Epidemic Outcomes Research Articles

Erratum for the Research Article: "Epidemic outcomes following government responses to COVID-19: Insights from nearly 100,000 models".

Erratum for the Research Article: "Epidemic outcomes following government responses to COVID-19: Insights from nearly 100,000 models".

Generalized contact matrices allow integrating socioeconomic variables into epidemic models.

Variables related to socioeconomic status (SES), including income, ethnicity, and education, shape contact structures and affect the spread of infectious diseases. However, these factors are often overlooked in epidemic models, which typically stratify social contacts by age and interaction contexts. Here, we introduce and study generalized contact matrices that stratify contacts across multiple dimensions. We demonstrate a lower-bound theorem proving that disregarding additional dimensions, besides age and context, might lead to an underestimation of the basic reproductive number. By using SES variables in both synthetic and empirical data, we illustrate how generalized contact matrices enhance epidemic models, capturing variations in behaviors such as heterogeneous levels of adherence to nonpharmaceutical interventions among demographic groups. Moreover, we highlight the importance of integrating SES traits into epidemic models, as neglecting them might lead to substantial misrepresentation of epidemic outcomes and dynamics. Our research contributes to the efforts aiming at incorporating socioeconomic and other dimensions into epidemic modeling.

Why aphid virus retention needs more attention: Modelling aphid behaviour and virus manipulation in non-persistent plant virus transmission.

Plant viruses threaten food security and are often transmitted by insect vectors. Non-persistently transmitted (NPT) plant viruses are transmitted almost exclusively by aphids. Because virions attach to the aphid's stylet (mouthparts) and are acquired and inoculated via brief epidermal probes, the aphid-virus interaction is highly transient, with a very short aphid virus retention time. Many NPT viruses manipulate their host plant's phenotype to change aphid behaviour to optimise virus transmission. Epidemiological models of this have overlooked a key feature of aphid NPT virus retention: probing or feeding on a plant causes aphids to lose the virus. Furthermore, experimental studies suggest aphids could possibly inoculate multiple healthy plants within one infective period if they do not feed. Consequences of this for virus manipulation of host plant phenotype have not been explored. Our new compartmental epidemiological model includes both behaviour-based aphid dispersal and infectivity loss rates, and the ability of infective aphids to probe multiple plants before virus loss. We use our model to explore how NPT virus-induced host phenotypes affect epidemic outcomes, comparing these results to representative previous models. We find that previous models behave fundamentally differently and underestimate the benefit of an 'attract-and-deter' phenotype, where the virus induces increased aphid attraction to infected plants but deters them from prolonged feeding. Our results also highlight the importance of characterising NPT virus retention upon the aphid during probing. Allowing for multiple infective probes increases disease incidence and the effectiveness of virus manipulation, with implications for epidemic prediction and control.

Development and calibration of a mathematical model of HIV outcomes among Rwandan adults: informing equitable achievement of targets in Rwanda.

We developed and calibrated the Central Africa-International epidemiology Databases to Evaluate AIDS (CA-IeDEA) HIV policy model to inform equitable achievement of global goals, overall and across sub-populations, in Rwanda. We created a deterministic dynamic model to project adult HIV epidemic and care continuum outcomes, overall and for 25 subpopulations (age group, sex, HIV acquisition risk, urbanicity). Data came from the Rwanda cohort of CA-IeDEA, 2004-2020; Rwanda Demographic and Health Surveys, 2005, 2010, 2015; Rwanda Population-based HIV Impact Assessment, 2019; and the literature and reports. We calibrated the model to 47 targets by selecting the 50 best-fitting parameter sets among 20,000 simulations. Calibration targets reflected epidemic (HIV prevalence, incidence), global goals (percentage on antiretroviral therapy (ART) among diagnosed, percentage virally suppressed among on ART) and other (number on ART, percentage virally suppressed) indicators, overall and by sex. Best-fitting sets minimized the summed absolute value of the percentage deviation (AVPD) between model projections and calibration targets. Good model performance was mean AVPD ≤5% across the 50 best-fitting sets and/or projections within the target confidence intervals; acceptable was mean AVPD >5% and ≤15%. Across indicators, 1,841 of 2,350 (78.3%) model projections were a good or acceptable fit to calibration targets. For HIV epidemic indicators, 256 of 300 (85.3%) projections were a good fit to targets, with the model performing better for women (83.3% a good fit) than for men (71.7% a good fit). For global goals indicators, 96 of 100 (96.0%) projections were a good fit; model performance was similar for women and men. For other indicators, 653 of 950 (68.7%) projections were a good or acceptable fit. Fit was better for women than for men (percentage virally suppressed only) and when restricting targets for number on ART to 2013 and beyond. The CA-IeDEA HIV policy model fits historical data and can inform policy solutions for equitably achieving global goals to end the HIV epidemic in Rwanda. High-quality, unbiased population-based data, as well as novel approaches that account for calibration target quality, are critical to ongoing use of mathematical models for programmatic planning.

Global stability for age-structured heroin model with general nonlinear incidence rate and time delay

In this article, we consider a mathematical model on the consumption of Heroin, it is an epidemiological model describing the interactions between heroin consumers and the rest of the population. The model is a system of differential equations with delay, integro-differential equations and partial differential equations. The first equation describes the evolution of healthy individuals, who do not consume Heroin. The second equation describes the evolution of consumer individuals, and in the last equation we find the evolution of individuals under treatment, so that they become healthy. In this work, we are interested in the qualitative study of the system considered. We examine the effects of a nonlinear incidence function with lag on the dynamics of an age-of-infection structured Heroin consumption model in the framework of mathematical epidemiology. We prove that incorporating the lag into the model does not change the asymptotic behavior of its equilibrium states. By defining the basic reproduction number R0 as a critical threshold parameter, we show that if R0 < 1, the disease-free equilibrium (DFE) is globally stable regardless of the lag τ. Conversely, if R0 < 1, the model exhibits an endemic equilibrium (EE) that remains locally and globally asymptotically stable for any lag τ. Our results highlight the robustness of the equilibrium stability in response to variations in the lag and provide important insights into the long-term dynamics of Heroin consumption, providing a clearer understanding of the conditions under which epidemic outcomes are stable or unstable.

Stochastic modeling of influenza transmission: Insights into disease dynamics and epidemic management

The stochastic SEIR model was employed to investigate the dynamics of influenza transmission. By incorporating transmission rates and prevalence ratios, this model provides the most comprehensive explanation of the virus’s unpredictable dissemination. To simulate the stochastic components of influenza transmission, we implemented conventional Brownian motions and stochastic differential equations. The investigation examines the uniqueness and presence of the solutions to demonstrate the conditions needed for eliminating the infection under random disturbances. The transmission rate coefficient (β) strongly impacts disease transmission speed. as demonstrated by the simulation results.Thus, the proper usage of safe transmission control methods is another decisive factor that determines the outcome of epidemics. Actual data of the Kingdom of Saudi Arabia was used. The results highlighted practicality of stochastic models and their usefulness to address and formulate and even execute the public health related policies. Regarding this, this study sets a high bar for other studies on modeling viral diseases on the grounds that stochastic and dynamic factors are also very important. These subsequent improvements in the model shall enable us to pinpoint the best strategies for the prevention and eradication of influenza and any other subsequent epidemic diseases, with reference to epidemic, epidemiology and public health.

VP1 is the primary determinant of neuropathogenesis in a mouse model of enterovirus D68 acute flaccid myelitis.

Emerging viruses allow us to investigate mutations leading to increased disease severity. Enterovirus D68 (EV-D68), once the cause of rare cases of respiratory illness, recently acquired the ability to cause severe respiratory and neurologic disease. Chimeric viruses were used to demonstrate that viral structural protein VP1 determines growth in the spinal cord, motor neuron loss, and paralysis following intramuscular (IM) injection of neonatal Swiss Webster (SW) mice with EV-D68. These results have relevance for predicting the clinical outcome of future EV-D68 epidemics as well as targeting retrograde transport as a potential strategy for treating virus-induced neurologic disease.

Epidemic outcomes following government responses to COVID-19: Insights from nearly 100,000 models.

Government responses to COVID-19 are among the most globally impactful events of the 21st century. The extent to which responses-such as school closures-were associated with changes in COVID-19 outcomes remains unsettled. Multiverse analyses offer a systematic approach to testing a large range of models. We used daily data on 16 government responses in 181 countries in 2020-2021, and 4 outcomes-cases, infections, COVID-19 deaths, and all-cause excess deaths-to construct 99,736 analytic models. Among those, 42% suggest outcomes improved following more stringent responses ("helpful"). No subanalysis (e.g. limited to cases as outcome) demonstrated a preponderance of helpful or unhelpful associations. Among the 14 associations with P values < 1 × 10-30, 5 were helpful and 9 unhelpful. In summary, we find no patterns in the overall set of models that suggests a clear relationship between COVID-19 government responses and outcomes. Strong claims about government responses' impacts on COVID-19 may lack empirical support.

Why aphid virus retention needs more attention: modelling aphid behaviour and virus manipulation in non-persistent plant virus transmission.

Abstract Plant viruses threaten food security and are often transmitted by insect vectors. Non-persistently transmitted (NPT) plant viruses are transmitted almost exclusively by aphids. Because virions attach to the aphid's stylet (mouthparts) and are acquired and inoculated via brief epidermal probes, the aphid-virus interaction is highly transient, with a very short aphid virus retention time. Many NPT viruses manipulate their host plant's phenotype to change aphid behaviour to optimise virus transmission. Epidemiological models of this have overlooked a key feature of aphid NPT virus retention: probing or feeding on a plant causes aphids to lose the virus. Additionally, experimental studies suggest aphids could possibly inoculate multiple healthy plants within one infective period. However, consequences of this for virus manipulation of host plant phenotype have not been explored. Our new compartmental epidemiological model includes both behaviour-based aphid dispersal and infectivity loss rates, and the ability of infective aphids to probe more than one plant before virus loss. We use our model to explore how NPT virus-induced host phenotypes affect epidemic outcomes, comparing these results to representative previous models. We find that previous models behave fundamentally differently and underestimate the benefit of an 'attract-and-deter' phenotype, where the virus induces increased aphid attraction to infected plants but deters them from prolonged feeding. Our results also highlight the importance of characterising NPT virus retention upon the aphid during probing. Allowing for multiple infective probes increases disease incidence and the effectiveness of virus manipulation, with implications for epidemic prediction and control.

Modeling and analysis of a fractional order spatio-temporal SEIR model: Stability and prediction

This study introduces a novel fractional-order spatio-temporal SEIR model for epidemic modeling, providing an advanced approach to understanding disease dynamics. Our model, categorizing the population into Susceptible (S), Exposed (E), Infected (I), and Recovered (R), incorporates fractional calculus to accurately reflect the complex, non-linear nature of infectious diseases. Key findings include the confirmation of the existence and uniqueness of the model’s solutions, ensuring reliability for epidemiological predictions. Through rigorous stability analysis at both disease-free and endemic equilibrium points, we identified critical parameters influencing epidemic outcomes. Numerical simulations reveal that the fractional order significantly impacts disease progression, offering valuable insights for intervention strategies.

Examining the effects of voluntary avoidance behaviour and policy-mediated behaviour change on the dynamics of SARS-CoV-2: A mathematical model

BackgroundThroughout the SARS-CoV-2 pandemic, policymakers have had to navigate between recommending voluntary behaviour change and policy-driven behaviour change to mitigate the impact of the virus. While individuals will voluntarily engage in self-protective behaviour when there is an increasing infectious disease risk, the extent to which this occurs and its impact on an epidemic is not known. MethodsThis paper describes a deterministic disease transmission model exploring the impact of individual avoidance behaviour and policy-mediated avoidance behaviour on epidemic outcomes during the second wave of SARS-CoV-2 infections in Ontario, Canada (September 1, 2020 to February 28, 2021). The model incorporates an information feedback function based on empirically derived behaviour data describing the degree to which avoidance behaviour changed in response to the number of new daily cases COVID-19. ResultsVoluntary avoidance behaviour alone was estimated to reduce the final attack rate by 23.1%, the total number of hospitalizations by 26.2%, and cumulative deaths by 27.5% over 6 months compared to a counterfactual scenario in which there were no interventions or avoidance behaviour. A provincial shutdown order issued on December 26, 2020 was estimated to reduce the final attack rate by 66.7%, the total number of hospitalizations by 66.8%, and the total number of deaths by 67.2% compared to the counterfactual scenario. ConclusionGiven the dynamics of SARS-CoV-2 in a pre-vaccine era, individual avoidance behaviour in the absence of government action would have resulted in a moderate reduction in disease however, it would not have been sufficient to entirely mitigate transmission and the associated risk to the population in Ontario. Government action during the second wave of the COVID-19 pandemic in Ontario reduced infections, protected hospital capacity, and saved lives.

Heterogeneous risk tolerance, in-groups, and epidemic waves.

There is a growing interest in the joint modeling of the dynamics of disease and health-related beliefs and attitudes, but coupling mechanisms are yet to be understood. We introduce a model where risk information, which can be delayed, comes in two flavors, including historical risk derived from perceived incidence data and predicted risk information. Our model also includes an interpretation domain where the behavioral response to risk information is subject to in-group pressure. We then simulate how the strength of behavioral reaction impacts epidemic severity as measured by epidemic peak size, number of waves, and final size. Simulated behavioral response is not effective when the level of protection that prophylactic behavior provides is as small as 50% or lower. At a higher level of 75% or more, we see the emergence of multiple epidemic waves. In addition, simulations show that different behavioral response profiles can lead to various epidemic outcomes that are non-monotonic with the strength of reaction to risk information. We also modeled heterogeneity in the response profile of a population and find they can lead to less severe epidemic outcome in terms of peak size.

A Study of a Class Continuous SIR Epidemic Model with History

The SIR model, an epidemiological model, divides a population into three compartments: Susceptible (S), Infected (I), and Recovered (R). It is widely used to understand the spread of infectious diseases and predict epidemic outcomes based on factors such as transmission rates and population dynamics. A deterministic epidemic mathematical model to describe the transmission dynamics of an infectious disease was constructed and analyzed by incorporating memory term which provides information on the current and past disease states. The model revealed two key equilibria: a disease-free equilibrium and an endemic equilibrium. The calculated basic reproductive number R0, was employed to establish that when R0&lt;1, the disease-free equilibrium is locally asymptotically stable, while the endemic equilibrium is locally asymptotically stable when R0&gt;1. Additionally, we explored the global stability of these equilibria using Lyapunov functions and Dulac's method, respectively. To validate our analytical findings, we conducted numerical simulations of the model which show the importance of history in the dynamic spread and elimination of disease.

Reconciling the efficacy and effectiveness of masking on epidemic outcomes.

During the COVID-19 pandemic, mask wearing in public settings has been a key control measure. However, the reported effectiveness of masking has been much lower than laboratory measures of efficacy, leading to doubts on the utility of masking. Here, we develop an agent-based model that comprehensively accounts for individual masking behaviours and infectious disease dynamics, and test the impact of masking on epidemic outcomes. Using realistic inputs of mask efficacy and contact data at the individual level, the model reproduces the lower effectiveness as reported in randomized controlled trials. Model results demonstrate that transmission within households, where masks are rarely used, can substantially lower effectiveness, and reveal the interaction of nonlinear epidemic dynamics, control measures and potential measurement biases. Overall, model results show that, at the individual level, consistent masking can reduce the risk of first infection and, over time, reduce the frequency of repeated infection. At the population level, masking can provide direct protection to mask wearers, as well as indirect protection to non-wearers, collectively reducing epidemic intensity. These findings suggest it is prudent for individuals to use masks during an epidemic, and for policymakers to recognize the less-than-ideal effectiveness of masking when devising public health interventions.

Complex Dynamics and Fractional-Order Optimal Control of an Epidemic Model with Saturated Treatment and Incidence

In this study, we have developed a novel SIR epidemic model by incorporating fractional-order differential equations and utilizing saturated-type functions to describe both disease incidence and treatment. The intricate dynamical characteristics of the proposed model, encompassing the determination of the conditions for the existence of all possible feasible equilibria with their local and global stability criteria, are investigated thoroughly. The model undergoes backward bifurcation with respect to the parameter representing the side effects due to treatment. This phenomenon emphasizes the critical role of treatment control parameters in shaping epidemic outcomes. In addition, to understand the optimal role of the treatment in mitigating the disease prevalence and minimizing the associated cost, we investigated a fractional-order optimal control problem. To further visualize the analytical results, we have conducted simulation works considering feasible parameter values for the model. Finally, we have employed local and global sensitivity analysis techniques to identify the factors that have the greatest potential to reduce the impact of the disease.

How enlightened self-interest guided global vaccine sharing benefits all: A modeling study.

Despite consensus that vaccines play an important role in combatting the global spread of infectious diseases, vaccine inequity is still a prevalent issue due to a deep-seated mentality of self-priority. We aimed to evaluate the existence and possible outcomes of a more equitable global vaccine distribution and explore a concrete incentive mechanism that promotes vaccine equity. We designed a metapopulation epidemiological model that simultaneously considers global vaccine distribution and human mobility, which we then calibrated by the number of infections and real-world vaccination records during the coronavirus disease 2019 (COVID-19) pandemic from March 2020 to July 2021. We explored the possibility of the enlightened self-interest incentive mechanism, which comprises improving one's own epidemic outcomes by sharing vaccines with other countries, by evaluating the number of infections and deaths under various vaccine sharing strategies using the proposed model. To understand how these strategies affect the national interests, we distinguished imported from local cases for further cost-benefit analyses that rationalise the enlightened self-interest incentive mechanism behind vaccine sharing. The proposed model accurately reproduces the real-world cumulative infections for both global and regional epidemics (R2>0.990), which can support the following evaluations of different vaccine sharing strategies: High-income countries can reduce 16.7 (95% confidence interval (CI) = 8.4-24.9, P < 0.001) million infection cases and 82.0 (95% CI = 76.6-87.4, P < 0.001) thousand deaths on average by more actively sharing vaccines in an enlightened self-interest manner, where the reduced internationally imported cases outweigh the threat from increased local infections. Such vaccine sharing strategies can also reduce 4.3 (95% CI = 1.2-7.5, P < 0.01) million infections and 7.0 (95% CI = 5.7-8.3, P < 0.001) thousand deaths in middle- and low-income countries, effectively benefiting the whole global population. Lastly, the more equitable vaccine distribution could help largely reduce the global mobility reduction needed for pandemic control. The incentive mechanism of enlightened self-interest we explored here could motivate vaccine equity by realigning the national interest to more equitable vaccine distributions. The positive results could promote multilateral collaborations in global vaccine redistribution and reconcile conflicted national interests, which could in turn benefit the global population.

The unequal effects of the health-economy trade-off during the COVID-19 pandemic.

Despite the global impact of the coronavirus disease 2019 pandemic, the question of whether mandated interventions have similar economic and public health effects as spontaneous behavioural change remains unresolved. Addressing this question, and understanding differential effects across socioeconomic groups, requires building quantitative and fine-grained mechanistic models. Here we introduce a data-driven, granular, agent-based model that simulates epidemic and economic outcomes across industries, occupations and income levels. We validate the model by reproducing key outcomes of the first wave of coronavirus disease 2019 in the New York metropolitan area. The key mechanism coupling the epidemic and economic modules is the reduction in consumption due to fear of infection. In counterfactual experiments, we show that a similar trade-off between epidemic and economic outcomes exists both when individuals change their behaviour due to fear of infection and when non-pharmaceutical interventions are imposed. Low-income workers, who perform in-person occupations in customer-facing industries, face the strongest trade-off.

Disease Simulation in Airport Scenario Based on Individual Mobility Model

As the rapid-spreading disease COVID-19 occupies the world, most governments adopt strict control policies to alleviate the impact of the virus. These policies successfully reduced the prevalence and delayed the epidemic peak, while they are also associated with high economic and social costs. To bridge the microscopic epidemic transmission patterns and control policies, simulation systems play an important role. In this work, we propose an agent-based disease simulator for indoor public spaces, which contribute to most of the transmission in cities. As an example, we study Guangzhou Baiyun International Airport, which is one of the most bustling aviation hubs in China. Specifically, we design a high-efficiency mobility generation module to reconstruct the individual trajectories considering both lingering behavior and crowd mobility, which greatly enhances the credibility of the simulated mobility and ensures real-time performance. Based on the individual trajectories, we propose a multi-path disease transmission module optimized for indoor public spaces, which includes three main transmission paths as close contact transmission, aerosol transmission, and object surface transmission. We design a novel convolution-based algorithm to mimic the diffusion process, which can leverage the high concurrent capability of the graphics processing unit to accelerate the simulation process. Leveraging our simulation paradigm, the effectiveness of common policy interventions can be quantitatively evaluated. For mobility interventions, we find that lingering control is the most effective mobility intervention with 32.35% fewer infections, while increasing social distance and increasing walking speed have a similar effect with 15.15% and 18.02% fewer infections. It demonstrates the importance of introducing crowd mobility into disease transmission simulation. For transmission processes, we find the aerosol transmission involves in 99.99% of transmission, which highlights the importance of ventilation in indoor public spaces. Our simulation also demonstrates that without strict entrance detection to identify the input infections, only performing frequent disinfection cannot achieve desirable epidemic outcomes. Based on our simulation paradigm, we can shed light on better policy designs that achieve a good balance between disease spreading control and social costs.

Collective epidemics with asymptomatics and functional infection rates

ABSTRACT This paper discusses a generalized SIR epidemic model that incorporates infectives with or without symptoms, allows arbitrary distributions for infectious periods and assumes infection rates depending on the current size of susceptibles. Our interest lies in the joint distribution of the state of the population and the severity of the disease at the end of infection. The approach is based on a formulation of the epidemic as a so-called collective model. First, a set of martingales is constructed which provides the distribution of this final epidemic outcome. Then, its corresponding distributional transform is expressed in terms of a family of pseudo-polynomials of Abel-Gontcharoff type. Some of the results obtained are illustrated numerically.

Age-differentiated incentives for adaptive behavior during epidemics produce oscillatory and chaotic dynamics.

Heterogeneity in contact patterns, mortality rates, and transmissibility among and between different age classes can have significant effects on epidemic outcomes. Adaptive behavior in response to the spread of an infectious pathogen may give rise to complex epidemiological dynamics. Here we model an infectious disease in which adaptive behavior incentives, and mortality rates, can vary between two and three age classes. The model indicates that age-dependent variability in infection aversion can produce more complex epidemic dynamics at lower levels of pathogen transmissibility and that those at less risk of infection can still drive complexity in the dynamics of those at higher risk of infection. Policymakers should consider the interdependence of such heterogeneous groups when making decisions.