A multiscale model of virus pandemic: Heterogeneous interactive entities in a globally connected world

Data-driven mathematical modeling approaches for COVID-19: A survey

In this review, we successively present the methods for phenomenological modeling of the evolution of reported and unreported cases of COVID-19, both in the exponential phase of growth and then in a complete epidemic wave. After the case of an isolated wave, we present the modeling of several successive waves separated by endemic stationary periods. Then, we treat the case of multi-compartmental models without or with age structure. Eventually, we review the literature, based on 260 articles selected in 11 sections, ranging from the medical survey of hospital cases to forecasting the dynamics of new cases in the general population. This review favors the phenomenological approach over the mechanistic approach in the choice of references and provides simulations of the evolution of the number of observed cases of COVID-19 for 10 states (California, China, France, India, Israel, Japan, New York, Peru, Spain and United Kingdom).

Interacting particle models on the impact of spatially heterogeneous human behavioral factors on dynamics of infectious diseases

Human behaviors have non-negligible impacts on spread of contagious disease. For instance, large-scale gathering and high mobility of population could lead to accelerated disease transmission, while public behavioral changes in response to pandemics may effectively reduce contacts and suppress the peak of the outbreak. In order to understand how spatial characteristics like population mobility and clustering interplay with epidemic outbreaks, we formulate a stochastic-statistical environment-epidemic dynamic system (SEEDS) via an agent-based biased random walk model on a two-dimensional lattice. The "popularity" and "awareness" variables are taken into consideration to capture human natural and preventive behavioral factors, which are assumed to guide and bias agent movement in a combined way. It is found that the presence of the spatial heterogeneity, like social influence locality and spatial clustering induced by self-aggregation, potentially suppresses the contacts between agents and consequently flats the epidemic curve. Surprisedly, disease responses might not necessarily reduce the susceptibility of informed individuals and even aggravate disease outbreak if each individual responds independently upon their awareness. The disease control is achieved effectively only if there are coordinated public-health interventions and public compliance to these measures. Therefore, our model may be useful for quantitative evaluations of a variety of public-health policies.

Stochastic transmission in epidemiological models

Recent empirical evidence suggests that the transmission coefficient in susceptible-exposed-infected-removed-like (SEIR-like) models evolves with time, presenting random patterns, and some stylized facts, such as mean-reversion and jumps. To address such observations we propose the use of jump-diffusion stochastic processes to parameterize the transmission coefficient in an SEIR-like model that accounts for death and time-dependent parameters. We provide a detailed theoretical analysis of the proposed model proving the existence and uniqueness of solutions as well as studying its asymptotic behavior. We also compare the proposed model with some variations possibly including jumps. The forecast performance of the considered models, using reported COVID-19 infections from New York City, is then tested in different scenarios. Despite the simplicity of the epidemiological model, by considering stochastic transmission, the forecasted scenarios were fairly accurate.

Impact of general incidence function on three-strain SEIAR model

We investigate the behavior of a complex three-strain model with a generalized incidence rate. The incidence rate is an essential aspect of the model as it determines the number of new infections emerging. The mathematical model comprises thirteen nonlinear ordinary differential equations with susceptible, exposed, symptomatic, asymptomatic and recovered compartments. The model is well-posed and verified through existence, positivity and boundedness. Eight equilibria comprise a disease-free equilibria and seven endemic equilibrium points following the existence of three strains. The basic reproduction numbers $ \mathfrak{R}_{01} $, $ \mathfrak{R}_{02} $ and $ \mathfrak{R}_{03} $ represent the dominance of strain 1, strain 2 and strain 3 in the environment for new strain emergence. The model establishes local stability at a disease-free equilibrium point. Numerical simulations endorse the impact of general incidence rates, including bi-linear, saturated, Beddington DeAngelis, non-monotone and Crowley Martin incidence rates.

COVID-19 dynamics and immune response: Linking within-host and between-host dynamics

The global impact of COVID-19 has led to the development of numerous mathematical models to understand and control the pandemic. However, these models have not fully captured how the disease's dynamics are influenced by both within-host and between-host factors. To address this, a new mathematical model is proposed that links these dynamics and incorporates immune response. The model is compartmentalized with a fractional derivative in the sense of Caputo-Fabrizio, and its properties are studied to show a unique solution. Parameter estimation is carried out by fitting real-life data, and sensitivity analysis is conducted using various methods. The model is then numerically implemented to demonstrate how the dynamics within infected hosts drive human-to-human transmission, and various intervention strategies are compared based on the percentage of averted deaths. The simulations suggest that a combination of medication to boost the immune system, prevent infected cells from producing the virus, and adherence to COVID-19 protocols is necessary to control the spread of the virus since no single intervention strategy is sufficient.

The coevolution of the spread of a disease and competing opinions in multiplex networks

The COVID-19 pandemic has resulted in a proliferation of conflicting opinions on physical distancing across various media platforms, which has had a significant impact on human behavior and the transmission dynamics of the disease. Inspired by this social phenomenon, we present a novel UAP-SIS model to study the interaction between conflicting opinions and epidemic spreading in multiplex networks, in which individual behavior is based on diverse opinions. We distinguish susceptibility and infectivity among individuals who are unaware, pro-physical distancing and anti-physical distancing, and we incorporate three kinds of mechanisms for generating individual awareness. The coupled dynamics are analyzed in terms of a microscopic Markov chain approach that encompasses the aforementioned elements. With this model, we derive the epidemic threshold which is related to the diffusion of competing opinions and their coupling configuration. Our findings demonstrate that the transmission of the disease is shaped in a significant manner by conflicting opinions, due to the complex interaction between such opinions and the disease itself. Furthermore, the implementation of awareness-generating mechanisms can help to mitigate the overall prevalence of the epidemic, and global awareness and self-awareness can be interchangeable in certain instances. To effectively curb the spread of epidemics, policymakers should take steps to regulate social media and promote physical distancing as the mainstream opinion.

A Spatial Kinetic Model of Crowd Evacuation Dynamics with Infectious Disease Contagion

This paper proposes a kinetic theory approach coupling together the modeling of crowd evacuation from a bounded domain with exit doors and infectious disease contagion. The spatial movement of individuals in the crowd is modeled by a proper description of the interactions with people in the crowd and the environment, including walls and exits. At the same time, interactions among healthy and infectious individuals may generate disease spreading if exposure time is long enough. Immunization of the population and individual awareness to contagion is considered as well. Interactions are modeled by tools of game theory, that let us propose the so-called tables of games that are introduced in the general kinetic equations. The proposed model is qualitatively studied and, through a series of case studies, we explore different scenarios related to crowding and gathering formation within indoor venues under the spread of a respiratory infectious disease, obtaining insights on specific policies to reduce contagion that may be implemented.

Modulating Immune Response in Viral Infection for Quantitative Forecasts of Drug Efficacy

The antiretroviral drug, the total level of viral production, and the effectiveness of immune responses are the main topics of this review because they are all dynamically interrelated. Immunological and viral processes interact in extremely complex and non-linear ways. For reliable analysis and quantitative forecasts that may be used to follow the immune system and create a disease profile for each patient, mathematical models are helpful in characterizing these non-linear interactions. To increase our ability to treat patients and identify individual differences in disease development, immune response profiling might be useful. Identifying which patients are moving from mild to severe disease would be more beneficial using immune system parameters. Prioritize treatments based on their inability to control the immune response and prevent T cell exhaustion. To increase treatment efficacy and spur additional research in this field, this review intends to provide examples of the effects of modelling immune response in viral infections, as well as the impact of pharmaceuticals on immune response.

Time-dependent vaccine efficacy estimation quantified by a mathematical model

In this paper we calculate the variation of the estimated vaccine efficacy (VE) due to the time-dependent force of infection resulting from the difference between the moment the Clinical Trial (CT) begins and the peak in the outbreak intensity. Using a simple mathematical model we tested the hypothesis that the time difference between the moment the CT begins and the peak in the outbreak intensity determines substantially different values for VE. We exemplify the method with the case of the VE efficacy estimation for one of the vaccines against the new coronavirus SARS-CoV-2.

What is life? Active particles tools towards behavioral dynamics in social-biology and economics

This review paper is devoted to study the conceptual difficulties that mathematics meets when attempting to describe the complexity of living matter focusing on the challenging perspective of developing a mathematical theory for living systems including mutations and selection. The quest starts with the identification of a number of common complexity features of living systems. Then, mathematical structures are derived to include these features, while mathematical models are derived by inserting in the structures models of individual based interactions. Three applications are examined by active particles methods, i.e., models of SARS2-CoV-2 pandemics, models of idiosyncratic learning in open markets and of the dynamics of prices accounting for human behaviors. A critical study, which pervades the whole paper, shows that also economics can be viewed as a behavioral science thus accounting for specific aspects typical of living systems.

The numerical solution of a mathematical model of the Covid-19 pandemic utilizing a meshless local discrete Galerkin method

It was in early December 2019 that the terrible news of the outbreak of new coronavirus disease (Covid-19) was reported by the world media, which appeared in Wuhan, China, and is rapidly spreading to other parts of China and several overseas countries. In the field of infectious diseases, modeling, evaluating, and predicting the rate of disease transmission are very important for epidemic prevention and control. Several preliminary mathematical models for Covid-19 are formulated by various international study groups. In this article, the SEIHR(D) compartmental model is proposed to study this epidemic and the factors affecting it, including vaccination. The proposed model can be used to compute the trajectory of the spread of the disease in different countries. Most importantly, it can be used to predict the impact of different inhibition strategies on the development of Covid-19. A computational approach is applied to solve the offered model utilizing the Galerkin method based on the moving least squares approximation constructed on a set of scattered points as a locally weighted least square polynomial fitting. As the method does not need any background meshes, its algorithm can be easily implemented on computers. Finally, illustrative examples clearly show the reliability and efficiency of the new technique and the obtained results are in good agreement with the known facts about the Covid-19 pandemic.

Modeling nonlocal behavior in epidemics via a reaction-diffusion system incorporating population movement along a network

The outbreak of COVID-19, beginning in 2019 and continuing through the time of writing, has led to renewed interest in the mathematical modeling of infectious disease. Recent works have focused on partial differential equation (PDE) models, particularly reaction-diffusion models, able to describe the progression of an epidemic in both space and time. These studies have shown generally promising results in describing and predicting COVID-19 progression. However, people often travel long distances in short periods of time, leading to nonlocal transmission of the disease. Such contagion dynamics are not well-represented by diffusion alone. In contrast, ordinary differential equation (ODE) models may easily account for this behavior by considering disparate regions as nodes in a network, with the edges defining nonlocal transmission. In this work, we attempt to combine these modeling paradigms via the introduction of a network structure within a reaction-diffusion PDE system. This is achieved through the definition of a population-transfer operator, which couples disjoint and potentially distant geographic regions, facilitating nonlocal population movement between them. We provide analytical results demonstrating that this operator does not disrupt the physical consistency or mathematical well-posedness of the system, and verify these results through numerical experiments. We then use this technique to simulate the COVID-19 epidemic in the Brazilian region of Rio de Janeiro, showcasing its ability to capture important nonlocal behaviors, while maintaining the advantages of a reaction-diffusion model for describing local dynamics.

Global dynamics of SARS-CoV-2/malaria model with antibody immune response

Coronavirus disease 2019 (COVID-19) is a new viral disease caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Malaria is a parasitic disease caused by Plasmodium parasites. In this paper, we explore a within-host model of SARS-CoV-2/malaria coinfection. This model consists of seven ordinary differential equations that study the interactions between uninfected red blood cells, infected red blood cells, free merozoites, uninfected epithelial cells, infected epithelial cells, free SARS-CoV-2 particles, and antibodies. We show that the model has bounded and nonnegative solutions. We compute all steady state points and derive their existence conditions. We use appropriate Lyapunov functions to confirm the global stability of all steady states. We enhance the reliability of the theoretical results by performing numerical simulations. The steady states reflect the monoinfection and coinfection with malaria and SARS-CoV-2. The shared immune response reduces the concentrations of malaria merozoites and SARS-CoV-2 particles in coinfected patients. This response reduces the severity of SARS-CoV-2 infection in this group of patients.

Pandemics of mutating virus and society: a multi-scale active particles approach

This article presents, within a multiscale framework, a search for a unified approach towards modelling the COVID-19 pandemic, from contagion to within-host dynamics. The modelling is focused on vaccination and therapeutical actions in general. The first part of our article is devoted to understanding the complex features of the system and to the design of a modelling rationale. Then, the modelling approach follows mainly focused on the competition between the proliferating virus and the immune system. Modelling considers also the action of vaccination plans related to the onset of new variants. This article is part of the theme issue 'Kinetic exchange models of societies and economies'.

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.

Dynamical analysis of a stochastic delayed SIR epidemic model with vertical transmission and vaccination

In order to describe the dynamic process of epidemic transmission with vertical transmission and vaccination in more detail and to better track the factors that lead to the occurrence of epidemics, we construct a stochastic delayed model with a specific functional response to describe its epidemic dynamics. We first prove the existence and uniqueness of the positive solution of the model. Moreover, we analyze the sufficient conditions for the extinction and persistence of the model. Finally, numerical simulations are presented to illustrate our mathematical findings.

Regional opening strategies with commuter testing and containment of new SARS-CoV-2 variants in Germany

BACKGROUND

Despite the vaccination process in Germany, a large share of the population is still susceptible to SARS-CoV-2. In addition, we face the spread of novel variants. Until we overcome the pandemic, reasonable mitigation and opening strategies are crucial to balance public health and economic interests.

METHODS

We model the spread of SARS-CoV-2 over the German counties by a graph-SIR-type, metapopulation model with particular focus on commuter testing. We account for political interventions by varying contact reduction values in private and public locations such as homes, schools, workplaces, and other. We consider different levels of lockdown strictness, commuter testing strategies, or the delay of intervention implementation. We conduct numerical simulations to assess the effectiveness of the different intervention strategies after one month. The virus dynamics in the regions (German counties) are initialized randomly with incidences between 75 and 150 weekly new cases per 100,000 inhabitants (red zones) or below (green zones) and consider 25 different initial scenarios of randomly distributed red zones (between 2 and 20% of all counties). To account for uncertainty, we consider an ensemble set of 500 Monte Carlo runs for each scenario.

RESULTS

We find that the strength of the lockdown in regions with out of control virus dynamics is most important to avoid the spread into neighboring regions. With very strict lockdowns in red zones, commuter testing rates of twice a week can substantially contribute to the safety of adjacent regions. In contrast, the negative effect of less strict interventions can be overcome by high commuter testing rates. A further key contributor is the potential delay of the intervention implementation. In order to keep the spread of the virus under control, strict regional lockdowns with minimum delay and commuter testing of at least twice a week are advisable. If less strict interventions are in favor, substantially increased testing rates are needed to avoid overall higher infection dynamics.

CONCLUSIONS

Our results indicate that local containment of outbreaks and maintenance of low overall incidence is possible even in densely populated and highly connected regions such as Germany or Western Europe. While we demonstrate this on data from Germany, similar patterns of mobility likely exist in many countries and our results are, hence, generalizable to a certain extent.

Factors Associated with COVID-19 Vaccine Booster Hesitancy: A Retrospective Cohort Study, Fukushima Vaccination Community Survey

This was a retrospective cohort study, which aimed to investigate the factors associated with hesitancy to receive a third dose of a coronavirus disease 2019 (COVID-19) vaccine. A paper-based questionnaire survey was administered to all participants. This study included participants who provided answers in the questionnaire about whether they had an intent to receive a third dose of a vaccine. Data on sex, age, area of residence, adverse reactions after the second vaccination, whether the third vaccination was desired, and reasons to accept or hesitate over the booster vaccination were retrieved. Among the 2439 participants, with a mean (±SD) age of 52.6 ± 18.9 years, and a median IgG-S antibody titer of 324.9 (AU/mL), 97.9% of participants indicated their intent to accept a third vaccination dose. The logistic regression revealed that participants of a younger age (OR = 0.98; 95% CI: 0.96–1.00) and with a higher antibody level (OR = 2.52; 95% CI: 1.27–4.99) were positively associated with hesitancy over the third vaccine. The efficacy of the COVID-19 vaccine and concerns about adverse reactions had a significant impact on behavior regarding the third vaccination. A rapid increase in the booster dose rate is needed to control the pandemic, and specific approaches should be taken with these groups that are likely to hesitate over the third vaccine, subsequently increasing booster contact rate.

Mathematical models for dengue fever epidemiology: A 10-year systematic review

Mathematical models have a long history in epidemiological research, and as the COVID-19 pandemic progressed, research on mathematical modeling became imperative and very influential to understand the epidemiological dynamics of disease spreading. Mathematical models describing dengue fever epidemiological dynamics are found back from 1970. Dengue fever is a viral mosquito-borne infection caused by four antigenically related but distinct serotypes (DENV-1 to DENV-4). With 2.5 billion people at risk of acquiring the infection, it is a major international public health concern. Although most of the cases are asymptomatic or mild, the disease immunological response is complex, with severe disease linked to the antibody-dependent enhancement (ADE) - a disease augmentation phenomenon where pre-existing antibodies to previous dengue infection do not neutralize but rather enhance the new infection. Here, we present a 10-year systematic review on mathematical models for dengue fever epidemiology. Specifically, we review multi-strain frameworks describing host-to-host and vector-host transmission models and within-host models describing viral replication and the respective immune response. Following a detailed literature search in standard scientific databases, different mathematical models in terms of their scope, analytical approach and structural form, including model validation and parameter estimation using empirical data, are described and analyzed. Aiming to identify a consensus on infectious diseases modeling aspects that can contribute to public health authorities for disease control, we revise the current understanding of epidemiological and immunological factors influencing the transmission dynamics of dengue. This review provide insights on general features to be considered to model aspects of real-world public health problems, such as the current epidemiological scenario we are living in.

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.

Global analysis of within-host SARS-CoV-2/HIV coinfection model with latency

The coronavirus disease 2019 (COVID-19) is a respiratory disease caused by a virus called the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). In this paper, we analyze a within-host SARS-CoV-2/HIV coinfection model. The model is made up of eight ordinary differential equations. These equations describe the interactions between healthy epithelial cells, latently infected epithelial cells, productively infected epithelial cells, SARS-CoV-2 particles, healthy CD 4 + T cells, latently infected CD 4 + T cells, productively infected CD 4 + T cells, and HIV particles. We confirm that the solutions of the developed model are bounded and nonnegative. We calculate the different steady states of the model and derive their existence conditions. We choose appropriate Lyapunov functions to show the global stability of all steady states. We execute some numerical simulations to assist the theoretical contributions. Based on our results, weak CD 4 + T cell immunity in SARS-CoV-2/HIV coinfected patients causes an increase in the concentrations of productively infected epithelial cells and SARS-CoV-2 particles. This may lead to severe SARS-CoV-2 infection in HIV patients. This result agrees with many studies that discussed the high risk of severe infection and death in HIV patients when they get SARS-CoV-2 infection. On the other hand, increasing the death rate of infected epithelial cells during the latency period can reduce the severity of SARS-CoV-2 infection in HIV patients. More studies are needed to understand the dynamics of SARS-CoV-2/HIV coinfection and find better ways to treat this vulnerable group of patients.

Intention to Receive the COVID-19 Vaccine Booster Dose in a University Community in Italy

This cross-sectional study, conducted in Naples (Italy) between 16 November and 6 December 2021, explored the willingness to receive the booster dose of the COVID-19 vaccine among a random sample selected from the list of those who had completed a primary vaccination series at the immunization center of a teaching hospital in Naples and the associated factors. Females had a significantly higher perceived risk of getting the SARS-CoV-2 infection, whereas those not-having a cohabitant were less worried. 85.7% were willing to receive the booster dose. Those older respondents who perceived a better health status after the primary vaccination series, who have friends/family members who were diagnosed with COVID-19, who had received information from official government organizations, and those who did not need information would be willing to get the booster dose. 24.7% was hesitant with a Vaccine Hesitancy Scale (VHS) score ≥ 25. Respondents who self-rated a lower health status after the primary vaccination series, who did not have friends/family members who were diagnosed with COVID-19, who had not received information from official government organizations, and who needed information were hesitant. Information and communication regarding the benefits and efficacy of the booster dose are needed in order to control the pandemic.

Multivalue Collocation Methods for Ordinary and Fractional Differential Equations

The present paper illustrates some classes of multivalue methods for the numerical solution of ordinary and fractional differential equations. In particular, it focuses on two-step and mixed collocation methods, Nordsieck GLM collocation methods for ordinary differential equations, and on two-step spline collocation methods for fractional differential equations. The construction of the methods together with the convergence and stability analysis are reported and some numerical experiments are carried out to show the efficiency of the proposed methods.

A stochastic model for the influence of social distancing on loneliness

The short-term economic consequences of the critical measures employed to curb the transmission of Covid-19 are all too familiar, but the consequences of isolation and loneliness resulting from those measures on the mental well-being of the population and their ensuing long-term economic effects are largely unknown. Here we offer a stochastic agent-based model to investigate social restriction measures in a community where the feelings of loneliness of the agents dwindle when they are socializing and grow when they are alone. In addition, the intensity of those feelings, which are measured by a real variable that we term degree of loneliness, determines whether the agent will seek social contact or not. We find that decrease of the number, quality or duration of social contacts lead the community to enter a regime of burnout in which the degree of loneliness diverges, although the number of lonely agents at a given moment amounts to only a fraction of the total population. This regime of mental breakdown is separated from the healthy regime, where the degree of loneliness is finite, by a continuous phase transition. We show that the community dynamics is described extremely well by a simple mean-field theory so our conclusions can be easily verified for different scenarios and parameter settings. The appearance of the burnout regime illustrates neatly the side effects of social distancing, which give to many of us the choice between physical infection and mental breakdown.

Policy Lessons From Medical Responses to the COVID-19 Crisis

This article discusses the medical/therapeutical responses to the COVID-19 pandemic and their political economy context. First, the very quick development of several vaccines highlights the richness of the basic knowledge waiting for therapeutical exploitation. Such knowledge has largely originated in public or non-profit institutions. Second, symmetrically, there is longer-term evidence that the private sector (essentially big pharma) has decreased its investment in basic research in general and has long been uninterested in vaccines in particular. Only when flooded with an enormous amount of public money did it become eager to undertake applied research, production scale-up and testing. Third, the political economy of the underlying public-private relationship reveals a profound dysfunctionality with the public being unable to determine the rates and direction of innovation, but at the same time confined to the role of payer of first and last resort, with dire consequences for both advanced, and more so developing countries. Fourth, on normative grounds, measures like ad hoc patent waivers are certainly welcome, but this will not address the fundamental challenge, involving a deep reform of the intellectual property rights regimes and their international protection.

Global stability of a within-host SARS-CoV-2/cancer model with immunity and diffusion

Coronavirus disease 2019 (COVID-19) is a new respiratory disease caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). It started in China and spread quickly to all continents. This virus has changed the life style and the education system in many countries. As for other viruses, mathematical models have been rated as a useful tool to support the research on COVID-19. In this work, we develop a reaction–diffusion model to describe the within-host dynamics of SARS-CoV-2 in cancer patients. This model studies the interactions between nutrient, healthy epithelial cells, cancer cells, SARS-CoV-2 particles, and immune cells. The model incorporates the spatial mobility of the cells and viruses. The model includes parameters for measuring the effect of lymphopenia on SARS-CoV-2/cancer patients. We verify the basic features of the model’s solutions including the uniqueness, nonnegativity and boundedness. We list all equilibrium points of the proposed model. We show the global stability and the local instability of the most meaningful equilibria. We display some numerical simulations to enhance our theoretical results. The results indicate that diffusion can have a clear effect at the beginning of SARS-CoV-2 infection. Lymphopenia in SARS-CoV-2/cancer patients impairs the immune responses against cancer and SARS-CoV-2, and worsens the health state of patients.

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.

Assessing the Spatio-temporal Spread of COVID-19 via Compartmental Models with Diffusion in Italy, USA, and Brazil

The outbreak of COVID-19 in 2020 has led to a surge in interest in the mathematical modeling of infectious diseases. Such models are usually defined as compartmental models, in which the population under study is divided into compartments based on qualitative characteristics, with different assumptions about the nature and rate of transfer across compartments. Though most commonly formulated as ordinary differential equation models, in which the compartments depend only on time, recent works have also focused on partial differential equation (PDE) models, incorporating the variation of an epidemic in space. Such research on PDE models within a Susceptible, Infected, Exposed, Recovered, and Deceased framework has led to promising results in reproducing COVID-19 contagion dynamics. In this paper, we assess the robustness of this modeling framework by considering different geometries over more extended periods than in other similar studies. We first validate our code by reproducing previously shown results for Lombardy, Italy. We then focus on the U.S. state of Georgia and on the Brazilian state of Rio de Janeiro, one of the most impacted areas in the world. Our results show good agreement with real-world epidemiological data in both time and space for all regions across major areas and across three different continents, suggesting that the modeling approach is both valid and robust.

Cure and death play a role in understanding dynamics for COVID-19: Data-driven competing risk compartmental models, with and without vaccination

Several factors have played a strong role in influencing the dynamics of COVID-19 in the U.S. One being the economy, where a tug of war has existed between lockdown measures to control disease versus loosening of restrictions to address economic hardship. A more recent effect has been availability of vaccines and the mass vaccination efforts of 2021. In order to address the challenges in analyzing this complex process, we developed a competing risk compartmental model framework with and without vaccination compartment. This framework separates instantaneous risk of removal for an infectious case into competing risks of cure and death, and when vaccinations are present, the vaccinated individual can also achieve immunity before infection. Computations are performed using a simple discrete time algorithm that utilizes a data driven contact rate. Using population level pre-vaccination data, we are able to identify and characterize three wave patterns in the U.S. Estimated mortality rates for second and third waves are 1.7%, which is a notable decrease from 8.5% of a first wave observed at onset of disease. This analysis reveals the importance cure time has on infectious duration and disease transmission. Using vaccination data from 2021, we find a fourth wave, however the effect of this wave is suppressed due to vaccine effectiveness. Parameters playing a crucial role in this modeling were a lower cure time and a signficantly lower mortality rate for the vaccinated.

Quantifying collective intelligence and behaviours of SARS-CoV-2 via environmental resources from virus' perspectives

Collective intelligence of viruses is witnessed in many research articles. Most of the researches focus on the qualitative properties or observations. In this research, we model the behaviours and collective intelligence of SARS-CoV-2 by minimal spanning trees (MSTs), which specify the underlying mechanisms of resource allocation in the viral colony. The vertices of the trees are 50 states, DC and NYC in the USA. The weights of the edges are assigned by the reciprocal of the sum of cases or deaths of COVID-19. The types of trees are decided by the chosen 18 factors. We sample 304 time-series data and compute their MST-based auto-correlations for stability analysis. Then we perform correlated analysis and comparative analysis on these stable factors. Our results show MST approach fits the collective intelligence modelling very well; the total cases and total deaths over areas are highly correlated in terms of MSTs; and these stable factors have little to do with the geographical distance. The results also indicate the colonisation of SARS-CoV-2 is pretty mature and organised. Based on the results, for environmental or health policies, we should also turn our attention to the transmission routes that are independent of or far away from human population or densities. The viruses' colonies might already exist in the wild in a large scale, not only in the populated or polluted cities. We shall build or conduct a monitoring system of their colonisation and survival techniques, in order to terminate, contain or live with their communities.

Data-driven methods for present and future pandemics: Monitoring, modelling and managing

This survey analyses the role of data-driven methodologies for pandemic modelling and control. We provide a roadmap from the access to epidemiological data sources to the control of epidemic phenomena. We review the available methodologies and discuss the challenges in the development of data-driven strategies to combat the spreading of infectious diseases. Our aim is to bring together several different disciplines required to provide a holistic approach to epidemic analysis, such as data science, epidemiology, and systems-and-control theory. A 3M-analysis is presented, whose three pillars are: Monitoring, Modelling and Managing. The focus is on the potential of data-driven schemes to address three different challenges raised by a pandemic: (i) monitoring the epidemic evolution and assessing the effectiveness of the adopted countermeasures; (ii) modelling and forecasting the spread of the epidemic; (iii) making timely decisions to manage, mitigate and suppress the contagion. For each step of this roadmap, we review consolidated theoretical approaches (including data-driven methodologies that have been shown to be successful in other contexts) and discuss their application to past or present epidemics, such as Covid-19, as well as their potential application to future epidemics.

The paradox of productivity during quarantine: an agent-based simulation

ABSTRACT

Economies across the globe were brought to their knees due to lockdowns and social restriction measures to contain the spread of the SARS-CoV-2, despite the quick switch to remote working. This downfall may be partially explained by the "water cooler effect", which holds that higher levels of social interaction lead to higher productivity due to a boost in people's mood. Somewhat paradoxically, however, there are reports of increased productivity in the remote working scenario. Here we address quantitatively this issue using a variety of experimental findings of social psychology that address the interplay between mood, social interaction and productivity to set forth an agent-based model for a workplace composed of extrovert and introvert agent stereotypes that differ solely on their propensities to initiate a social interaction. We find that the effects of curtailing social interactions depend on the proportion of the stereotypes in the working group: while the social restriction measures always have a negative impact on the productivity of groups composed predominantly of introverts, they may actually improve the productivity of groups composed predominantly of extroverts. Our results offer a proof of concept that the paradox of productivity during quarantine can be explained by taking into account the distinct effects of the social distancing measures on extroverts and introverts.

GRAPHIC ABSTRACT

Adaptive mesh refinement and coarsening for diffusion-reaction epidemiological models

The outbreak of COVID-19 in 2020 has led to a surge in the interest in the mathematical modeling of infectious diseases. Disease transmission may be modeled as compartmental models, in which the population under study is divided into compartments and has assumptions about the nature and time rate of transfer from one compartment to another. Usually, they are composed of a system of ordinary differential equations in time. A class of such models considers the Susceptible, Exposed, Infected, Recovered, and Deceased populations, the SEIRD model. However, these models do not always account for the movement of individuals from one region to another. In this work, we extend the formulation of SEIRD compartmental models to diffusion-reaction systems of partial differential equations to capture the continuous spatio-temporal dynamics of COVID-19. Since the virus spread is not only through diffusion, we introduce a source term to the equation system, representing exposed people who return from travel. We also add the possibility of anisotropic non-homogeneous diffusion. We implement the whole model in libMesh, an open finite element library that provides a framework for multiphysics, considering adaptive mesh refinement and coarsening. Therefore, the model can represent several spatial scales, adapting the resolution to the disease dynamics. We verify our model with standard SEIRD models and show several examples highlighting the present model's new capabilities.

Analysis of a within-host HIV/HTLV-I co-infection model with immunity

Human immunodeficiency virus (HIV) and human T-lymphotropic virus type I (HTLV-I) are two retroviruses that attack the immune cells and impair their functions. Both HIV and HTLV-I can be transmitted between individuals through direct contact with certain body fluids from infected individuals. Therefore, a person can be co-infected with both viruses. HIV causes acquired immunodeficiency syndrome, while HTLV-I is the causative agent for adult T-cell leukemia and HTLV-I-associated myelopathy/tropical spastic paraparesis. Several mathematical models have been developed in the literature to describe the within-host dynamics of HIV and HTLV-I mono-infections. However, modeling a within-host dynamics of HIV/HTLV-I co-infection has not been involved. In the present paper, we are concerned to formulate and analyze a new HIV/HTLV co-infection model under the effect of Cytotoxic T lymphocytes (CTLs) immune response. The model describes the interaction between susceptible CD4⁺T cells, silent HIV-infected cells, active HIV-infected cells, silent HTLV-infected cells, Tax-expressing HTLV-infected cells, free HIV particles, HIV-specific CTLs and HTLV-specific CTLs. The HIV can spread by two routes of transmission, virus-to-cell and cell-to-cell. On the other side, HTLV-I has two modes of transmission, (i) horizontal transmission via direct cell-to-cell contact, and (ii) vertical transmission through mitotic division of Tax-expressing HTLV-infected cells. The well-posedness of the model is established by showing that the solutions of the model are nonnegative and bounded. We define a set of threshold parameters which govern the existence and stability of all equilibria of the model. We explore the global asymptotic stability of all equilibria by utilizing Lyapunov function and LaSalle's invariance principle. We have presented numerical simulations to justify the applicability and effectiveness of the theoretical results. In addition, we evaluate the effect of HTLV-I infection on the HIV dynamics and vice versa.

Economic Segregation Under the Action of Trading Uncertainties

We study the distribution of wealth in a market economy in which the trading propensity of the agents is uncertain. Our approach is based on kinetic models for collective phenomena, which, at variance with the classical kinetic theory of rarefied gases, has to face the lack of fundamental principles, which are replaced by empirical social forces of which we have at most statistical information. The proposed kinetic description allows recovering emergent wealth distribution profiles, which are described by the steady states of a Fokker–Planck-type equation with uncertain parameters. A statistical study of the stationary profiles of the Fokker–Planck equation then shows that the wealth distribution can develop a multimodal shape in the presence of observable highly stressful economic situations.

Unequal societies in usual times, unjust societies in pandemic ones

The explosion of the pandemic has been optimistically considered as the “last straw that breaks the camel’s back”. At the time of writing, after three months since its outburst, we can hardly find any sign of a “broken camel”: indeed, it could have been the opportunity to collectively question the current regime of production and appropriation, exclusion and marketization characterizing this phase of unjust “rentified capitalism”, but the route taken has largely seen a frightening combination of “business as usual” on the production side and pervasive forms of social control, limitations of individual and collective rights and the perpetuation of a false dichotomy between economic and health security. This pandemic, which under decent public health provisions might have been a controlled disease, is producing the most severe crisis after the Great Depression and has been used to implement forms of massive social control hardly conceivable in “advanced democracies”. Butterfly effects are well-known in complexity sciences. However, social scientists have still difficulties in understanding how a grain can make the sandcastle fall down. On the contrary, we are now under the actual risk of starting a “new normal” without dealing with the deep routes and origins of this crisis, with the dominant intellectual discourse pushing for maintaining and indeed reinforcing the status quo, established power and social blocks. This myopic strategy might end up in collectively disruptive socio-political transformations.