Epidemic Size Research Articles

ESTIMATING AND ANALYZING COVID-19 TRANSMISSION IN THAILAND THROUGH DEEP NEURAL NETWORK

The COVID-19 pandemic has caused significant global suffering and mortality, and effective control measures have been elusive. This study aims to develop an accurate and reliable prediction model using deep neural networks (DNN) to estimate the epidemic size and trends of COVID-19 cases, as well as the effective reproduction number, R(t). The efficacy of various control measures for COVID-19 has been questioned, and an efficient prediction model can aid in decision-making and planning. Overfitting is a common issue in neural networks, which can limit their accuracy and reliability. A modified dropout regularization technique and particle swarm optimization (PSO) are employed to enhance the accuracy of the DNN. The proposed model outperforms conventional neural networks and previous studies in terms of accuracy and reliability. The estimated R(t) values are consistent with measured values, which demonstrates the usefulness of this model in analyzing the situation and informing effective intervention strategies. The developed dropout-DNN-PSO model is an accurate and reliable predictor of COVID-19 trends and R(t) values. It can aid decision-makers in planning and implementing effective control measures. The proposed model can be extended to other countries to analyze and predict the trends of COVID-19 cases.

Effectiveness evaluation of mosquito suppression strategies on dengue transmission under changing temperature and precipitation

Widespread resurgence of dengue outbreaks has seriously threatened the global health. Due to lack of treatments and vaccines, one key strategy in dengue control is to reduce the vector population size. As an environment-friendly mosquito control approach, releasing male mosquitoes transinfected with specific Wolbachia strain into the field to suppress the wild mosquito population size has become wildly accepted. The current study evaluates the effectiveness of this suppression strategy on dengue control under changing temperature and precipitation profiles. We formulate a mathematical model which includes larval intra-specific competition, the maturation period for mosquitoes, the extrinsic incubation period (EIP) and intrinsic incubation period (IIP). The persistence of mosquitoes and disease is discussed in terms of two basic reproduction numbers (RM and R0) and the release ratio pw. Further numerical simulations are carried out to not only validate theoretical results, but also provide interesting quantitative observations. Sensitivity analysis on the reproduction numbers, peak size, peak time and the final epidemic size is performed with respect to model parameters, which highlights effective control measures against dengue transmission. Moreover, by assuming temperature and precipitation dependent mosquito-related parameters, the model can be used to project the effectiveness of releasing Wolbachia-carrying males under climatic variations. It is shown that the effectiveness of various control strategies is highly dependent on the changing temperature and precipitation profiles. In particular, the model projects that it is most challenging to control the disease at the favorable temperature (around 27∼30∘C) and precipitation (5∼8mm/day) range, during which the basic reproduction number R0 is very high and more Wolbachia-infected males should be released.

Ethical dilemma arises from optimizing interventions for epidemics in heterogeneous populations.

Interventions to mitigate the spread of infectious diseases, while succeeding in their goal, have economic and social costs associated with them. These limit the duration and intensity of the interventions. We study a class of interventions which reduce the reproduction number and find the optimal strength of the intervention which minimizes the final epidemic size for an immunity inducing infection. The intervention works by eliminating the overshoot part of an epidemic, and avoids a second wave of infections. We extend the framework by considering a heterogeneous population and find that the optimal intervention can pose an ethical dilemma for decision and policymakers. This ethical dilemma is shown to be analogous to the trolley problem. We apply this optimization strategy to real-world contact data and case fatality rates from three pandemics to underline the importance of this ethical dilemma in real-world scenarios.

Determinants of epidemic size and the impacts of lulls in seasonal influenza virus circulation

During the COVID-19 pandemic, levels of seasonal influenza virus circulation were unprecedentedly low, leading to concerns that a lack of exposure to influenza viruses, combined with waning antibody titres, could result in larger and/or more severe post-pandemic seasonal influenza epidemics. However, in most countries the first post-pandemic influenza season was not unusually large and/or severe. Here, based on an analysis of historical influenza virus epidemic patterns from 2002 to 2019, we show that historic lulls in influenza virus circulation had relatively minor impacts on subsequent epidemic size and that epidemic size was more substantially impacted by season-specific effects unrelated to the magnitude of circulation in prior seasons. From measurements of antibody levels from serum samples collected each year from 2017 to 2021, we show that the rate of waning of antibody titres against influenza virus during the pandemic was smaller than assumed in predictive models. Taken together, these results partially explain why the re-emergence of seasonal influenza virus epidemics was less dramatic than anticipated and suggest that influenza virus epidemic dynamics are not currently amenable to multi-season prediction.

Estimating the basic reproduction number and final epidemic size of white spot syndrome virus outbreak in Penaeus japonicus in aquaculture ponds

White spot syndrome virus (WSSV) triggers white spot disease and high mortality in farmed shrimp. To control the WSSV epidemic, understanding its dynamics through epidemiological analysis is essential. However, measuring the mortality by WSSV infection is difficult due to the rapid increase in mortality and the availability of epidemiological data on WSSV epidemics in aquaculture ponds is limited. In this study, we conducted an epidemiological analysis using field data collected during the early phase of the outbreak to estimate the complete picture of the outbreak. Thereafter, we constructed a mathematical model describing the WSSV epidemic in aquaculture ponds and fitted our model with data on WSSV outbreaks among kuruma shrimp (Penaeus japonicus) farmed in 40,000 m2 aquaculture ponds in Japan. We estimated the basic reproduction number (R0), which measures the average number of secondary infections by a single infected individual, i.e. the transmissibility of a pathogen. The estimated R0 per pond was large (3.21–4.56), suggesting that with no intervention WSSV outbreaks will likely result in large final epidemic size, with 98.0–99.7% of entire population infected by the virus. Once WSSV infection is detected in a pond, urgent intervention, such as enhanced removal of dead shrimp and harvesting all farmed shrimps immediately, is required.

The Impacts of Testing Susceptible and Exposed Individuals on Emerging Infectious Diseases with Infectiousness in Incubation Period

On the premise that both susceptible and exposed individuals in incubation period are asymptomatic, in this paper, we establish epidemic models with compulsory testing or voluntary testing to study the impact of susceptible and exposed individuals’ testing rate on the emerging infectious diseases. Results show that when compulsory testing is performed on individuals, sometimes the testing rate of susceptible and exposed individuals can be increased to prevent epidemic from spreading among the population. Sometimes both the testing rate of susceptible, exposed and symptomatic infected individuals need to reach a certain level, and sometimes it can be achieved by increasing the testing rate of symptomatic infected individuals. When individuals take voluntary testing, if individuals think the risk of epidemic is low, increasing the individual’s trust in medical treatment is conducive to increasing the testing number of exposed individuals. However, if individuals think the risk is high, the change in medical trust can not affect the testing number of exposed individuals. Comparing these two models, it is interesting to note that the epidemic size corresponding to average testing rate of voluntary testing is almost the same as the epidemic size corresponding to the same testing rate of compulsory testing, reflecting the effectiveness of voluntary testing.

Effects of behavioral observability and social proof on the coupled epidemic-awareness dynamics in multiplex networks.

Despite much progress in exploring the coupled epidemic-awareness dynamics in multiplex networks, little attention has been paid to the joint impacts of behavioral observability and social proof on epidemic spreading. Since both the protective actions taken by direct neighbors and the observability of these actions have essential influence on individuals' decisions. Thus, we propose a UAPU-SIR model by integrating the effects of these two factors into the decision-making process of taking preventive measures. Specifically, a new state called taken protective actions is introduced into the original unaware-aware-unaware (UAU) model to characterize the action-taken state of individuals after getting epidemic-related information. Using the Microscopic Markov Chain Approach (MMCA), the methods and model are described, and the epidemic threshold is analytically derived. We find that both observability of protecting behaviors and social proof can reduce the epidemic prevalence and raise the epidemic threshold. Moreover, only if observability of protection actions reaches a certain threshold can accelerating information diffusion is able to inhibit disease spreading and result in higher epidemic threshold. We also discover that, reducing the forgetting rate of information is able to decrease epidemic size.

Optimal policy for control of epidemics with constrained time intervals and region-based interactions

<p>We introduce a policy model coupled with the susceptible–infected- recovered (SIR) epidemic model to study interactions between policy-making and the dynamics of epidemics. We considered both single-region policies as well as game-theoretic models involving interactions among several regions and hierarchical interactions among policy-makers modeled as multi-layer games. We assumed that the policy functions are piece-wise constant with a minimum time interval for each policy stage, considering that policies cannot change frequently in time or be easily followed. The optimal policy was obtained by minimizing a cost function that consists of an implementation cost, an impact cost, and, in the case of multi-layer games, a non-compliance cost. We show, in a case study of COVID-19 in France, that when the cost function is reduced to the impact cost and parameterized as the final epidemic size, the solution approximates that of the optimal control in Bliman et al, (2021) for a sufficiently small minimum policy time interval. For a larger time interval, however, the optimal policy is a step down function, quite different from the step up structure typically deployed during the COVID-19 pandemic. In addition, we present a counterfactual study of how the pandemic would have evolved if herd immunity was reached during the second wave in the county of Los Angeles, California. Finally, we study a case of three interacting counties with and without a governing state.</p>

Final and peak epidemic sizes of immuno-epidemiological SIR models

Final and peak epidemic sizes of immuno-epidemiological SIR models

Leveraging Human Mobility Data for Efficient Parameter Estimation in Epidemic Models of COVID-19

Effectively predicting the evolution of COVID-19 is of great significance to contain the pandemic. Extensive previous studies proposed a great number of SIR variants, which are efficient to capture the transmission characteristics of COVID-19. However, the parameter estimation methods in previous studies are based on data from epidemiological investigations, which inevitably have caused a large delay. The popularity of digital trajectory data world-wide makes it possible to understand epidemic spreading from human mobility perspective. The major advantage of digital trajectory data lies in that the co-location level of a population is reflected at every moment, making it possible to forecast the evolution in advance. We showed that the mobility data contributed by mobile phone users could be exploited to estimate the contact probability between individuals, thus revealing the dynamic transmission of COVID-19. Specifically, we developed an estimation method to obtain human co-location levels and quantified the variations of human mobility during the epidemic. Then, we extended the infection rate with a real-time co-location level to further forecast the transmission of an epidemic, predicting the epidemic size much more accurately than conventional methods. Finally, the proposed method was applied to evaluate the quantitative effect of different non-pharmacological interventions by predicting the epidemic situations with various mobility characteristics. The empirical results and simulations corroborated our theoretical analysis, providing effective guidance to contain the pandemic.

Final epidemic size and critical times for susceptible-infectious-recovered models with a generalized contact rate.

During the spread of an infectious disease, the contact rate or the incidence rate may affect disease characteristics. For simplicity, most disease models assume standard incidence or mass action rates to calculate the basic reproduction number, final epidemic size, and peak time of an epidemic. For standard incidence, the contact rate remains constant resulting in the incidence rate is inversely proportional to the population size, while for the mass action rate, this contact rate is proportional to the total population size resulting in the incidence rate is independent of the population size. In this paper, we consider susceptible-infectious-recovered epidemic models with a generalized contact rate C(N) and a nonlinear incidence rate in view of the behavioral change from susceptible or infectious individuals when an infectious disease appears. The basic reproduction number and the final size equation are derived. The impact of different types of contact rates on them is studied. Moreover, two critical times (peak time and epidemic duration) of an epidemic are considered. Explicit formulas for the peak time and epidemic duration are obtained. These formulas are helpful not only for taking early effective epidemic precautions but also for understanding how the epidemic duration can be changed by acting on the model parameters, especially when the epidemic model is used to make public health policy.

An agent-based nested model integrating within-host and between-host mechanisms to predict an epidemic

The COVID-19 pandemic has remarkably heightened concerns regarding the prediction of communicable disease spread. This study introduces an innovative agent-based modeling approach. In this model, the quantification of human-to-human transmission aligns with the dynamic variations in the viral load within an individual, termed “within-host” and adheres to the susceptible–infected–recovered (SIR) process, referred to as “between-host.” Variations in the viral load over time affect the infectivity between individual agents. This model diverges from the traditional SIR model, which employs a constant transmission probability, by incorporating a dynamic, time-dependent transmission probability influenced by the viral load in a host agent. The proposed model retains the time-integrated transmission probability characteristic of the conventional SIR model. As observed in this model, the overall epidemic size remains consistent with the predictions of the standard SIR model. Nonetheless, compared to predictions based on the classical SIR process, notable differences existed in the peak number of the infected individuals and the timing of this peak. These nontrivial differences are induced by the direct correlation between the time-evolving transmission probability and the viral load within a host agent. The developed model can inform targeted intervention strategies and public health policies by providing detailed insights into disease spread dynamics, crucial for effectively managing epidemics.

A hybrid one-vertex model for susceptible–infected–susceptible diseases on networks with partial connection information

We analyze the propagation of the susceptible–infected–susceptible model on the network, where the partial connection information is known. In order to analyze the spread of network epidemics, the quenched mean-field method requires complete connection information, while the heterogeneous mean-field method requires complete topology information. When only partial connection information is available, the quenched mean-field method may be disabled. In view of this situation, a hybrid model consisting of connection and topology information is proposed. The theoretical results are in good agreement with stochastic simulations on scale-free networks. In addition, as the proportion of connection information in the network increases, model predictions about final epidemic size become more accurate when the effective transmission rate is slightly larger than the simulation threshold.

Male pathology regardless of behaviour drives transmission in an avian host-pathogen system.

Host sex is an important source of heterogeneity in the severity of epidemics. Pinpointing the mechanisms causing this heterogeneity can be difficult because differences in behaviour among sexes (e.g. greater territorial aggression in males) can bias exposure risk, obfuscating the role of immune function, which can lead to differences in pathology, in driving differential susceptibility between sexes. Thus, sex-biased transmission driven by differences in immune function independent of behaviour is poorly understood, especially in non-mammalian systems. Here we examine the previously unexplored potential for male-biased pathology to affect transmission using an avian host-pathogen system. We employ a sex-dependent multistate transmission model parameterized with isolated, individual-based experimental exposures of domestic canaries and experimental transmission data of house finches. The experiment revealed that male birds have shorter incubation periods, longer recovery periods, higher pathogen burdens and greater disease pathology than females. Our model revealed that male-biased pathology led to epidemic size rapidly increasing with the proportion of male birds, with a nearly 10-fold increase in total epidemic size from an all-female to an all-male simulation. Our results demonstrate that female-biased resistance, independent of male behaviour, can drive sex-dependent transmission in wildlife, indicating that sex-based differences in immune function, not just differences in exposure risk, can shape epidemic dynamics.

An Outbreak of Vancomycin-Resistant Enterococci in a City Hospital Intensive Care Unit: Molecular Characterization of Resistance.

Background and Objectives: Vancomisin-resistant Enterococci (VRE), is a resistant microorganism that colonizes and causes infections in hospitalized patients. The aim of this study was to show the spread of vancomycin-resistant Enterococcus faecium (VREfm) step-by-step in all intensive care units, which started with the growth of VREfm on 2 December 2021 in the blood culture of a patient hospitalized in the anesthesia intensive care unit of our hospital and was found to have reached epidemic size in the surveys. Materials and Methods: Rectal swab samples were taken from all patients hospitalized in intensive care units, VRE colonization was determined, the VanA and VanB resistance genes associated with the vancomycin resistance of VREfm isolates were determined by PCR method, and clonal association analysis was performed by Arbitrarily Primed-PCR (AP-PCR) and PFGE (pulsed-field gel electrophoresis). Results: In our study, VRE were detected in 61 of 2601 rectal swab samples. In total, fifty-four (85.52%) of the VRE isolates were Enterococcus faecium, three (4.91%) was Enterococcus faecalis, three (4.91%) was Enterococcus gallinorum, and one (1.63%) was Enterococcus casseliflavus. It was determined that all of the 54 VREfm isolates, which were the most detected among all VRE isolates, carried the vanA gene. In the clonal association analysis of the isolates by AP-PCR and PFGE methods, it was found that they had 12 different genotypes, 48 of them were included in any cluster, the clustering rate was 88.8%, and the largest cluster was the genotype 1 cluster, with 36 isolates. Of the 54 patients with VREfm isolated recently, 18.51 percent of the clinical samples were isolated before the survey, and 9.25% were isolated after the survey. It was determined that 100% of VREfm isolates were resistant to ampicillin, levofloxacin, ciprofloxacin, high-level gentamicin, trimethoprimsulfamethoxazole, and teicoplanin, 7.4% to tigecycline, and 1.85% to linezolid. Conclusions: In our study, in the clonal association analysis performed by isolating VREfm in rectal swab samples, it was found that 88.8% of the samples were indistinguishably similar, and that the increase in the number of VREfm infections after the index case in our hospital was associated with the epidemic. VREfm infections cause long-term hospitalization, costs and also deaths, which shows the seriousness of the event, and the importance of the combination of epidemiological and molecular analysis in epidemic research.

Effects of Mitigation and Control Policies in Realistic Epidemic Models Accounting for Household Transmission Dynamics.

Compartmental infectious disease (ID) models are often used to evaluate nonpharmaceutical interventions (NPIs) and vaccines. Such models rarely separate within-household and community transmission, potentially introducing biases in situations in which multiple transmission routes exist. We formulated an approach that incorporates household structure into ID models, extending the work of House and Keeling. We developed a multicompartment susceptible-exposed-infectious-recovered-susceptible-vaccinated (MC-SEIRSV) modeling framework, allowing nonexponentially distributed duration in exposed and infectious compartments, that tracks within-household and community transmission. We simulated epidemics that varied by community and household transmission rates, waning immunity rate, household size (3 or 5 members), and numbers of exposed and infectious compartments (1-3 each). We calibrated otherwise identical models without household structure to the early phase of each parameter combination's epidemic curve. We compared each model pair in terms of epidemic forecasts and predicted NPI and vaccine impacts on the timing and magnitude of the epidemic peak and its total size. Meta-analytic regressions characterized the relationship between household structure inclusion and the size and direction of biases. Otherwise similar models with and without household structure produced equivalent early epidemic curves. However, forecasts from models without household structure were biased. Without intervention, they were upward biased on peak size and total epidemic size, with biases also depending on the number of exposed and infectious compartments. Model-estimated NPI effects of a 60% reduction in community contacts on peak time and size were systematically overestimated without household structure. Biases were smaller with a 20% reduction NPI. Because vaccination affected both community and household transmission, their biases were smaller. ID models without household structure can produce biased outcomes in settings in which within-household and community transmission differ. Infectious disease models rarely separate household transmission from community transmission. The pace of household transmission may differ from community transmission, depends on household size, and can accelerate epidemic growth.Many infectious disease models assume exponential duration distributions for infected states. However, the duration of most infections is not exponentially distributed, and distributional choice alters modeled epidemic dynamics and intervention effectiveness.We propose a mathematical framework for household and community transmission that allows for nonexponential duration times and a suite of interventions and quantified the effect of accounting for household transmission by varying household size and duration distributions of infected states on modeled epidemic dynamics.Failure to include household structure induces biases in the modeled overall course of an epidemic and the effects of interventions delivered differentially in community settings. Epidemic dynamics are faster and more intense in populations with larger household sizes and for diseases with nonexponentially distributed infectious durations. Modelers should consider explicitly incorporating household structure to quantify the effects of non-pharmaceutical interventions (e.g., shelter-in-place).

Life-expectancy changes from 2019 to 22: A case study of Japan using provisional death count

Many countries struggled with suppressing the incidence of COVID-19 caused by SARS-CoV-2 Omicron variant (B.1.1.529). As the epidemic size of COVID-19 in 2022 became bigger than earlier years in Japan, the present study aimed to estimate life expectancy at birth at the end of 2022, using provisional death datasets in Aichi and Fukui prefectures. We collected monthly death count from 2019 to the end of 2022, computing the period life table. While the life expectancy at birth in Aichi, 2019 was 84.6 years, it was very slightly extended to 84.7 years in 2020 and 2021, followed by a shortening for nearly 0.4 years in 2022. In Fukui, monotonous extension pattern was seen, i.e., 85.5 years in 2019, 85.6 in 2020, followed by 85.8 and 86.2 years in 2021 and 2022, respectively. Although decades-long trend of extending life expectancy at birth was partly discontinued from 2020 due to the pandemic at the national level, we have shown that the pandemic impact was still small in Japan by the end of 2022. First Omicron wave occurred shortly after primary series vaccination, and even real time booster program was underway during that wave. Different demographic consequences between Aichi and Fukui are explained by differential epidemic sizes prior to vaccination.

Pathways linking nutrient enrichment, habitat structure, and parasitism to host-resource interactions.

Human activities simultaneously alter nutrient levels, habitat structure, and levels of parasitism. These activities likely have individual and joint impacts on food webs. Furthermore, there is particular concern that nutrient additions and changes to habitat structure might exacerbate the size of epidemics and impacts on host density. We used a well-studied zooplankton-fungus host-parasite system and experimental whole water column enclosures to factorially manipulate nutrient levels, habitat structure (specifically: mixing), and presence of parasites. Nutrient addition increased infection prevalence, density of infected hosts, and total host density. We hypothesized that nutrients, mixing, and parasitism were linked in multiple ways, including via their combined effects on phytoplankton (resource) abundance, and we used structural equation modeling to disentangle these pathways. In the absence of the parasite, both nutrients and mixing increased abundance of phytoplankton, whereas host density was negatively related to phytoplankton abundance, suggesting a mixture of bottom-up and top-down control of phytoplankton. In the presence of the parasite, nutrients still increased phytoplankton abundance but mixing no longer did, and there was no longer a significant relationship between host density and phytoplankton. This decoupling of host-resource dynamics may have resulted from reduced grazing due to illness-mediated changes in feeding behavior. Overall, our results show that the impact of one human activity (e.g., altered habitat structure) might depend on other human impacts (e.g., parasite introduction). Fortunately, carefully designed experiments and analyses can help tease apart these multifaceted relationships, allowing us to understand how human activities alter food webs, including interactions between hosts and their parasites and resources.

Edge-based compartmental modeling for the spread of cholera on random networks: A case study in Somalia

Cholera remains a major public health problem that threatens human health worldwide and its severity is continuing. In this paper, an edge-based model for cholera transmission on random networks is proposed and investigated. The model assumes that two communities share a common water source and includes three transmission routes, namely intra- and inter-community human-to-human transmission as well as water-to-human transmission. Intra-community human-to-human contacts are modeled through a random contact network, while both inter-community and water-to-human transmission are modeled through external nodes that reach each individual in the network to the same extent. The basic reproduction number and the equations of the final epidemic size are obtained. In addition, our study considers the cholera situation in Banadir, which is one of the most severely infected regions in Somalia, during the period (2019-2021). According to the geographical location, two adjacent districts are selected and our model fits well with the real data on the monthly cumulative cholera cases of these two districts during the above-mentioned period. From the perspective of network topology, cutting off high-risk contacts by supervising, isolating, quarantining and closing places with high-degree cholera-infected individuals to reduce degree heterogeneity is an effective measure to control cholera transmission. Our findings might offer some useful insights on cholera control.

Coupled dynamics of endemic disease transmission and gradual awareness diffusion in multiplex networks

Understanding the interplay between human behavioral phenomena and infectious disease dynamics has been one of the central challenges of mathematical epidemiology. However, socio-cognitive processes critical for the initiation of desired behavioral responses during an outbreak have often been neglected or oversimplified in earlier models. Combining the microscopic Markov chain approach with the law of total probability, we herein institute a mathematical model describing the dynamic interplay between stage-based progression of awareness diffusion and endemic disease transmission in multiplex networks. We analytically derived the epidemic thresholds for both discrete-time and continuous-time versions of our model, and we numerically demonstrated the accuracy of our analytic arguments in capturing the time course and the steady state of the coupled disease-awareness dynamics. We found that our model is exact for arbitrary unclustered multiplex networks, outperforming a widely adopted probability-tree-based method, both in the prediction of the time-evolution of a contagion and in the final epidemic size. Our findings show that informing the unaware individuals about the circulating disease will not be sufficient for the prevention of an outbreak unless the distributed information triggers strong awareness of infection risks with adequate protective measures, and that the immunity of highly-aware individuals can elevate the epidemic threshold, but only if the rate of transition from weak to strong awareness is sufficiently high. Our study thus reveals that awareness diffusion and other behavioral parameters can nontrivially interact when producing their effects on epidemiological dynamics of an infectious disease, suggesting that future public health measures should not ignore this complex behavioral interplay and its influence on contagion transmission in multilayered networked systems.