An age and space structured SIR model describing the Covid-19 pandemic

Infectious Disease Spreading Fought by Multiple Vaccines Having a Prescribed Time Effect

We propose a framework for the description of the effects of vaccinations on the spreading of an epidemic disease. Different vaccines can be dosed, each providing different immunization times and immunization levels. Differences due to individuals' ages are accounted for through the introduction of either a continuous age structure or a discrete set of age classes. Extensions to gender differences or to distinguish fragile individuals can also be considered. Within this setting, vaccination strategies can be simulated, tested and compared, as is explicitly described through numerical integrations.

Socio-economic analysis of short-term trends of COVID-19: modeling and data analytics

BACKGROUND

COVID-19 caused a worldwide outbreak leading the majority of human activities to a rough breakdown. Many stakeholders proposed multiple interventions to slow down the disease and number of papers were devoted to the understanding the pandemic, but to a less extend some were oriented socio-economic analysis. In this paper, a socio-economic analysis is proposed to investigate the early-age effect of socio-economic factors on COVID-19 spread.

METHODS

Fifty-two countries were selected for this study. A cascade algorithm was developed to extract the R0 number and the day J*; these latter should decrease as the pandemic flattens. Subsequently, R0 and J* were modeled according to socio-economic factors using multilinear stepwise-regression.

RESULTS

The findings demonstrated that low values of days before lockdown should flatten the pandemic by reducing J*. Hopefully, DBLD is only parameter to be tuned in the short-term; the other socio-economic parameters cannot easily be handled as they are annually updated. Furthermore, it was highlighted that the elderly is also a major influencing factor especially because it is involved in the interactions terms in R0 model. Simulations proved that the health care system could improve the pandemic damping for low elderly. In contrast, above a given elderly, the reproduction number R0 cannot be reduced even for developed countries (showing high HCI values), meaning that the disease's severity cannot be smoothed regardless the performance of the corresponding health care system; non-pharmaceutical interventions are then expected to be more efficient than corrective measures.

DISCUSSION

The relationship between the socio-economic factors and the pandemic parameters R0 and J* exhibits complex relations compared to the models that are proposed in the literature. The quadratic regression model proposed here has discriminated the most influencing parameters within the following approximated order, DLBL, HCI, Elderly, Tav, CO2, and WC as first order, interaction, and second order terms.

CONCLUSIONS

This modeling allowed the emergence of interaction terms that don't appear in similar studies; this led to emphasize more complex relationship between the infection spread and the socio-economic factors. Future works will focus on enriching the datasets and the optimization of the controlled parameters to short-term slowdown of similar pandemics.

The influence of gender on COVID-19 infections and mortality in Germany: Insights from age- and gender-specific modeling of contact rates, infections, and deaths in the early phase of the pandemic

Recent research points towards age- and gender-specific transmission of COVID-19 infections and their outcomes. The effect of gender, however, has been overlooked in past modelling approaches of COVID-19 infections. The aim of our study is to explore how gender-specific contact behavior affects gender-specific COVID-19 infections and deaths. We consider a compartment model to establish short-term forecasts of the COVID-19 epidemic over a time period of 75 days. Compartments are subdivided into different age groups and genders, and estimated contact patterns, based on previous studies, are incorporated to account for age- and gender-specific social behaviour. The model is fitted to real data and used for assessing the effect of hypothetical contact scenarios all starting at a daily level of 10 new infections per million population. On day 75 after the end of the lockdown, infection rates are highest among the young and working-age, but they also have increased among the old. Sex ratios reveal higher infection risks among women than men at working ages; the opposite holds true at old age. Death rates in all age groups are twice as high for men as for women. Small changes in contact rates at working and young ages have a considerable effect on infections and mortality at old age, with elderly men being always at higher risk of infection and mortality. Our results underline the high importance of the non-pharmaceutical mitigation measures (NPMM) in low-infection phases of the pandemic to prevent that an increase in contact rates leads to higher mortality among the elderly, even if easing measures take place among the young. At young and middle ages, women's contribution to increasing infections is higher due to their higher number of contacts. Gender differences in contact rates may be one pathway that contributes to the spread of the disease and results in gender-specific infection rates and their mortality outcome. To further explore possible pathways, more data on contact behavior and COVID-19 transmission is needed, which includes gender- and socio-demographic information.

Mathematical Analysis of Two Waves of COVID-19 Disease with Impact of Vaccination as Optimal Control

This paper is devoted to answering some questions using a mathematical model by analyzing India’s first and second phases of the COVID-19 pandemic. A new mathematical model is introduced with a nonmonotonic incidence rate to incorporate the psychological effect of COVID-19 in society. The paper also discusses the local stability and global stability of an endemic equilibrium and a disease-free equilibrium. The basic reproduction number is evaluated using the proposed COVID-19 model for disease spread in India based on the actual data sets. The study of nonperiodic solutions at a positive equilibrium point is also analyzed. The model is rigorously studied using MATLAB to alert the decision-making bodies to hinder the emergence of any other pandemic outbreaks or the arrival of subsequent pandemic waves. This paper shows the excellent prediction of the first wave and very commanding for the second wave. The exciting results of the paper are as follows: (i) psychological effect on the human population has an impact on propagation; (ii) lockdown is a suitable technique mathematically to control the COVID spread; (iii) different variants produce different waves; (iv) the peak value always crosses its past value.

Effects of Vaccination Efficacy on Wealth Distribution in Kinetic Epidemic Models

The spread of the COVID-19 pandemic has highlighted the close link between economics and health in the context of emergency management. A widespread vaccination campaign is considered the main tool to contain the economic consequences. This paper will focus, at the level of wealth distribution modeling, on the economic improvements induced by the vaccination campaign in terms of its effectiveness rate. The economic trend during the pandemic is evaluated, resorting to a mathematical model joining a classical compartmental model including vaccinated individuals with a kinetic model of wealth distribution based on binary wealth exchanges. The interplay between wealth exchanges and the progress of the infectious disease is realized by assuming, on the one hand, that individuals in different compartments act differently in the economic process and, on the other hand, that the epidemic affects risk in economic transactions. Using the mathematical tools of kinetic theory, it is possible to identify the equilibrium states of the system and the formation of inequalities due to the pandemic in the wealth distribution of the population. Numerical experiments highlight the importance of the vaccination campaign and its positive effects in reducing economic inequalities in the multi-agent society.

A Data-Based Approach Using a Multi-Group SIR Model with Fuzzy Subsets: Application to the COVID-19 Simulation in the Islands of Guadeloupe

In this paper, we propose a multi-group SIR to simulate the spread of COVID-19 in an island context. The multi-group aspect enables us to modelize transmissions of the virus between non-vaccinated individuals within an age group as well as between different age groups. In addition, fuzzy subsets and aggregation operators are used to account for the increased risks associated with age and obesity within these different groups. From a conceptual point of view, the model emphasizes the notion of Hospitalization which is the major stake of this pandemic by replacing the compartment R (Removed) by compartment H (Hospitalization). The experimental results were carried out using medical and demographic data from the archipelago, Guadeloupe (French West Indies) in the Caribbean. These results show that without the respect of barrier gestures, a first wave would concern the elderly then a second the adults and the young people, which conforms to the real data.

Two-Age-Structured COVID-19 Epidemic Model: Estimation of Virulence Parameters to Interpret Effects of National and Regional Feedback Interventions and Vaccination

The COVID-19 epidemic has recently led in Italy to the implementation of different external strategies in order to limit the spread of the disease in response to its transmission rate: strict national lockdown rules, followed first by a weakening of the social distancing and contact reduction feedback interventions and finally the implementation of coordinated intermittent regional actions, up to the application, in this last context, of an age-stratified vaccine prioritization strategy. This paper originally aims at identifying, starting from the available age-structured real data at the national level during the specific aforementioned scenarios, external-scenario-dependent sets of virulence parameters for a two-age-structured COVID-19 epidemic compartmental model, in order to provide an interpretation of how each external scenario modifies the age-dependent patterns of social contacts and the spread of COVID-19.

Spatial spread of COVID-19 outbreak in Italy using multiscale kinetic transport equations with uncertainty

In this paper we introduce a space-dependent multiscale model to describe the spatial spread of an infectious disease under uncertain data with particular interest in simulating the onset of the COVID-19 epidemic in Italy. While virus transmission is ruled by a SEIAR type compartmental model, within our approach the population is given by a sum of commuters moving on a extra-urban scale and non commuters interacting only on the smaller urban scale. A transport dynamics of the commuter population at large spatial scales, based on kinetic equations, is coupled with a diffusion model for non commuters at the urban scale. Thanks to a suitable scaling limit, the kinetic transport model used to describe the dynamics of commuters, within a given urban area coincides with the diffusion equations that characterize the movement of non-commuting individuals. Because of the high uncertainty in the data reported in the early phase of the epidemic, the presence of random inputs in both the initial data and the epidemic parameters is included in the model. A robust numerical method is designed to deal with the presence of multiple scales and the uncertainty quantification process. In our simulations, we considered a realistic geographical domain, describing the Lombardy region, in which the size of the cities, the number of infected individuals, the average number of daily commuters moving from one city to another, and the epidemic aspects are taken into account through a calibration of the model parameters based on the actual available data. The results show that the model is able to describe correctly the main features of the spatial expansion of the first wave of COVID-19 in northern Italy.

A Control Based Mathematical Model for the Evaluation of Intervention Lines in COVID-19 Epidemic Spread: The Italian Case Study

This paper addresses the problem of describing the spread of COVID-19 by a mathematical model introducing all the possible control actions as prevention (informative campaign, use of masks, social distancing, vaccination) and medication. The model adopted is similar to SEIQR, with the infected patients split into groups of asymptomatic subjects and isolated ones. This distinction is particularly important in the current pandemic, due to the fundamental the role of asymptomatic subjects in the virus diffusion. The influence of the control actions is considered in analysing the model, from the calculus of the equilibrium points to the determination of the reproduction number. This choice is motivated by the fact that the available organised data have been collected since from the end of February 2020, and almost simultaneously containment measures, increasing in typology and effectiveness, have been applied. The characteristics of COVID-19, not fully understood yet, suggest an asymmetric diffusion among countries and among categories of subjects. Referring to the Italian situation, the containment measures, as applied by the population, have been identified, showing their relation with the government’s decisions; this allows the study of possible scenarios, comparing the impact of different possible choices.

Verification results for age-structured models of economic-epidemics dynamics

In this paper we propose a macro-dynamic age-structured set-up for the analysis of epidemics/economic dynamics in continuous time. The resulting optimal control problem is reformulated in an infinite dimensional Hilbert space framework where we perform the basic steps of dynamic programming approach. Our main result is a verification theorem which allows to guess the feedback form of optimal strategies. This will be a departure point to discuss the behavior of the models of the family we introduce and their policy implications.