Oscillations in epidemic models with spread of awareness

A minimal model for multigroup adaptive SIS epidemics

We propose a generalization of the adaptive N-Intertwined Mean-Field Approximation (aNIMFA) model studied in Achterberg and Sensi [Nonlinear Dyn. 111, 12657-12670 (2023)] to a heterogeneous network of communities. In particular, the multigroup aNIMFA model describes the impact of both local and global disease awareness on the spread of a disease in a network. We obtain results on the existence and stability of the equilibria of the system, in terms of the basic reproduction number R0. Assuming individuals have no reason to decrease their contacts in the absence of disease, we show that the basic reproduction number R0 is equivalent to the basic reproduction number of the NIMFA model on static networks. Based on numerical simulations, we demonstrate that with just two communities periodic behavior can occur, which contrasts the case with only a single community, in which periodicity was ruled out analytically. We also find that breaking connections between communities is more fruitful compared to breaking connections within communities to reduce the disease outbreak on dense networks, but both strategies are viable in networks with fewer links. Finally, we emphasize that our method of modeling adaptivity is not limited to Susceptible-Infected-Susceptible models, but has huge potential to be applied in other compartmental models in epidemiology.

Differences in COVID-19 cyclicity and predictability among U.S. counties and states reflect the effectiveness of protective measures

During the COVID-19 pandemic, many quantitative approaches were employed to predict the course of disease spread. However, forecasting faces the challenge of inherently unpredictable spread dynamics, setting a limit to the accuracy of all models. Here, we analyze COVID-19 data from the USA to explain variation among jurisdictions in disease spread predictability (that is, the extent to which predictions are possible), using a combination of statistical and simulation models. We show that for half the counties and states the spread rate of COVID-19, r(t), was predictable at most 9 weeks and 8 weeks ahead, respectively, corresponding to at most 40% and 35% of an average cycle length of 23 weeks and 26 weeks. High predictability was associated with high cyclicity of r(t) and negatively associated with R0 values from the pandemic's onset. Our statistical evidence suggests the following explanation: jurisdictions with a severe initial outbreak, and where individuals and authorities took strong and sustained protective measures against COVID-19, successfully curbed subsequent waves of disease spread, but at the same time unintentionally decreased its predictability. Decreased predictability of disease spread should be viewed as a by-product of positive and sustained steps that people take to protect themselves and others.

Individual risk-aversion responses tune epidemics to critical transmissibility (R = 1)

Changes in human behaviour are a major determinant of epidemic dynamics. Collective activity can be modified through imposed control measures, but spontaneous changes can also arise as a result of uncoordinated individual responses to the perceived risk of contagion. Here, we introduce a stochastic epidemic model implementing population responses driven by individual time-varying risk aversion. The model reveals an emergent mechanism for the generation of multiple infection waves of decreasing amplitude that progressively tune the effective reproduction number to its critical value R = 1. In successive waves, individuals with gradually lower risk propensity are infected. The overall mechanism shapes well-defined risk-aversion profiles over the whole population as the epidemic progresses. We conclude that uncoordinated changes in human behaviour can by themselves explain major qualitative and quantitative features of the epidemic process, like the emergence of multiple waves and the tendency to remain around R = 1 observed worldwide after the first few waves of COVID-19.

Game-theoretic modeling of collective decision making during epidemics

The spreading dynamics of an epidemic and the collective behavioral pattern of the population over which it spreads are deeply intertwined and the latter can critically shape the outcome of the former. Motivated by this, we design a parsimonious game-theoretic behavioral-epidemic model, in which an interplay of realistic factors shapes the coevolution of individual decision making and epidemics on a network. Although such a coevolution is deeply intertwined in the real world, existing models schematize population behavior as instantaneously reactive, thus being unable to capture human behavior in the long term. Our paradigm offers a unified framework to model and predict complex emergent phenomena, including successful collective responses, periodic oscillations, and resurgent epidemic outbreaks. The framework also allows us to provide analytical insights on the epidemic process and to assess the effectiveness of different policy interventions on ensuring a collective response that successfully eradicates the outbreak. Two case studies, inspired by real-world diseases, are presented to illustrate the potentialities of the proposed model.

Modeling the effects of prosocial awareness on COVID-19 dynamics: Case studies on Colombia and India

The ongoing COVID-19 pandemic has affected most of the countries on Earth. It has become a pandemic outbreak with more than 50 million confirmed infections and above 1 million deaths worldwide. In this study, we consider a mathematical model on COVID-19 transmission with the prosocial awareness effect. The proposed model can have four equilibrium states based on different parametric conditions. The local and global stability conditions for awareness-free, disease-free equilibrium are studied. Using Lyapunov function theory and LaSalle invariance principle, the disease-free equilibrium is shown globally asymptotically stable under some parametric constraints. The existence of unique awareness-free, endemic equilibrium and unique endemic equilibrium is presented. We calibrate our proposed model parameters to fit daily cases and deaths from Colombia and India. Sensitivity analysis indicates that the transmission rate and the learning factor related to awareness of susceptibles are very crucial for reduction in disease-related deaths. Finally, we assess the impact of prosocial awareness during the outbreak and compare this strategy with popular control measures. Results indicate that prosocial awareness has competitive potential to flatten the COVID-19 prevalence curve.

The role of social structure and dynamics in the maintenance of endemic disease

Social interactions are required for the direct transmission of infectious diseases. Consequently, the social network structure of populations plays a key role in shaping infectious disease dynamics. A huge research effort has examined how specific social network structures make populations more (or less) vulnerable to damaging epidemics. However, it can be just as important to understand how social networks can contribute to endemic disease dynamics, in which pathogens are maintained at stable levels for prolonged periods of time. Hosts that can maintain endemic disease may serve as keystone hosts for multi-host pathogens within an ecological community, and also have greater potential to act as key wildlife reservoirs of agricultural and zoonotic diseases. Here, we examine combinations of social and demographic processes that can foster endemic disease in hosts. We synthesise theoretical and empirical work to demonstrate the importance of both social structure and social dynamics in maintaining endemic disease. We also highlight the importance of distinguishing between the local and global persistence of infection and reveal how different social processes drive variation in the scale at which infectious diseases appear endemic. Our synthesis provides a framework by which to understand how sociality contributes to the long-term maintenance of infectious disease in wildlife hosts and provides a set of tools to unpick the social and demographic mechanisms involved in any given host-pathogen system.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s00265-021-03055-8.

Robustness of behaviorally induced oscillations in epidemic models under a low rate of imported cases

This paper is concerned with the robustness of the sustained oscillations predicted by an epidemic ODE model defined on contact networks. The model incorporates the spread of awareness among individuals and, moreover, a small inflow of imported cases. These cases prevent stochastic extinctions when we simulate the epidemics and, hence, they allow to check whether the average dynamics for the fraction of infected individuals are accurately predicted by the ODE model. Stochastic simulations confirm the existence of sustained oscillations for different types of random networks, with a sharp transition from a nonoscillatory asymptotic regime to a periodic one as the alerting rate of susceptible individuals increases from very small values. This abrupt transition to periodic epidemics of high amplitude is quite accurately predicted by the Hopf-bifurcation curve computed from the ODE model using the alerting rate and the infection transmission rate for aware individuals as tuning parameters.

THE COMPUTATION OF REPRODUCTION NUMBERS FOR THE ENVIRONMENT-HOST-ENVIRONMENT CHOLERA TRANSMISSION DYNAMICS

This study presents a new model for the environment-host-environment transmission dynamics of V. cholerae in a community with an interconnected aquatic pond–river water network. For the case when the human host is the sole target of anti-cholera control and the volume of water in the pond is maximum, the disease-free equilibrium of the model is shown to be globally asymptotically stable whenever a certain epidemiological threshold, known as the basic reproduction number [Formula: see text], is less than unity. The epidemiological implication of this result is that cholera can be eliminated from the community if the control strategies implemented can bring (and maintain) [Formula: see text] to a value less than unity. Four scenarios, that represent different interpretations of the role of the V. cholerea pathogen within the environment, were studied. The corresponding basic reproduction numbers were shown to exhibit the same threshold property with respect to the value unity (i.e., if one is less (equal, greater) than unity, then the three others are also less (equal, greater) than unity. Further, it was shown that for the case where anti-cholera control is focused on the human host population, the associated type reproduction number of the model (corresponding to each of the four transmission scenarios considered) is unique. The implication of this result is that the estimate of the effort needed for disease elimination (i.e., the required herd immunity threshold) is unique, regardless of which of the four transmission scenarios is considered. However, when any of the other two bacterial population types in the aquatic environment (i.e., bacterial in the pond or river) is the focus of the control efforts, this study shows that the associated type reproduction number is not unique. Extensive numerical simulations of the model, using a realistic set of parameters from the published literature, show that the community-wide implementation of a strategy that focus on improved water quality, sanitation, and hygiene (known as WASH-only strategy), using the current estimated coverage of 50% and efficacy of 60%, is unable to lead to the elimination of the disease. Such elimination is attainable if the coverage and efficacy are increased (e.g., to 80% and 90%, respectively). Further, elimination can be achieved using a strategy that focuses on oral rehydration therapy and the use of antibiotics to treat the infected humans (i.e., treatment-only strategy) for moderate effectiveness and coverage levels. The combined hybrid WASH-treatment strategy provides far better population-level impact vis a vis disease elimination. This study ranks the three interventions in the following order of population-level effectiveness: combined WASH-treatment, followed by treatment-only and then WASH-only strategy.

A model of insect control with imperfect treatment

Insecticide spraying of housing units is an important control measure for vector-borne infections such as Chagas disease. However, some vectors may survive treatment, due to imperfect spraying by the operator or because they hide deep in the cracks or other places, and re-emerge in the same unit when the effect of the insecticide wears off. While several mathematical models of this phenomenon have been previously described and studied in the literature, the model presented here is more basic than existing ones. Thus it is more amenable to mathematical analysis, which is carried out here. In particular, we demonstrate that an initially very high spraying rate may push the system into a region of the state space with low endemic levels of infestation that can be maintained in the long run at relatively moderate cost, while in the absence of an aggressive initial intervention the same average cost would only allow a much less significant reduction in long-term infestation levels.