The impact of spatial and social structure on an SIR epidemic on a weighted multilayer network

A key factor in the transmission of infectious diseases is the structure of disease transmitting contacts. In the context of the current COVID-19 pandemic and with some data based on the Hungarian population we develop a theoretical epidemic model (susceptible-infected-removed, SIR) on a multilayer network. The layers include the Hungarian household structure, with population divided into children, adults and elderly, as well as schools and workplaces, some spatial embedding and community transmission due to sharing communal spaces, service and public spaces. We investigate the sensitivity of the model (via the time evolution and final size of the epidemic) to the different contact layers and we map out the relation between peak prevalence and final epidemic size. When compared to the classic compartmental model and for the same final epidemic size, we find that epidemics on multilayer network lead to higher peak prevalence meaning that the risk of overwhelming the health care system is higher. Based on our model we found that keeping cliques/bubbles in school as isolated as possible has a major effect while closing workplaces had a mild effect as long as workplaces are of relatively small size.

Asymptomatic individuals can increase the final epidemic size under adaptive human behavior

Infections produced by non-symptomatic (pre-symptomatic and asymptomatic) individuals have been identified as major drivers of COVID-19 transmission. Non-symptomatic individuals, unaware of the infection risk they pose to others, may perceive themselves—and be perceived by others—as not presenting a risk of infection. Yet, many epidemiological models currently in use do not include a behavioral component, and do not address the potential consequences of risk misperception. To study the impact of behavioral adaptations to the perceived infection risk, we use a mathematical model that incorporates the behavioral decisions of individuals, based on a projection of the system’s future state over a finite planning horizon. We found that individuals’ risk misperception in the presence of non-symptomatic individuals may increase or reduce the final epidemic size. Moreover, under behavioral response the impact of non-symptomatic infections is modulated by symptomatic individuals’ behavior. Finally, we found that there is an optimal planning horizon that minimizes the final epidemic size.

Assessing the impact of adherence to Non-pharmaceutical interventions and indirect transmission on the dynamics of COVID-19: a mathematical modelling study

Adherence to public health policies such as the non-pharmaceutical interventions implemented against COVID-19 plays a major role in reducing infections and controlling the spread of the diseases. In addition, understanding the transmission dynamics of the disease is also important in order to make and implement efficient public health policies. In this paper, we developed an SEIR-type compartmental model to assess the impact of adherence to COVID-19 non-pharmaceutical interventions and indirect transmission on the dynamics of the disease. Our model considers both direct and indirect transmission routes and stratifies the population into two groups: those that adhere to COVID-19 non-pharmaceutical interventions (NPIs) and those that do not adhere to the NPIs. We compute the control reproduction number and the final epidemic size relation for our model and study the effect of different parameters of the model on these quantities. Our results show that direct transmission has more effect on the reproduction number and final epidemic size, relative to indirect transmission. In addition, we showed that there is a significant benefit in adhering to the COVID-19 NPIs.

Modeling the COVID-19 spread, a case study of Egypt

In this article, the authors applied a logistic growth model explaining the dynamics of the spread of COVID-19 in Egypt. The model which is simple follows well-known premises in population dynamics. Our aim is to calculate an approximate estimate of the total number of infected persons during the course of the disease. The model predicted—to a high degree of correctness—the timing of the pandemic peak$$t_{{\text{m}}}$$ t m and the final epidemic size$$P$$ P ; the latter was foreseen by the model long before it was announced by the Egyptian authorities. The estimated values from the model were also found to match significantly with the nation reported data during the course of the disease. The period in which we applied the model was from the first of April 2020 until the beginning of October of the same year. By the time the manuscript was returned for revision, the second wave swept through Egypt and the authors felt obliged to renew their study. Finally, a comparison is made with the SIR model showing that ours is much simpler; yet leading to the same results.

Adaptive Human Behavior in Epidemics: the Impact of Risk Misperception on the Spread of Epidemics

Infections produced by pre-symptomatic and asymptomatic (non-symptomatic) individuals have been identified as major drivers of COVID-19 transmission. Non-symptomatic individuals unaware of the infection risk they pose to others, may perceive themselves --and being perceived by others-- as not representing risk of infection. Yet many epidemiological models currently in use do not include a behavioral component, and do not address the potential consequences of risk misperception. To study the impact of behavioral adaptations to the perceived infection risk, we use a mathematical model that incorporates individuals' behavioral decisions based on a projection of the future system's state over a finite planning horizon. We found that individuals' risk misperception in the presence of asymptomatic individuals may increase or reduce the final epidemic size. Moreover, under behavioral response the impact of asymptomatic infections is modulated by symptomatic individuals' behavior. Finally, we found that there is an optimal planning horizon that minimizes the final epidemic size.

How much do superspreaders matter? Epidemic dynamics in inhomogeneous populations

A variant of the SIR model for an inhomogeneous population is introduced in order to account for the effect of variability in susceptibility and infectiousness across a population. An initial formulation of this dynamics leads to infinitely many differential equations. Our model, however, can be reduced to a single first-order one-dimensional differential equation. Using this approach, we provide quantitative solutions for different distributions. In particular, we use GPS data from ∼ 107 cellphones to determine an empirical distribution of the number of individual contacts and use this to infer a possible distribution of susceptibility and infectivity. We quantify the effect of ℛ0 superspreaders on the early growth rate 0 of the infection and on the final epidemic size, the total number of people who are ever infected. We discuss the features of the distribution that contribute most to the dynamics of the infection.

Mobility Restrictions and the Control of COVID-19

A recent study on the impact of mobility controls on the final size of epidemics by Espinoza, Castillo-Chavez, and Perrings (2020) found that mobility restrictions between areas experiencing different levels of disease risk and with different public health infrastructures do not always reduce the final epidemic size. Indeed, restrictions on the mobility of people from high-risk to low-risk areas can increase, not reduce, the total number of infections. Since the first response of many countries to the COVID-19 pandemic was to implement mobility restrictions, it is worth bearing in mind the implications of the Espinoza result when considering the effectiveness of such restrictions.

Assessing the impact of adherence to Non-pharmaceutical interventions and indirect transmission on the dynamics of COVID-19: a mathematical modelling study

<abstract><p>Adherence to public health policies such as the non-pharmaceutical interventions implemented against COVID-19 plays a major role in reducing infections and controlling the spread of the diseases. In addition, understanding the transmission dynamics of the disease is also important in order to make and implement efficient public health policies. In this paper, we developed an SEIR-type compartmental model to assess the impact of adherence to COVID-19 non-pharmaceutical interventions and indirect transmission on the dynamics of the disease. Our model considers both direct and indirect transmission routes and stratifies the population into two groups: those that adhere to COVID-19 non-pharmaceutical interventions (NPIs) and those that do not adhere to the NPIs. We compute the control reproduction number and the final epidemic size relation for our model and study the effect of different parameters of the model on these quantities. Our results show that there is a significant benefit in adhering to the COVID-19 NPIs.</p></abstract>

Dynamical analysis in disease transmission and final epidemic size

<p style='text-indent:20px;'>We propose two compartment models to study the disease transmission dynamics, then apply the models to the current COVID-19 pandemic and to explore the potential impact of the interventions, and try to provide insights into the future health care demand. Starting with an SEAIQR model by combining the effect from exposure, asymptomatic and quarantine, then extending the model to the one with ages below and above 65 years old, and classify the infectious individuals according to their severity. We focus our analysis on each model with and without vital dynamics. In the models with vital dynamics, we study the dynamical properties including the global stability of the disease free equilibrium and the existence of endemic equilibrium, with respect to the basic reproduction number. Whereas in the models without vital dynamics, we address the final epidemic size rigorously, which is one of the common but difficult questions regarding an epidemic. Finally, we apply our models to estimate the basic reproduction number and the final epidemic size of disease by using the data of COVID-19 confirmed cases in Canada and Newfoundland &amp; Labrador province.</p>