemiological safety must be ensured not only in gathering places, but also in home and work environments. It is especially challenging in public transportation, which is a perfect environment for the spread of infectious disease. Therefore, the aim of the study was the identification of bacteria in crowded places and the evaluation of the effect of fumigation with peracetic acid (PAA) in public transportation. Inactivation of microorganisms in buses and long-distance coaches was carried out using an automatic commercial fogging device filled with a solution of peracetic acid stabilized with acetic acid (AA) and hydrogen peroxide (H₂O₂). Before and after disinfection, samples were taken for microbiological tests. The most prevalent bacteria were Micrococcus luteus and Bacillus licheniformis.Staphylococcus epidermidis was only present in buses, whereas Staphylococcus hominis and Exiguobacterium acetylicum were only present in coaches. Statistical analysis showed a significant reduction in the number of microorganisms in samples taken from different surfaces after disinfection in vehicles. The overall effectiveness of disinfection was 81.7% in buses and 66.5% in coaches. Dry fog fumigation with peracetic acid is an effective method of disinfecting public transport vehicles.

Dynamics of Caputo Fractional Order SEIRV Epidemic Model with Optimal Control and Stability Analysis

In mid-March 2020, the World Health Organization declared COVID-19, a worldwide public health emergency. This paper presents a study of an SEIRV epidemic model with optimal control in the context of the Caputo fractional derivative of order \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0 < \nu \le 1$$\end{document}0<ν≤1. The stability analysis of the model is performed. We also present an optimum control scheme for an SEIRV model. The real time data for India COVID-19 cases have been used to determine the parameters of the fractional order SEIRV model. The Adam-Bashforth-Moulton predictor–corrector method is implemented to solve the SEIRV model numerically. For analyzing COVID-19 transmission dynamics, the fractional order of the SEIRV model is found to be better than the integral order. Graphical demonstration and numerical simulations are presented using MATLAB (2018a) software.

The modeling and analysis of the COVID-19 pandemic with vaccination and treatment control: a case study of Maharashtra, Delhi, Uttarakhand, Sikkim, and Russia in the light of pharmaceutical and non-pharmaceutical approaches

Nonlinear dynamics is an exciting approach to describe the dynamical practices of COVID-19 disease. Mathematical modeling is a necessary method for investigating the dynamics of epidemic diseases. In the current article, an effort has been made to cultivate a novel COVID-19 compartment mathematical model by incorporating vaccinated populations. Primarily, the fundamental characteristics of the model, such as positivity and boundedness of solutions, are established. Thereafter, equilibrium analysis of steady states has been illustrated through vaccine reproduction number. Further, a nonlinear least square curve fitting technique has been employed to recognize the best fitted model parameters from the COVID-19 mortality data of five regions, namely Maharashtra, Delhi, Uttarakhand, Sikkim, and Russia. The numerical framework of the model has been added to interpret the consequence of various control schemes (pharmaceutical or non-pharmaceutical) on COVID-19 dynamics, and it has been ascertained that all the control protocols have a positive influence on curtailing the COVID-19 transference in the aforementioned regions. In addition, the essence of vaccine efficacy and vaccine-induced immunity are examined by considering different scenarios. Our analysis demonstrates that the disease will be wiped off from the Maharashtra, Delhi, Uttarakhand and Sikkim regions of India, while it shall persist in Russia for some more time. It is also found that, if a vaccine calamity arises, the government should majorly focus on permanent drug treatment of hospitalized individuals rather than vaccination.

Vaccinations, Mobility and COVID-19 Transmission

In order to prevent the spread of coronavirus disease 2019 (COVID-19), 52.4% of the world population had received at least one dose of a vaccine at17 November 2021, but little is known about the non-pharmaceutical aspect of vaccination. Here we empirically examine the impact of vaccination on human behaviors and COVID-19 transmission via structural equation modeling. The results suggest that, from a non-pharmaceutical perspective, the effectiveness of COVID-19 vaccines is related to human behaviors, in this case, mobility; vaccination slows the spread of COVID-19 in the regions where vaccination is negatively related to mobility, but such an effect is not observed in the regions where vaccination and mobility have positive correlations. This article highlights the significance of mobility in realizing the effectiveness of COVID-19 vaccines; even with large-scale vaccination, non-pharmaceutical interventions, such as social distancing, are still required to contain the transmission of COVID-19.

Modeling the importance of temporary hospital beds on the dynamics of emerged infectious disease

To explore the impact of available and temporarily arranged hospital beds on the prevention and control of an infectious disease, an epidemic model is proposed and investigated. The stability analysis of the associated equilibria is carried out, and a threshold quantity basic reproduction number ( R₀) that governs the disease dynamics is derived and observed whether it depends both on available and temporarily arranged hospital beds. We have used the center manifold theory to derive the normal form and have shown that the proposed model undergoes different types of bifurcations including transcritical (backward and forward), Bogdanov-Takens, and Hopf-bifurcation. Bautin bifurcation is obtained at which the first Lyapunov coefficient vanishes. We have taken advantage of Sotomayor's theorem to establish the saddle-node bifurcation. Numerical simulations are performed to support the theoretical findings.

Estimation of exogenous drivers to predict COVID-19 pandemic using a method from nonlinear control theory

The currently ongoing COVID-19 pandemic confronts governments and their health systems with great challenges for disease management. Epidemiological models play a crucial role, thereby assisting policymakers to predict the future course of infections and hospitalizations. One difficulty with current models is the existence of exogenous and unmeasurable variables and their significant effect on the infection dynamics. In this paper, we show how a method from nonlinear control theory can complement common compartmental epidemiological models. As a result, one can estimate and predict these exogenous variables requiring the reported infection cases as the only data source. The method allows to investigate how the estimates of exogenous variables are influenced by non-pharmaceutical interventions and how imminent epidemic waves could already be predicted at an early stage. In this way, the concept can serve as an "epidemometer" and guide the optimal timing of interventions. Analyses of the COVID-19 epidemic in various countries demonstrate the feasibility and potential of the proposed approach. The generic character of the method allows for straightforward extension to different epidemiological models.

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.

A data-driven model of the COVID-19 spread among interconnected populations: epidemiological and mobility aspects following the lockdown in Italy

An epidemic multi-group model formed by interconnected SEIR-like structures is formulated and used for data fitting to gain insight into the COVID-19 dynamics and into the role of non-pharmaceutical control actions implemented to limit the infection spread since its outbreak in Italy. The single submodels provide a rather accurate description of the COVID-19 evolution in each subpopulation by an extended SEIR model including the class of asymptomatic infectives, which is recognized as a determinant for disease diffusion. The multi-group structure is specifically designed to investigate the effects of the inter-regional mobility restored at the end of the first strong lockdown in Italy (June 3, 2020). In its time-invariant version, the model is shown to enjoy some analytical stability properties which provide significant insights on the efficacy of the implemented control measurements. In order to highlight the impact of human mobility on the disease evolution in Italy between the first and second wave onset, the model is applied to fit real epidemiological data of three geographical macro-areas in the period March-October 2020, including the mass departure for summer holidays. The simulation results are in good agreement with the data, so that the model can represent a useful tool for predicting the effects of the combination of containment measures in triggering future pandemic scenarios. Particularly, the simulation shows that, although the unrestricted mobility alone appears to be insufficient to trigger the second wave, the human transfers were crucial to make uniform the spatial distribution of the infection throughout the country and, combined with the restart of the production, trade, and education activities, determined a time advance of the contagion increase since September 2020.