A Novel Statistical Model to Estimate Host Genetic Effects Affecting Disease Transmission

There is increasing recognition that genetic diversity can affect the spread of diseases, potentially affecting plant and livestock disease control as well as the emergence of human disease outbreaks. Nevertheless, even though computational tools can guide the control of infectious diseases, few epidemiological models can simultaneously accommodate the inherent individual heterogeneity in multiple infectious disease traits influencing disease transmission, such as the frequently modeled propensity to become infected and infectivity, which describes the host ability to transmit the infection to susceptible individuals. Furthermore, current quantitative genetic models fail to fully capture the heritable variation in host infectivity, mainly because they cannot accommodate the nonlinear infection dynamics underlying epidemiological data. We present in this article a novel statistical model and an inference method to estimate genetic parameters associated with both host susceptibility and infectivity. Our methodology combines quantitative genetic models of social interactions with stochastic processes to model the random, nonlinear, and dynamic nature of infections and uses adaptive Bayesian computational techniques to estimate the model parameters. Results using simulated epidemic data show that our model can accurately estimate heritabilities and genetic risks not only of susceptibility but also of infectivity, therefore exploring a trait whose heritable variation is currently ignored in disease genetics and can greatly influence the spread of infectious diseases. Our proposed methodology offers potential impacts in areas such as livestock disease control through selective breeding and also in predicting and controlling the emergence of disease outbreaks in human populations.     

Controlling emerging infectious diseases like SARS

To control emerging infectious diseases like SARS, it is necessary to resort to basic control measures that limit exposures to infectious individuals. These measures include isolating cases at diagnosis, quarantining household members and tracing contacts of diagnosed cases, providing the community with advice on how to reduce exposures, and closing schools. To justify such intervention it is important to understand how well each of these measures helps to limit transmission. In this paper, we determine the effect of a number of different interventions on the effective reproduction number and estimate requirements to achieve elimination of the infectious disease. We find that the strategy of tracing and quarantining contacts of diagnosed cases can be very successful in reducing transmission.     

Determining Important Parameters in the Spread of Malaria Through the Sensitivity Analysis of a Mathematical Model

We perform sensitivity analyses on a mathematical model of malaria transmission to determine the relative importance of model parameters to disease transmission and prevalence. We compile two sets of baseline parameter values: one for areas of high transmission and one for low transmission. We compute sensitivity indices of the reproductive number (which measures initial disease transmission) and the endemic equilibrium point (which measures disease prevalence) to the parameters at the baseline values. We find that in areas of low transmission, the reproductive number and the equilibrium proportion of infectious humans are most sensitive to the mosquito biting rate. In areas of high transmission, the reproductive number is again most sensitive to the mosquito biting rate, but the equilibrium proportion of infectious humans is most sensitive to the human recovery rate. This suggests strategies that target the mosquito biting rate (such as the use of insecticide-treated bed nets and indoor residual spraying) and those that target the human recovery rate (such as the prompt diagnosis and treatment of infectious individuals) can be successful in controlling malaria.     

Some remarks on definition and validity of terms used in models for infectious disease spread.

The epidemiology of infectious diseases makes use of a number of terms, such as exposure, infected, carrier, attack rate, and immunity. Researchers who intend to model the spread of epidemics should be aware of the problems with some of these terms. The role played by inapparent, or subclinical, infections is receiving increased attention in infectious disease epidemiology. Patients with such infections may never be reported as cases, which could give rise to problems when, for example, data from national surveillance bodies are being used for modeling. The assignment of patients to different transmission groups must, in most cases, rely on self-reported data from the medical interview. This possible source of bias should be recognized.     

Prediction and Control of Brucellosis Transmission of Dairy Cattle in Zhejiang Province,China

Brucellosis is a bacterial disease caused by brucella; mainly spread by direct contact transmission through the brucella carriers, or indirect contact transmission by the environment containing large quantities of bacteria discharged by the infected individuals. At the beginning of 21st century, the epidemic among dairy cows in Zhejiang province, began to come back and has become a localized prevalent epidemic. Combining the pathology of brucellosis, the reported positive data characteristics, and the feeding method in Zhejiang province, this paper establishes an dynamic model to excavate the internal transmission dynamics, fit the real disease situation, predict brucellosis tendency and assess control measures in dairy cows. By careful analysis, we give some quantitative results as follows. (1) The external input of dairy cows from northern areas may lead to high fluctuation of the number of the infectious cows in Zhejiang province that can reach several hundreds. In this case, the disease cannot be controlled and the infection situation cannot easily be predicted. Thus, this paper encourages cows farms to insist on self-supplying production of the dairy cows. (2) The effect of transmission rate of brucella in environment to dairy cattle on brucellosis spreading is greater than transmission rate of the infectious dairy cattle to susceptible cattle. The prevalence of the epidemic is mainly aroused by environment transmission. (3) Under certain circumstances, the epidemic will become a periodic phenomenon. (4) For Zhejiang province, besides measures that have already been adopted, sterilization times of the infected regions is suggested as twice a week, and should be combined with management of the birth rate of dairy cows to control brucellosis spread.     

Modeling scenarios for mitigating outbreaks in congregate settings

The explosive outbreaks of COVID-19 seen in congregate settings such as prisons and nursing homes, has highlighted a critical need for effective outbreak prevention and mitigation strategies for these settings. Here we consider how different types of control interventions impact the expected number of symptomatic infections due to outbreaks. Introduction of disease into the resident population from the community is modeled as a stochastic point process coupled to a branching process, while spread between residents is modeled via a deterministic compartmental model that accounts for depletion of susceptible individuals. Control is modeled as a proportional decrease in the number of susceptible residents, the reproduction number, and/or the proportion of symptomatic infections. This permits a range of assumptions about the density dependence of transmission and modes of protection by vaccination, depopulation and other types of control. We find that vaccination or depopulation can have a greater than linear effect on the expected number of cases. For example, assuming a reproduction number of 3.0 with density-dependent transmission, we find that preemptively reducing the size of the susceptible population by 20% reduced overall disease burden by 47%. In some circumstances, it may be possible to reduce the risk and burden of disease outbreaks by optimizing the way a group of residents are apportioned into distinct residential units. The optimal apportionment may be different depending on whether the goal is to reduce the probability of an outbreak occurring, or the expected number of cases from outbreak dynamics. In other circumstances there may be an opportunity to implement reactive disease control measures in which the number of susceptible individuals is rapidly reduced once an outbreak has been detected to occur. Reactive control is most effective when the reproduction number is not too high, and there is minimal delay in implementing control. We highlight the California state prison system as an example for how these findings provide a quantitative framework for understanding disease transmission in congregate settings. Our approach and accompanying interactive website (https://phoebelu.shinyapps.io/DepopulationModels/) provides a quantitative framework to evaluate the potential impact of policy decisions governing infection control in outbreak settings.     

The thymus is a common target organ in infectious diseases

Infectious disease immunology has largely focused on the effector immune response, changes in the blood and peripheral lymphoid organs of infected individuals, and vaccine development. Studies of the thymus in infected individuals have been neglected, although this is progressively changing. The thymus is a primary lymphoid organ, able to generate mature T cells that eventually colonize secondary lymphoid organs, and is therefore essential for peripheral T cell renewal. Recent data show that normal thymocyte development and export can be altered as a result of an infectious disease. One common feature is the severe atrophy of the infected organ, mainly due to the apoptosis-related depletion of immature CD4+CD8+ thymocytes. Additionally, thymocyte proliferation is frequently diminished. The microenvironmental compartment of the thymus is also affected, particularly in acute infectious diseases, with a densification of the epithelial network and an increase in the deposition of extracellular matrix. In the murine model of Chagas disease, intrathymic chemokine production is also enhanced, and thymocytes from Trypanosoma cruzi-infected mice exhibit greater numbers of cell migration-related receptors for chemokines and extracellular matrix, as well as increased migratory responses to the corresponding ligands. This profile is correlated with the appearance of potentially autoreactive thymus-derived immature CD4+CD8+ T cells in peripheral organs of infected animals. A variety of infectious agents--including viruses, protozoa, and fungi--invade the thymus, raising the hypothesis of the generation of central immunological tolerance for at least some of the infectious agent-derived antigens. It seems clear that the thymus is targeted in a variety of infections, and that such targeting may have consequences on the behavior of peripheral T lymphocytes. In this context, thymus-centered immunotherapeutic approaches potentially represent a new tool for the treatment of severe infectious diseases.     

An epidemic model with infector and exposure dependent severity

A stochastic epidemic model allowing for both mildly and severely infectious individuals is defined, where an individual can become severely infectious directly upon infection or if additionally exposed to infection. It is shown that, assuming a large community, the initial phase of the epidemic may be approximated by a suitable branching process and that the main part of an epidemic that becomes established admits a law of large numbers and a central limit theorem, leading to a normal approximation for the final outcome of such an epidemic. Effects of vaccination prior to an outbreak are studied and the critical vaccination coverage, above which only small outbreaks can occur, is derived. The results are illustrated by simulations that demonstrate that the branching process and normal approximations work well for finite communities, and by numerical examples showing that the final outcome may be close to discontinuous in certain model parameters and that the fraction mildly infected may actually increase as an effect of vaccination.     

Disease Induction by Virus Derived from Molecular Clones of Equine Infectious Anemia Virus

Equine infectious anemia virus (EIAV), a macrophage-tropic lentivirus, causes persistent infections of horses. A number of biologic features, including the rapid development of acute disease, the episodic nature of chronic disease, the propensity for viral genetic variation, and the ability for many infected animals to eventually control virus replication, render EIAV a potentially useful model system for the testing of antiretroviral therapies and vaccine strategies. The utility of the EIAV system has been hampered by the lack of proviral clones that encode promptly pathogenic viral stocks. In this report, we describe the generation and characterization of two infectious molecular clones capable of causing acute clinical syndromes similar to those seen in natural infections. Virus derived from clone p19/wenv17 caused severe debilitating disease at 5 to 7 days postinfection; initial febrile episodes were fatal in two of three infected animals. Virus derived from a second clone, p19/wenv16, caused somewhat milder primary febrile episodes by 10 to 12 days postinfection in two of two infected animals. Virus derived from both clones caused persistent infections such that some animals exhibited chronic equine infectious anemia, characterized by multiple disease episodes. The two virulent clones differ in envelope and rev sequences.     

Estimating individual and household reproduction numbers in an emerging epidemic

Reproduction numbers, defined as averages of the number of people infected by a typical case, play a central role in tracking infectious disease outbreaks. The aim of this paper is to develop methods for estimating reproduction numbers which are simple enough that they could be applied with limited data or in real time during an outbreak. I present a new estimator for the individual reproduction number, which describes the state of the epidemic at a point in time rather than tracking individuals over time, and discuss some potential benefits. Then, to capture more of the detail that micro-simulations have shown is important in outbreak dynamics, I analyse a model of transmission within and between households, and develop a method to estimate the household reproduction number, defined as the number of households infected by each infected household. This method is validated by numerical simulations of the spread of influenza and measles using historical data, and estimates are obtained for would-be emerging epidemics of these viruses. I argue that the household reproduction number is useful in assessing the impact of measures that target the household for isolation, quarantine, vaccination or prophylactic treatment, and measures such as social distancing and school or workplace closures which limit between-household transmission, all of which play a key role in current thinking on future infectious disease mitigation.     

Influenza Infectious Dose May Explain the High Mortality of the Second and Third Wave of 1918–1919 Influenza Pandemic

Background

It is widely accepted that the shift in case-fatality rate between waves during the 1918 influenza pandemic was due to a genetic change in the virus. In animal models, the infectious dose of influenza A virus was associated to the severity of disease which lead us to propose a new hypothesis. We propose that the increase in the case-fatality rate can be explained by the dynamics of disease and by a dose-dependent response mediated by the number of simultaneous contacts a susceptible person has with infectious ones.

Methods

We used a compartment model with seasonality, waning of immunity and a Holling type II function, to model simultaneous contacts between a susceptible person and infectious ones. In the model, infected persons having mild or severe illness depend both on the proportion of infectious persons in the population and on the level of simultaneous contacts between a susceptible and infectious persons. We further allowed for a high or low rate of waning immunity and volunteer isolation at different times of the epidemic.

Results

In all scenarios, case-fatality rate was low during the first wave (Spring) due to a decrease in the effective reproduction number. The case-fatality rate in the second wave (Autumn) depended on the ratio between the number of severe cases to the number of mild cases since, for each 1000 mild infections only 4 deaths occurred whereas for 1000 severe infections there were 20 deaths. A third wave (late Winter) was dependent on the rate for waning immunity or on the introduction of new susceptible persons in the community. If a group of persons became voluntarily isolated and returned to the community some days latter, new waves occurred. For a fixed number of infected persons the overall case-fatality rate decreased as the number of waves increased. This is explained by the lower proportion of infectious individuals in each wave that prevented an increase in the number of severe infections and thus of the case-fatality rate.

Conclusion

The increase on the proportion of infectious persons as a proxy for the increase of the infectious dose a susceptible person is exposed, as the epidemic develops, can explain the shift in case-fatality rate between waves during the 1918 influenza pandemic.     

A new approach for designing disease intervention strategies in metapopulation models

We describe a new approach for investigating the control strategies of compartmental disease transmission models. The method rests on the construction of various alternative next-generation matrices, and makes use of the type reproduction number and the target reproduction number. A general metapopulation SIRS (susceptible–infected–recovered–susceptible) model is given to illustrate the application of the method. Such model is useful to study a wide variety of diseases where the population is distributed over geographically separated regions. Considering various control measures such as vaccination, social distancing, and travel restrictions, the procedure allows us to precisely describe in terms of the model parameters, how control methods should be implemented in the SIRS model to ensure disease elimination. In particular, we characterize cases where changing only the travel rates between the regions is sufficient to prevent an outbreak.     

SVIR epidemic models with vaccination strategies

Vaccination is important for the elimination of infectious diseases. To finish a vaccination process, doses usually should be taken several times and there must be some fixed time intervals between two doses. The vaccinees (susceptible individuals who have started the vaccination process) are different from both susceptible and recovered individuals. Considering the time for them to obtain immunity and the possibility for them to be infected before this, two SVIR models are established to describe continuous vaccination strategy and pulse vaccination strategy (PVS), respectively. It is shown that both systems exhibit strict threshold dynamics which depend on the basic reproduction number. If this number is below unity, the disease can be eradicated. And if it is above unity, the disease is endemic in the sense of global asymptotical stability of a positive equilibrium for continuous vaccination strategy and disease permanence for PVS. Mathematical results suggest that vaccination is helpful for disease control by decreasing the basic reproduction number. However, there is a necessary condition for successful elimination of disease. If the time for the vaccinees to obtain immunity or the possibility for them to be infected before this is neglected, this condition disappears and the disease can always be eradicated by some suitable vaccination strategies. This may lead to over-evaluating the effect of vaccination.     

Multiple infections, immune dynamics, and the evolution of virulence

Understanding the effect of multiple infections is essential for the prediction (and eventual control) of virulence evolution. Some theoretical studies have considered the possibility that several strains coexist in the same host (coinfection), but few have taken their within-host dynamics explicitly into account. Here, we develop a nested approach based on a simple model for the interaction of parasite strains with their host's immune system. We study virulence evolution by linking the within-host dynamics to an epidemiological framework that incorporates multiple infections. Our model suggests that antigenically similar parasite strains cannot coexist in the long term inside a host. We also find that the optimal level of virulence increases with the efficiency of multiple infections. Finally, we notice that coinfections create heterogeneity in the host population (with susceptible hosts and infected hosts), which can lead to evolutionary branching in the parasite population and the emergence of a hypervirulent parasite strategy. We interpret this result as a parasite specialization to the infectious state of the hosts. Our study has experimental and theoretical implications in a virulence management perspective.     

Sliding Mode Control of Outbreaks of Emerging Infectious Diseases

This paper proposes and analyzes a mathematical model of an infectious disease system with a piecewise control function concerning threshold policy for disease management strategy. The proposed models extend the classic models by including a piecewise incidence rate to represent control or precautionary measures being triggered once the number of infected individuals exceeds a threshold level. The long-term behaviour of the proposed non-smooth system under this strategy consists of the so-called sliding motion-a very rapid switching between application and interruption of the control action. Model solutions ultimately approach either one of two endemic states for two structures or the sliding equilibrium on the switching surface, depending on the threshold level. Our findings suggest that proper combinations of threshold densities and control intensities based on threshold policy can either preclude outbreaks or lead the number of infecteds to a previously chosen level.     

Detecting Differential Transmissibilities That Affect the Size of Self-Limited Outbreaks

Our ability to respond appropriately to infectious diseases is enhanced by identifying differences in the potential for transmitting infection between individuals. Here, we identify epidemiological traits of self-limited infections (i.e. infections with an effective reproduction number satisfying ) that correlate with transmissibility. Our analysis is based on a branching process model that permits statistical comparison of both the strength and heterogeneity of transmission for two distinct types of cases. Our approach provides insight into a variety of scenarios, including the transmission of Middle East Respiratory Syndrome Coronavirus (MERS-CoV) in the Arabian peninsula, measles in North America, pre-eradication smallpox in Europe, and human monkeypox in the Democratic Republic of the Congo. When applied to chain size data for MERS-CoV transmission before 2014, our method indicates that despite an apparent trend towards improved control, there is not enough statistical evidence to indicate that has declined with time. Meanwhile, chain size data for measles in the United States and Canada reveal statistically significant geographic variation in , suggesting that the timing and coverage of national vaccination programs, as well as contact tracing procedures, may shape the size distribution of observed infection clusters. Infection source data for smallpox suggests that primary cases transmitted more than secondary cases, and provides a quantitative assessment of the effectiveness of control interventions. Human monkeypox, on the other hand, does not show evidence of differential transmission between animals in contact with humans, primary cases, or secondary cases, which assuages the concern that social mixing can amplify transmission by secondary cases. Lastly, we evaluate surveillance requirements for detecting a change in the human-to-human transmission of monkeypox since the cessation of cross-protective smallpox vaccination. Our studies lay the foundation for future investigations regarding how infection source, vaccination status or other putative transmissibility traits may affect self-limited transmission.     

Frequency-dependent incidence in models of sexually transmitted diseases: portrayal of pair-based transmission and effects of illness on contact behaviour

We explore the transmission process for sexually transmitted diseases (STDs). We derive the classical frequency-dependent incidence mechanistically from a pair-formation model, using an approximation that applies to populations with rapid pairing dynamics (such as core groups or non-pair-bonding animals). This mechanistic derivation provides a framework to assess how accurately frequency-dependent incidence portrays the pair-based transmission known to underlie STD dynamics. This accuracy depends strongly on the disease being studied: frequency-dependent formulations are more suitable for chronic less-transmissible infections than for transient highly transmissible infections. Our results thus support earlier proposals to divide STDs into these two functional classes, and we suggest guidelines to help assess under what conditions each class can be appropriately modelled using frequency-dependent incidence. We then extend the derivation to include situations where infected individuals exhibit altered pairing behaviour. For four cases of increasing behavioural complexity, analytic expressions are presented for the generalized frequency-dependent incidence rate, basic reproductive number (R0) and steady-state prevalence (i infinity) of an epidemic. The expression for R0 is identical for all cases, giving refined insights into determinants of invasibility of STDs. Potentially significant effects of infection-induced changes in contact behaviour are illustrated by simulating epidemics of bacterial and viral STDs. We discuss the application of our results to STDs (in humans and animals) and other infectious diseases.