An SEIR model of influenza A virus infection and reinfection within a farrow-to-finish swine farm

Spatial patterns of influenza A virus spread across compartments in commercial swine farms in the United States

AbstractMultiple genetic variants of H1 and H3 influenza A viruses (IAVs) circulate concurrently in US swine farms. Understanding the spatial transmission patterns of IAVs among these farms is crucial for developing effective control strategies and mitigating the emergence of novel IAVs. In this study, we analyzed 1,909 IAV genomic sequences from 785 US swine farms, representing 33 farming systems across 12 states, primarily in the Midwest from 2004 to 2023. Bayesian phylogeographic analyses were performed to identify the dispersal patterns of both H1 and H3 virus genetic lineages and to elucidate their spatial migration patterns within and between different systems. Our results showed that both intra-system and inter-system migrations occurred between the swine farms, with intra-system migrations being more frequent. However, migration rates for H1 and H3 IAVs were similar between intra-system and inter-system migration events. Spatial migration patterns aligned with expected pig movement across different compartments of swine farming systems. Sow-Farms were identified as key sources of viruses, with bi-directional migration observed between these farms and other parts of the system, including Wean-to-Finish and Gilt-Development-Units. High intra-system migration was detected across farms in the same region, while spread to geographically distant intra- and inter- system farms was less frequently. These findings suggest that prioritizing resources towards systems frequently confronting influenza problems and targeting pivotal source farms, such as sow farms, could be an effective strategy for controlling influenza in US commercial swine operations.

Mechanistic Models of Influenza Transmission in Commercial Swine Populations: A Systematic Review

Influenza in commercial swine populations leads to reduced gain in fattening pigs and reproductive issues in sows. This literature review aims to analyze the contributions of mathematical modeling in understanding influenza transmission and control among domestic swine. Twenty-two full-text research articles from seven databases were reviewed, categorized into swine-only (n = 13), swine-avian (n = 3), and swine-human models (n = 6). Strains of influenza models were limited to H1N1 (n = 7) and H3N2 (n = 1), with many studies generalizing the disease as influenza A. Half of the studies (n = 14) considered at least one control strategy, with vaccination being the primary investigated strategy. Vaccination was shown to reduce disease prevalence in single animal cohorts. With a continuous flow of new susceptible animals, such as in farrow-to-finish farms, it was shown that influenza became endemic despite vaccination strategies such as mass or batch-to-batch vaccination. Human vaccination was shown to be effective at mitigating human-to-human influenza transmission and to reduce spillover events from pigs. Current control strategies cannot stop influenza in livestock or prevent viral reassortment in swine, so mechanistic models are crucial for developing and testing new biosecurity measures to prevent future swine pandemics.

Simulating the impact of optimized prevention and control measures on the transmission of monkeypox in the United States: A model-based study

This study aimed to develop a modified susceptible-exposed-infected-recovered (SEIR) model to evaluate monkeypox epidemics in the United States and explore more optimized prevention and control measures. To further assess the impact of public health measures on the transmission of monkeypox, different intervention scenarios were developed based on the classic SEIR model, considering reducing contact, enhancing vaccination, diagnosis delay, and environmental transmission risk, respectively. We evaluated the impact of different measures by simulating their spread in different scenarios. During the simulation period, 8709 people were infected with monkeypox. The simulation analysis showed that: (1) the most effective measures to control monkeypox transmission during the early stage of the epidemic were reducing contact and enhancing vaccination, with cumulative infections at 51.20% and 41.90% of baseline levels, respectively; (2) shortening diagnosis time would delay the peak time of the epidemic by 96 days; and (3) the risk of environmental transmission of monkeypox virus was relatively low. This study indirectly proved the effectiveness of the prevention and control measures, such as reducing contact, enhancing vaccination, shortening diagnosis time, and low risk of environmental transmission, which also provided an important reference and containment experience for nonepidemic countries.

Does Vaccine-Induced Maternally-Derived Immunity Protect Swine Offspring against Influenza a Viruses? A Systematic Review and Meta-Analysis of Challenge Trials from 1990 to May 2021

It is unclear if piglets benefit from vaccination of sows against influenza. For the first time, methods of evidence-based medicine were applied to answer the question: "Does vaccine-induced maternally-derived immunity (MDI) protect swine offspring against influenza A viruses?". Challenge trials were reviewed that were published from 1990 to April 2021 and measured at least one of six outcomes in MDI-positive versus MDI-negative offspring (hemagglutination inhibition (HI) titers, virus titers, time to begin and time to stop shedding, risk of infection, average daily gain (ADG), and coughing) (n = 15). Screening and extraction of study characteristics was conducted in duplicate by two reviewers, with data extraction and assessment for risk of bias performed by one. Homology was defined by the antigenic match of vaccine and challenge virus hemagglutinin epitopes. Results: Homologous, but not heterologous MDI, reduced virus titers in piglets. There was no difference, calculated as relative risks (RR), in infection incidence risk over the entire study period; however, infection hazard (instantaneous risk) was decreased in pigs with MDI (log HR = -0.64, 95% CI: -1.13, -0.15). Overall, pigs with MDI took about a ½ day longer to begin shedding virus post-challenge (MD = 0.51, 95% CI: 0.03, 0.99) but the hazard of infected pigs ceasing to shed was not different (log HR = 0.32, 95% CI: -0.29, 0.93). HI titers were synthesized qualitatively and although data on ADG and coughing was extracted, details were insufficient for conducting meta-analyses. Conclusion: Homology of vaccine strains with challenge viruses is an important consideration when assessing vaccine effectiveness. Herd viral dynamics are complex and may include concurrent or sequential exposures in the field. The practical significance of reduced weaned pig virus titers is, therefore, not known and evidence from challenge trials is insufficient to make inferences on the effects of MDI on incidence risk, time to begin or to cease shedding virus, coughing, and ADG. The applicability of evidence from single-strain challenge trials to field practices is limited. Despite the synthesis of six outcomes, challenge trial evidence does not support or refute vaccination of sows against influenza to protect piglets. Additional research is needed; controlled trials with multi-strain concurrent or sequential heterologous challenges have not been conducted, and sequential homologous exposure trials were rare. Consensus is also warranted on (1) the selection of core outcomes, (2) the sizing of trial populations to be reflective of field populations, (3) the reporting of antigenic characterization of vaccines, challenge viruses, and sow exposure history, and (4) on the collection of non-aggregated individual pig data.

Quantitative measurement of influenza virus transmission in animal model: an overview of current state

Influenza virus transmission is a crucial factor in understanding the spread of the virus within populations and developing effective control strategies. Studying the transmission patterns of influenza virus allows for better risk assessment and prediction of disease outbreaks. By monitoring the spread of the virus and identifying high-risk populations and geographic areas, it is possible to allocate resources more effectively, implement timely interventions, and provide targeted healthcare interventions to diminish the burden of influenza virus on vulnerable populations. Theoretical models of virus transmission are used to study and simulate of influenza virus spread within populations. These models aim to capture the complex dynamics of transmission, including factors such as population size, contact patterns, infectiousness, and susceptibility. Animal models serve as valuable tools for studying the dynamics of influenza virus transmission. This article presents a brief overview of existing research on the qualitative and quantitative study of influenza virus transmission in animal models. We discuss the methodologies employed, key insights gained from these studies, and their relevance.

Praemonitus praemunitus: can we forecast and prepare for future viral disease outbreaks?

Understanding the origins of past and present viral epidemics is critical in preparing for future outbreaks. Many viruses, including SARS-CoV-2, have led to significant consequences not only due to their virulence, but also because we were unprepared for their emergence. We need to learn from large amounts of data accumulated from well-studied, past pandemics and employ modern informatics and therapeutic development technologies to forecast future pandemics and help minimize their potential impacts. While acknowledging the complexity and difficulties associated with establishing reliable outbreak predictions, herein we provide a perspective on the regions of the world that are most likely to be impacted by future outbreaks. We specifically focus on viruses with epidemic potential, namely SARS-CoV-2, MERS-CoV, DENV, ZIKV, MAYV, LASV, noroviruses, influenza, Nipah virus, hantaviruses, Oropouche virus, MARV, and Ebola virus, which all require attention from both the public and scientific community to avoid societal catastrophes like COVID-19. Based on our literature review, data analysis, and outbreak simulations, we posit that these future viral epidemics are unavoidable, but that their societal impacts can be minimized by strategic investment into basic virology research, epidemiological studies of neglected viral diseases, and antiviral drug discovery.

Evaluation of early single dose vaccination on swine influenza A virus transmission in piglets: From experimental data to mechanistic modelling

Swine influenza A virus (swIAV) is a major pathogen affecting pigs with a huge economic impact and potentially zoonotic. Epidemiological studies in endemically infected farms permitted to identify critical factors favoring on-farm persistence, among which maternally-derived antibodies (MDAs). Vaccination is commonly practiced in breeding herds and might be used for immunization of growing pigs at weaning. Althoughinterference between MDAs and vaccination was reported in young piglets, its impact on swIAV transmission was not yet quantified. To this aim, this study reports on a transmission experiment in piglets with or without MDAs, vaccinated with a single dose injection at four weeks of age, and challenged 17 days post-vaccination. To transpose small-scale experiments to real-life situation, estimated parameters were used in a simulation tool to assess their influence at the herd level. Based on a thorough follow-up of the infection chain during the experiment, the transmission of the swIAV challenge strain was highly dependent on the MDA status of the pigs when vaccinated. MDA-positive vaccinated animals showed a direct transmission rate 3.6-fold higher than the one obtained in vaccinated animals without MDAs, estimated to 1.2. Vaccination nevertheless reduced significantly the contribution of airborne transmission when compared with previous estimates obtained in unvaccinated animals. The integration of parameter estimates in a large-scale simulation model, representing a typical farrow-to-finish pig herd, evidenced an extended persistence of viral spread when vaccination of sows and single dose vaccination of piglets was hypothesized. When extinction was quasi-systematic at year 5 post-introduction in the absence of sow vaccination but with single dose early vaccination of piglets, the extinction probability fell down to 33% when batch-to-batch vaccination was implemented both in breeding herd and weaned piglets. These results shed light on a potential adverse effect of single dose vaccination in MDA-positive piglets, which might lead to longer persistence of the SwIAV at the herd level.

A stochastic compartmental model to simulate intra- and inter-species influenza transmission in an indoor swine farm

Common in swine production worldwide, influenza causes significant clinical disease and potential transmission to the workforce. Swine vaccines are not universally used in swine production, due to their limited efficacy because of continuously evolving influenza viruses. We evaluated the effects of vaccination, isolation of infected pigs, and changes to workforce routine (ensuring workers moved from younger pig batches to older pig batches). A Susceptible-Exposed-Infected-Recovered model was used to simulate stochastic influenza transmission during a single production cycle on an indoor hog growing unit containing 4000 pigs and two workers. The absence of control practices resulted in 3,957 pigs [0-3971] being infected and a 0.61 probability of workforce infection. Assuming incoming pigs had maternal-derived antibodies (MDAs), but no control measures were applied, the total number of infected pigs reduced to 1 [0-3958] and the probability of workforce infection was 0.25. Mass vaccination (40% efficacious) of incoming pigs also reduced the total number of infected pigs to 2362 [0-2374] or 0 [0-2364] in pigs assumed to not have MDAs and have MDAs, respectively. Changing the worker routine by starting with younger to older pig batches, reduced the number of infected pigs to 996 [0-1977] and the probability of workforce infection (0.22) in pigs without MDAs. In pigs with MDAs the total number of infected pigs was reduced to 0 [0-994] and the probability of workforce infection was 0.06. All other control practices alone, showed little improvement in reducing total infected pigs and the probability of workforce infection. Combining all control strategies reduced the total number of infected pigs to 0 or 1 with a minimal probability of workforce infection (<0.0002-0.01). These findings suggest that non-pharmaceutical interventions can reduce the impact of influenza on swine production and workers when efficacious vaccines are unavailable.

The multilevel hierarchical data EM-algorithm. Applications to discrete-time Markov chain epidemic models

The theory of multilevel hierarchical data Expectation Maximization (EM)-algorithm is introduced via discrete time Markov chain (DTMC) epidemic models. A general model for a multilevel hierarchical discrete data is derived. The observed sample Y in the system is a stochastic incomplete data, and the missing data Z exhibits a multilevel hierarchical data structure. The EM-algorithm to find ML-estimates for parameters in the stochastic system is derived. Applications of the EM-algorithm are exhibited in the two DTMC models, to find ML-estimates of the system parameters. Numerical results are given for influenza epidemics in the state of Georgia (GA), USA.

Estimating the transmissibility of hepatitis C: A modelling study in Yichang City, China

Yichang is a city in central China in the Hubei Province. This study aimed to estimate the dynamics of the transmissibility of hepatitis C using a mathematical model and predict the transmissibility of hepatitis C in 2030. Data of hepatitis C cases from 13 counties or districts (cities) in Yichang from 2008 to 2016 were collected. A susceptible-infectious-chronic-recovered (SICR) model was developed to fit the data. The transmissibility of hepatitis C at the counties or districts was calculated based on new infections (including infected or chronically infected cases) reported monthly in the city caused by one infectious individual (MNI). The trend of the MNI was fitted and predicted using 11 models, with the coefficient of determination (R² ) was being used to test the goodness of fit of these models. A total of 3065 cases of hepatitis C were reported in Yichang from 2008 to 2016. The median MNI of Yichang was 0.0768. According to the fitting results and analysis, the trend of transmissibility of hepatitis C in Yichang City conforms with the logarithmic (R²  = 0.918, p < 0.001):MNI = 0.265-0.108 log(t) and exponential (R²  = 0.939, p < 0.001): MNI = 0.344e^(-0.278t) models. Hence, the transmission of hepatitis C virus at the county level has a downward trend. In conclusion, the transmissibility of hepatitis C in Yichang has a downward trend. With the current preventive and control measures in place, the spread of hepatitis C can be controlled.

Modelling and optimal control of multi strain epidemics, with application to COVID-19

Reinfection and multiple viral strains are among the latest challenges in the current COVID-19 pandemic. In contrast, epidemic models often consider a single strain and perennial immunity. To bridge this gap, we present a new epidemic model that simultaneously considers multiple viral strains and reinfection due to waning immunity. The model is general, applies to any viral disease and includes an optimal control formulation to seek a trade-off between the societal and economic costs of mitigation. We validate the model, with and without mitigation, in the light of the COVID-19 epidemic in England and in the state of Amazonas, Brazil. The model can derive optimal mitigation strategies for any number of viral strains, whilst also evaluating the effect of distinct mitigation costs on the infection levels. The results show that relaxations in the mitigation measures cause a rapid increase in the number of cases, and therefore demand more restrictive measures in the future.

Effects of short-term travel on COVID-19 spread: A novel SEIR model and case study in Minnesota

The novel coronavirus responsible for COVID-19 was first identified in Hubei Province, China in December, 2019. Within a matter of months the virus had spread and become a global pandemic. In addition to international air travel, local travel (e.g. by passenger car) contributes to the geographic spread of COVID-19. We modify the common susceptible-exposed-infectious-removed (SEIR) virus spread model and investigate the extent to which short-term travel associated with driving influences the spread of the virus. We consider the case study of the US state of Minnesota, and calibrated the proposed model with travel and viral spread data. Using our modified SEIR model that considers local short-term travel, we are able to better explain the virus spread than using the long-term travel SEIR model. Short-term travel associated with driving is predicted to be a significant contributor to the historical and future spread of COVID-19. The calibrated model also predicts the proportion of infections that were detected. We find that if driving trips remain at current levels, a substantial increase in COVID-19 cases may be observed in Minnesota, while decreasing intrastate travel could help contain the virus spread.

Linking key intervention timings to rapid declining effective reproduction number to quantify lessons against COVID-19

Coronavirus disease 2019 (COVID-19) is currently under a global pandemic trend. The efficiency of containment measures and epidemic tendency of typical countries should be assessed. In this study, the efficiency of prevention and control measures in China, Italy, Iran, South Korea, and Japan was assessed, and the COVID-19 epidemic tendency among these countries was compared. Results showed that the effective reproduction number(Re) in Wuhan, China increased almost exponentially, reaching a maximum of 3.98 before a lockdown and rapidly decreased to below 1 due to containment and mitigation strategies of the Chinese government. The Re in Italy declined at a slower pace than that in China after the implementation of prevention and control measures. The Re in Iran showed a certain decline after the establishment of a national epidemic control command, and an evident stationary phase occurred because the best window period for the prevention and control of the epidemic was missed. The epidemic in Japan and South Korea reoccurred several times with the Re fluctuating greatly. The epidemic has hardly rebounded in China due to the implementation of prevention and control strategies and the effective enforcement of policies. Other countries suffering from the epidemic could learn from the Chinese experience in containing COVID-19.

Simulation of coronavirus disease 2019 (COVID-19) scenarios with possibility of reinfection

Epidemiological models of COVID-19 transmission assume that recovered individuals have a fully protected immunity. To date, there is no definite answer about whether people who recover from COVID-19 can be reinfected with the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). In the absence of a clear answer about the risk of reinfection, it is instructive to consider the possible scenarios. To study the epidemiological dynamics with the possibility of reinfection, I use a Susceptible-Exposed-Infectious-Resistant-Susceptible model with the time-varying transmission rate. I consider three different ways of modeling reinfection. The crucial feature of this study is that I explore both the difference between the reinfection and no-reinfection scenarios and how the mitigation measures affect this difference. The principal results are the following. First, the dynamics of the reinfection and no-reinfection scenarios are indistinguishable before the infection peak. Second, the mitigation measures delay not only the infection peak, but also the moment when the difference between the reinfection and no-reinfection scenarios becomes prominent. These results are robust to various modeling assumptions.

Modelling infectious viral diseases in swine populations: a state of the art

Mathematical modelling is nowadays a pivotal tool for infectious diseases studies, completing regular biological investigations. The rapid growth of computer technology allowed for development of computational tools to address biological issues that could not be unravelled in the past. The global understanding of viral disease dynamics requires to account for all interactions at all levels, from within-host to between-herd, to have all the keys for development of control measures. A literature review was performed to disentangle modelling frameworks according to their major objectives and methodologies. One hundred and seventeen articles published between 1994 and 2020 were found to meet our inclusion criteria, which were defined to target papers representative of studies dealing with models of viral infection dynamics in pigs. A first descriptive analysis, using bibliometric indexes, permitted to identify keywords strongly related to the study scopes. Modelling studies were focused on particular infectious agents, with a shared objective: to better understand the viral dynamics for appropriate control measure adaptation. In a second step, selected papers were analysed to disentangle the modelling structures according to the objectives of the studies. The system representation was highly dependent on the nature of the pathogens. Enzootic viruses, such as swine influenza or porcine reproductive and respiratory syndrome, were generally investigated at the herd scale to analyse the impact of husbandry practices and prophylactic measures on infection dynamics. Epizootic agents (classical swine fever, foot-and-mouth disease or African swine fever viruses) were mostly studied using spatio-temporal simulation tools, to investigate the efficiency of surveillance and control protocols, which are predetermined for regulated diseases. A huge effort was made on model parameterization through the development of specific studies and methodologies insuring the robustness of parameter values to feed simulation tools. Integrative modelling frameworks, from within-host to spatio-temporal models, is clearly on the way. This would allow to capture the complexity of individual biological variabilities and to assess their consequences on the whole system at the population level. This would offer the opportunity to test and evaluate in silico the efficiency of possible control measures targeting specific epidemiological units, from hosts to herds, either individually or through their contact networks. Such decision support tools represent a strength for stakeholders to help mitigating infectious diseases dynamics and limiting economic consequences.

Quantifying early COVID-19 outbreak transmission in South Africa and exploring vaccine efficacy scenarios

The emergence and fast global spread of COVID-19 has presented one of the greatest public health challenges in modern times with no proven cure or vaccine. Africa is still early in this epidemic, therefore the extent of disease severity is not yet clear. We used a mathematical model to fit to the observed cases of COVID-19 in South Africa to estimate the basic reproductive number and critical vaccination coverage to control the disease for different hypothetical vaccine efficacy scenarios. We also estimated the percentage reduction in effective contacts due to the social distancing measures implemented. Early model estimates show that COVID-19 outbreak in South Africa had a basic reproductive number of 2.95 (95% credible interval [CrI] 2.83-3.33). A vaccine with 70% efficacy had the capacity to contain COVID-19 outbreak but at very higher vaccination coverage 94.44% (95% Crl 92.44-99.92%) with a vaccine of 100% efficacy requiring 66.10% (95% Crl 64.72-69.95%) coverage. Social distancing measures put in place have so far reduced the number of social contacts by 80.31% (95% Crl 79.76-80.85%). These findings suggest that a highly efficacious vaccine would have been required to contain COVID-19 in South Africa. Therefore, the current social distancing measures to reduce contacts will remain key in controlling the infection in the absence of vaccines and other therapeutics.

Compartmental Models of the COVID-19 Pandemic for Physicians and Physician-Scientists

As the novel severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection spreads globally, physicians and physician-scientists are confronted with an enlarging body of literature about the nature of this pandemic. Understanding the current epidemiological models for disease spread, mortality, and recovery is more important than ever before. One of the most relevant mathematical models relating to the spread of a pandemic is the susceptible-infectious-removed (SIR) model. Other models worth exploring are the susceptible-exposed-infectious-removed (SEIR) and the susceptible-unquarantined-quarantined-confirmed (SUQC) model.

Mathematical Modelling to Assess the Impact of Lockdown on COVID-19 Transmission in India: Model Development and Validation

BACKGROUND

The World Health Organization has declared the novel coronavirus disease (COVID-19) to be a public health emergency; at present, India is facing a major threat of community spread. We developed a mathematical model for investigating and predicting the effects of lockdown on future COVID-19 cases with a specific focus on India.

OBJECTIVE

The objective of this work was to develop and validate a mathematical model and to assess the impact of various lockdown scenarios on COVID-19 transmission in India.

METHODS

A model consisting of a framework of ordinary differential equations was developed by incorporating the actual reported cases in 14 countries. After validation, the model was applied to predict COVID-19 transmission in India for different intervention scenarios in terms of lockdown for 4, 14, 21, 42, and 60 days. We also assessed the situations of enhanced exposure due to aggregation of individuals in transit stations and shopping malls before the lockdown.

RESULTS

The developed model is efficient in predicting the number of COVID-19 cases compared to the actual reported cases in 14 countries. For India, the model predicted marked reductions in cases for the intervention periods of 14 and 21 days of lockdown and significant reduction for 42 days of lockdown. Such intervention exceeding 42 days does not result in measurable improvement. Finally, for the scenario of "panic shopping" or situations where there is a sudden increase in the factors leading to higher exposure to infection, the model predicted an exponential transmission, resulting in failure of the considered intervention strategy.

CONCLUSIONS

Implementation of a strict lockdown for a period of at least 21 days is expected to reduce the transmission of COVID-19. However, a further extension of up to 42 days is required to significantly reduce the transmission of COVID-19 in India. Any relaxation in the lockdown may lead to exponential transmission, resulting in a heavy burden on the health care system in the country.

Bifurcation analysis of a SEIR epidemic system with governmental action and individual reaction

In this paper, the dynamical behavior of a SEIR epidemic system that takes into account governmental action and individual reaction is investigated. The transmission rate takes into account the impact of governmental action modeled as a step function while the decreasing contacts among individuals responding to the severity of the pandemic is modeled as a decreasing exponential function. We show that the proposed model is capable of predicting Hopf bifurcation points for a wide range of physically realistic parameters for the COVID-19 disease. In this regard, the model predicts periodic behavior that emanates from one Hopf point. The model also predicts stable oscillations connecting two Hopf points. The effect of the different model parameters on the existence of such periodic behavior is numerically investigated. Useful diagrams are constructed that delineate the range of periodic behavior predicted by the model.

Qualitative analysis of a stochastic SEITR epidemic model with multiple stages of infection and treatment

We present a mathematical analysis of the transmission of certain diseases using a stochastic susceptible-exposed-infectious-treated-recovered (SEITR) model with multiple stages of infection and treatment and explore the effects of treatments and external fluctuations in the transmission, treatment and recovery rates. We assume external fluctuations are caused by variability in the number of contacts between infected and susceptible individuals. It is shown that the expected number of secondary infections produced (in the absence of noise) reduces as treatment is introduced into the population. By defining RT,n and RT,n as the basic deterministic and stochastic reproduction numbers, respectively, in stage n of infection and treatment, we show mathematically that as the intensity of the noise in the transmission, treatment and recovery rates increases, the number of secondary cases of infection increases. The global stability of the disease-free and endemic equilibrium for the deterministic and stochastic SEITR models is also presented. The work presented is demonstrated using parameter values relevant to the transmission dynamics of Influenza in the United States from October 1, 2018 through May 4, 2019 influenza seasons.