Dynamics of indirectly transmitted infectious diseases with immunological threshold

Estimating Hidden Cholera Burden and Intervention Effectiveness

Cholera remains a significant public health threat in many parts of the world, with differing levels of compliance to intervention strategies and undocumented cases contributing to reservoir contamination with Vibrio cholerae at varying rates alongside reported cases. To address this, we incorporate an inapparent cholera-infected compartment into the iSIR model and equip it with parameters depicting vaccination and compliance levels for water and food sanitation, handwashing, and safe fecal disposal. Our model shows that the bacteria shedding from the inapparent infection can significantly affect the spread of cholera. Also, we identify that lowering the bacteria ingestion rate among the susceptible and controlling the bacteria shedding from reported infected are two key components for obtaining a disease-free state in the long run. The model fitting to cholera outbreaks in Haiti, Kenya, Malawi, and Zimbabwe implies that at least 88.5% of cases are inapparent, with the first reporting appearing up to 11 weeks after the start of the outbreak. Additionally, we find that the combination of water and food sanitation and handwashing is the most effective intervention strategy for reducing the cholera outbreak peak if compliance with these measures remains at moderate or high levels. However, with low compliance, safe fecal disposal of the reported infected individuals combined with vaccination coverage of the susceptible population is suggested to obtain the lowest outbreak peak.

Homogenization Reveals Large-Scale Dynamics in the Spread of Chronic Wasting Disease

Thresholds in environmental transmission can significantly alter the dynamics of disease spread in wildlife. However, the impact of thresholds in landscapes with high spatial variability is not well understood. We investigate this phenomenon in chronic wasting disease (CWD), a degenerative cervid illness exhibiting direct transmission between individuals and indirect transmission through environmental hazard. The indirect pathway exhibits threshold behavior analogous to a strong Allee effect. We derive a partial differential equation (PDE) model for CWD on the scale of hours and tens of meters. Leveraging highly variable landscape structure, we homogenize this model to yield an asymptotically accurate approximal model on the scale of years and kilometers. Our homogenized model describes the aggregate effect of thresholded transmission on large scales - to our knowledge, the first time such a description has been identified. The model predicts that direct transmission in CWD will lead to pulled fronts, whereas indirect transmission generates pushed fronts. Pushed fronts allow CWD to spread even when infectives infect less than one susceptible on average. We use a hypothetical binary distribution of habitat types to showcase the homogenized model's ability to predict how distribution of cover in a landscape can influence CWD spread and potential mitigation efforts.

Multistability bifurcation analysis and transmission pathways for the dynamics of the infectious disease-cholera model with microbial expansion inducing the Allee effect in terms of Guassian noise and crossover effects

Cholera is a life-threatening form of diarrhoea resulting from a bacterial infection of the gastrointestinal system caused by Vibrio cholerae. The aim of this article is to explore the dynamic characteristics of cholera disease transmission and the equilibrium level of recovery in a stochastic cholera framework by adopting piecewise fractional differential operator approaches. Firstly, we provide a detailed fractional-order form of the cholera model, showing the system's positivity and boundedness. Meanwhile, equilibrium analysis is performed to comprehend the model's behaviour and stability for disease-free as well as endemic-free equilibrium. Bacterial development rates have been reported to correlate with the Allee phenomenon. The resulting system exhibits multi-stability for forward and saddle-node bifurcations based on various settings. Global sensitivity is calculated employing the partial rank correlation coefficient approach. Furthermore, the model analyzes a stochastic fractional cholera system. Through a rigorous analysis, we demonstrate that the stochastic model offers a unique global positive solution. Lyapunov function theory is used to create criteria that ensure the model's unique erogodic stationary distribution at [Formula: see text]. Afterwards, the phenomenon that excessive noises can result in the elimination of cholera is discovered. Moreover, this model enables us to study a range of behaviors, from bridging to unpredictability, helping us to understand and predict the process from the beginning to the end of the virus. Moreover, the piecewise differential operators have chosen to extend novel pathways for researchers across several fields, enabling them to convey unique features in various time periods. These operators can be gathered with classical, Caputo, Atangana-Baleanu-Caputo fractional derivative, and random perturbation. As a result, the analytical insights are validated using computational modeling, providing a novel viewpoint on spreading diseases in a societal environment.

Neural network procedures for the cholera disease system with public health mediations

Severe gastrointestinal infections and watery diseases like cholera are still a major worldwide medical concern in the developing nations. A mathematical system contains some necessary dynamics based on the cholera spread to investigate the influence of public health education movements along with treatment and vaccination as control policies in restraining the infection. The cholera disease system with public health mediations divide the density of human population into seven categories based on the status of diseases, who are susceptible, educated, vaccinated, quarantined, infected, treated and removed individuals along with the aquatic bacteria population. The motive of current research is to present the numerical performances of the cholera disease system with public health mediations by using a stochastic computing process based on the Bayesian regularization neural network. A data is constructed by using a conventional Adam scheme that reduces the mean square error by distributing the data into training, validation and testing with some reasonable percentages. Twenty-five neurons, and sigmoid fitness function are used in the stochastic process to solve the model. The accuracy is justified by using comparison of the results, absolute error around 10-06 to 10-08 and some statistical operator performances.

Climate-dependent effectiveness of nonpharmaceutical interventions on COVID-19 mitigation

Environmental factors have a significant impact on the transmission of infectious diseases. Existing results show that the novel coronavirus can persist outside the host. We propose a susceptible-exposed-presymptomatic-infectious-asymptomatic-recovered-susceptible (SEPIARS) model with a vaccination compartment and indirect incidence to explore the effect of environmental conditions, temperature and humidity, on the transmission of the SARS-CoV-2 virus. Using climate data and daily confirmed cases data in two Canadian cities with different atmospheric conditions, we evaluate the mortality rates of the SARS-CoV-2 virus and further estimate the transmission rates by the inverse method, respectively. The numerical results show that high temperature or humidity can be helpful in mitigating the spread of COVID-19 during the warm summer months. Our findings verify that nonpharmaceutical interventions are less effective if the virus can persist for a long time on surfaces. Based on climate data, we can forecast the transmission rate and the infection cases up to four weeks in the future by a generalized boosting machine learning model.

Relating quanta conservation and compartmental epidemiological models of airborne disease outbreaks in buildings

We investigate the underlying assumptions and limits of applicability of several documented models for outbreaks of airborne disease inside buildings by showing how they may each be regarded as special cases of a system of equations which combines quanta conservation and compartmental epidemiological modelling. We investigate the behaviour of this system analytically, gaining insight to its behaviour at large time. We then investigate the characteristic timescales of an indoor outbreak, showing how the dilution rate of the space, and the quanta generation rate, incubation rate and removal rate associated with the illness may be used to predict the evolution of an outbreak over time, and may also be used to predict the relative performances of other indoor airborne outbreak models. The model is compared to a more commonly used model, in which it is assumed the environmental concentration of infectious aerosols adheres to a quasi-steady-state, so that the the dimensionless quanta concentration is equal to the the infectious fraction. The model presented here is shown to approach this limit exponentially to within an interval defined by the incubation and removal rates. This may be used to predict the maximum extent to which a case will deviate from the quasi steady state condition.

Modeling and analyzing an opinion network dynamics considering the environmental factor

With the development of Internet technology, social media has gradually become an important platform where users can express opinions about hot events. Research on the mechanism of public opinion evolution is beneficial to guide the trend of opinions, making users' opinions change in a positive direction or reach a consensus among controversial crowds. To design effective strategies for public opinion management, we propose a dynamic opinion network susceptible-forwarding-immune model considering environmental factors (NET-OE-SFI), which divides the forwarding nodes into two types: support and opposition based on the real data of users. The NET-OE-SFI model introduces environmental factors from infectious diseases into the study of network information transmission, which aims to explore the evolution law of users' opinions affected by the environment. We attempt to combine the complex media environmental factors in social networks with users' opinion information to study the influence of environmental factors on the evolution of public opinion. Data fitting of real information transmission data fully demonstrates the validity of this model. We have also made a variety of sensitivity analysis experiments to study the influence of model parameters, contributing to the design of reasonable and effective strategies for public opinion guidance.

Extensions of mean-field approximations for environmentally-transmitted pathogen networks

Many pathogens spread via environmental transmission, without requiring host-to-host direct contact. While models for environmental transmission exist, many are simply constructed intuitively with structures analogous to standard models for direct transmission. As model insights are generally sensitive to the underlying model assumptions, it is important that we are able understand the details and consequences of these assumptions. We construct a simple network model for an environmentally-transmitted pathogen and rigorously derive systems of ordinary differential equations (ODEs) based on different assumptions. We explore two key assumptions, namely homogeneity and independence, and demonstrate that relaxing these assumptions can lead to more accurate ODE approximations. We compare these ODE models to a stochastic implementation of the network model over a variety of parameters and network structures, demonstrating that with fewer restrictive assumptions we are able to achieve higher accuracy in our approximations and highlighting more precisely the errors produced by each assumption. We show that less restrictive assumptions lead to more complicated systems of ODEs and the potential for unstable solutions. Due to the rigour of our derivation, we are able to identify the reason behind these errors and propose potential resolutions.

Dynamic analysis and optimal control of a class of SISP respiratory diseases

In this paper, the actual background of the susceptible population being directly patients after inhaling a certain amount of PM2.5 is taken into account. The concentration response function of PM2.5 is introduced, and the SISP respiratory disease model is proposed. Qualitative theoretical analysis proves that the existence, local stability and global stability of the equilibria are all related to the daily emission P0 of PM2.5 and PM2.5 pathogenic threshold K. Based on the sensitivity factor analysis and time-varying sensitivity analysis of parameters on the number of patients, it is found that the conversion rate β and the inhalation rate η has the largest positive correlation. The cure rate γ of infected persons has the greatest negative correlation on the number of patients. The control strategy formulated by the analysis results of optimal control theory is as follows: The first step is to improve the clearance rate of PM2.5 by reducing the PM2.5 emissions and increasing the intensity of dust removal. Moreover, such removal work must be maintained for a long time. The second step is to improve the cure rate of patients by being treated in time. After that, people should be reminded to wear masks and go out less so as to reduce the conversion rate of susceptible people becoming patients.

Bacteria-bacteriophage cycles facilitate Cholera outbreak cycles: an indirect Susceptible-Infected-Recovered-Bacteria- Phage (iSIRBP) model-based mathematical study

Cholera is an acute enteric infectious disease caused by the Gram-negative bacterium Vibrio cholerae. Despite a huge body of research, the precise nature of its transmission dynamics has yet to be fully elucidated. Mathematical models can be useful to better understand how an infectious agent can spread and be properly controlled. We develop a compartmental model describing a human population, a bacterial population as well as a phage population. We show that there might be eight equilibrium points, one of which is a disease free equilibrium point. We carry out numerical simulations and sensitivity analyses and we show that the presence of phage can reduce the number of infectious individuals. Moreover, we discuss the main implications in terms of public health management and control strategies.

Mathematical Models for Cholera Dynamics-A Review

Cholera remains a significant public health burden in many countries and regions of the world, highlighting the need for a deeper understanding of the mechanisms associated with its transmission, spread, and control. Mathematical modeling offers a valuable research tool to investigate cholera dynamics and explore effective intervention strategies. In this article, we provide a review of the current state in the modeling studies of cholera. Starting from an introduction of basic cholera transmission models and their applications, we survey model extensions in several directions that include spatial and temporal heterogeneities, effects of disease control, impacts of human behavior, and multi-scale infection dynamics. We discuss some challenges and opportunities for future modeling efforts on cholera dynamics, and emphasize the importance of collaborations between different modeling groups and different disciplines in advancing this research area.

Stability Analysis and Optimal Control of a Fractional Cholera Epidemic Model

In this paper, a fractional model for the transmission dynamics of cholera was developed. In invariant regions of the model, solutions were generated. Disease-free and endemic equilibrium points were obtained. The basic reproduction number was evaluated, and the sensitivity analysis was performed. Under the support of Pontryagin’s maximum principle, the fractional order optimal control was obtained. Furthermore, an optimal strategy was discussed, which minimized the total number of infected individuals and the costs associated with control. Treatment, vaccination, and awareness programs were regarded as three means to reduce the number of infected. Finally, numerical simulations and cost-effectiveness analysis were presented to show the result that the best strategy was the combination of treatment and awareness programs.

A SIQRB delayed model for cholera and optimal control treatment

We improve a recent mathematical model for cholera by adding a time delay that represents the time between the instant at which an individual becomes infected and the instant at which he begins to have symptoms of cholera disease. We prove that the delayed cholera model is biologically meaningful and analyze the local asymptotic stability of the equilibrium points for positive time delays. An optimal control problem is proposed and analyzed, where the goal is to obtain optimal treatment strategies, through quarantine, that minimize the number of infective individuals and the bacterial concentration, as well as treatment costs. Necessary optimality conditions are applied to the delayed optimal control problem, with a L1 type cost functional. We show that the delayed cholera model fits better the cholera outbreak that occurred in the Department of Artibonite - Haiti, from 1 November 2010 to 1 May 2011, than the non-delayed model. Considering the data of the cholera outbreak in Haiti, we solve numerically the delayed optimal control problem and propose solutions for the outbreak control and eradication.

Threshold dynamics of a nonlocal and delayed cholera model in a spatially heterogeneous environment

A nonlocal and delayed cholera model with two transmission mechanisms in a spatially heterogeneous environment is derived. We introduce two basic reproduction numbers, one is for the bacterium in the environment and the other is for the cholera disease in the host population. If the basic reproduction number for the cholera bacterium in the environment is strictly less than one and the basic reproduction number of infection is no more than one, we prove globally asymptotically stability of the infection-free steady state. Otherwise, the infection will persist and there exists at least one endemic steady state. For the special homogeneous case, the endemic steady state is actually unique and globally asymptotically stable. Under some conditions, the basic reproduction number of infection is strictly decreasing with respect to the diffusion coefficients of cholera bacteria and infectious hosts. When these conditions are violated, numerical simulation suggests that spatial diffusion may not only spread the infection from high-risk region to low-risk region, but also increase the infection level in high-risk region.

Modeling the Effectiveness of TV and Social Media Advertisements on the Dynamics of Water-Borne Diseases

Cholera is a serious threat to the health of human-kind all over the world and its control is a problem of great concern. In this context, a nonlinear mathematical model to control the prevalence of cholera disease is proposed and analyzed by incorporating TV and social media advertisements as a dynamic variable. It is considered that TV and social media ads propagate the knowledge among the people regarding the severe effects of cholera disease on human health along with its precautionary measures. It is also assumed that the mode of transmission of cholera disease among susceptible individuals is due to consumption of contaminated drinking water containing Vibrio cholerae. Moreover, the propagation of knowledge through TV and social media ads makes the people aware to adopt precautionary measures and also the aware people make some effectual efforts to washout the bacteria from the aquatic environment. Model analysis reveals that increase in the washout rate of bacteria due to aware individuals causes the stability switch. It is found that TV and social media ads have the potential to reduce the number of infectives in the region and thus control the cholera epidemic. Numerical simulation is performed for a particular set of parameter values to support the analytical findings.

Comparing the Indirect Effects between Exploiters in Predator-Prey and Host-Pathogen Systems

AbstractIn multipredator and multipathogen systems, exploiters interact indirectly via shared victim species. Interspecific prey competition and the degree of predator specialization are known to influence whether predators have competitive (i.e., (-,-)) or noncompetitive (i.e., (-,+) or (+,+)) indirect interactions. Much less is known about the population-level indirect interactions between pathogens that infect the same populations of host species. In this study, we use two-predator-two-prey and two-host-two-pathogen models to compare the indirect effects between predators with the indirect effects between pathogens. We focus on how the indirect interactions between pathogens are affected by the competitive abilities of susceptible and infected hosts, whether the pathogens are specialists or generalists, and the transmission pathway (direct vs. environmental transmission). In many cases, indirect effects between pathogens and predators follow similar patterns, for example, more positive indirect effects with increased interspecific competition between victim species. However, the indirect effects between pathogens can qualitatively differ, for example, more negative indirect effects with increased interspecific host competition. These contrasting patterns show that an important mechanistic difference between predatory and parasitic interactions (specifically, whether interactions are immediately lethal) can have important population-level effects on the indirect interactions between exploiters.

Parameter and State Estimation in a Cholera Model with Threshold Immunology: A Case Study of Senegal

It is often impossible to measure all states affecting spread of a disease. In cholera, asymptomatic and cholera pathogen densities are not practically measurable despite playing a big role in its transmission. They are referred to as inaccessible states of the model and can only be manipulated using the measurable states of the given model. Our interest lies in estimating such states and the parameters catalyzing the spread. A mathematical model for cholera dynamics consisting of five compartments (susceptible, symptomatic, asymptomatic, recovered and bacteria population) with a minimum infection dose (MID) is considered. A method based on observer (from modern control theory) is proposed to estimate the state variables not accessible to measurement and the time-dependent parameters from real data of Senegal. We suppose that the total population of Senegal, the monthly reported cholera-induced deaths and the monthly recovered individuals are known inputs obtainable from real data, and the monthly new cholera cases the system output. An auxiliary system is used, an observer whose solutions converge exponentially to those of an original system and solely utilize known inputs and output of the model. Thus, the estimation of the unmeasured state variables like the pathogen density and the yearly asymptomatic population within the human community playing an important role in the spread of cholera is possible. We derive the expressions for time-dependent infection rate, induced cholera death rate and symptomatic recovery rate and their estimations done using real data. Numerical simulations are then performed for the validation of estimation results. The system together with the observer designed is detectable but is not observable. The observer delivered estimates reflect a close trend already ascertained by other researchers. They indicate the existence of bacteria and asymptomatic individuals in the population of Senegal at any single time for the duration of collection of the data. The ever existence of cholera pathogen explains the endemicity of Cholera in Senegal and other sub-Saharan-African countries owing to role played by the asymptomatic individual in the bacteria density. As such, the heath authorities in Senegal need to educate the general public on hygiene irrespective of observable symptoms to lower the possible number of new infections. We have analytically showed and numerically confirmed the exponential convergence to zero of the estimation errors resulting from the observer model hence the high quality of the estimates.

A non-invasive method to assess environmental contamination with avian pathogens: beak and feather disease virus (BFDV) detection in nest boxes

Indirect transmission of pathogens can pose major risks to wildlife, yet the presence and persistence of wildlife pathogens in the environment has been little studied. Beak and feather disease virus (BFDV) is of global conservation concern: it can infect all members of the Psittaciformes, one of the most threatened bird orders, with infection often being lethal. Indirect transmission of BFDV through contaminated nest hollows has been proposed as a major infection source. However, data on whether and for how long nest sites in the wild remain contaminated have been absent. We determined the BFDV status of birds (parents and nestlings) for 82 nests of Crimson Rosellas, Platycercus elegans and Eastern Rosellas, Platycercus eximius. In 11 of these nests (13.4%, 95% confidence interval 6.9-22.7), we found an infected parent or nestling. Using nest swabs, we then compared BFDV presence at three points in time (before, during and after breeding) in three groups of nest boxes. These were nest boxes occupied by infected birds, and two control groups (nest boxes occupied by uninfected birds, and unoccupied nest boxes). Detection of BFDV on nest swabs was strongly associated with the infection status of parents in each nest box and with the timing of breeding. During breeding, boxes occupied by BFDV-positive birds were significantly more likely to have BFDV-positive nest swabs than boxes occupied by BFDV-negative birds; nest swabs tested BFDV-positive in 80% (28.4-99.5) of nests with parental antigen excretion, 66.7% (9.4-99.2) of nests occupied by parents with BFDV-positive cloacal swabs and 66.7% (22.3-95.7) of nests occupied by parents with BFDV-positive blood. 0% (0-52.2) of nests with BFDV-positive nestlings had BFDV-positive nest swabs. Across all boxes occupied by BFDV-positive birds (parents or nestlings), no nest swabs were BFDV-positive before breeding, 36.4% (95% CI 10.9-69.2) were positive during breeding and 9.1% (0.2-41.3) remained positive after breeding. BFDV was present on nest swabs for up to 3.7 months. Our study provides novel insights into the potential role of nest cavities and other fomites in indirect transmission of BFDV, and possibly other pathogens, and offers a non-invasive method for surveillance of pathogens in wild bird populations.

Coupling the Macroscale to the Microscale in a Spatiotemporal Context to Examine Effects of Spatial Diffusion on Disease Transmission

There are many challenges to coupling the macroscale to the microscale in temporal or spatial contexts. In order to examine effects of an individual movement and spatial control measures on a disease outbreak, we developed a multiscale model and extended the semi-stochastic simulation method by linking individual movements to pathogen’s diffusion, linking the slow dynamics for disease transmission at the population level to the fast dynamics for pathogen shedding/excretion at the individual level. Numerical simulations indicate that during a disease outbreak individuals with the same infection status show the property of clustering and, in particular, individuals’ rapid movements lead to an increase in the average reproduction number \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0$$\end{document}R0, the final size and the peak value of the outbreak. It is interesting that a high level of aggregation the individuals’ movement results in low new infections and a small final size of the infected population. Further, we obtained that either high diffusion rate of the pathogen or frequent environmental clearance lead to a decline in the total number of infected individuals, indicating the need for control measures such as improving air circulation or environmental hygiene. We found that the level of spatial heterogeneity when implementing control greatly affects the control efficacy, and in particular, an uniform isolation strategy leads to low a final size and small peak, compared with local measures, indicating that a large-scale isolation strategy with frequent clearance of the environment is beneficial for disease control.

On modelling environmentally transmitted pathogens

Many pathogens are able to replicate or survive in abiotic environments. Disease transmission models that include environmental reservoirs and environment-to-host transmission have used a variety of functional forms and modelling frameworks without a clear connection to pathogen ecology or space and time scales. We present a conceptual framework to organize microparasites based on the role that abiotic environments play in their lifecycle. Mean-field and individual-based models for environmental transmission are analysed and compared. We show considerable divergence between both modelling approaches when conditions do not facilitate well mixing and for pathogens with fast dynamics in the environment. We conclude with recommendations for modelling environmentally transmitted pathogens based on the pathogen lifecycle and time and spatial scales of the host-pathogen system under consideration.

Reentrant phase transitions in threshold driven contagion on multiplex networks

Models of threshold driven contagion explain the cascading spread of information, behavior, systemic risk, and epidemics on social, financial, and biological networks. At odds with empirical observations, these models predict that single-layer unweighted networks become resistant to global cascades after reaching sufficient connectivity. We investigate threshold driven contagion on weight heterogeneous multiplex networks and show that they can remain susceptible to global cascades at any level of connectivity, and with increasing edge density pass through alternating phases of stability and instability in the form of reentrant phase transitions of contagion. Our results provide a theoretical explanation for the observation of large-scale contagion in highly connected but heterogeneous networks.

Multiple transmission routes sustain high prevalence of a virulent parasite in a butterfly host

Understanding factors that allow highly virulent parasites to reach high infection prevalence in host populations is important for managing infection risks to human and wildlife health. Multiple transmission routes have been proposed as one mechanism by which virulent pathogens can achieve high prevalence, underscoring the need to investigate this hypothesis through an integrated modelling-empirical framework. Here, we examine a harmful specialist protozoan infecting monarch butterflies that commonly reaches high prevalence (50–100%) in resident populations. We integrate field and modelling work to show that a combination of three empirically-supported transmission routes (vertical, adult transfer and environmental transmission) can produce and sustain high infection prevalence in this system. Although horizontal transmission is necessary for parasite invasion, most new infections post-establishment arise from vertical transmission. Our study predicts that multiple transmission routes, coupled with high parasite virulence, can reduce resident host abundance by up to 50%, suggesting that the protozoan could contribute to declines of North American monarchs.

Natural Disasters and Cholera Outbreaks: Current Understanding and Future Outlook

PURPOSE OF REVIEW

Diarrheal diseases remain a serious global public health threat, especially for those populations lacking access to safe water and sanitation infrastructure. Although association of several diarrheal diseases, e.g., cholera, shigellosis, etc., with climatic processes has been documented, the global human population remains at heightened risk of outbreak of diseases after natural disasters, such as earthquakes, floods, or droughts. In this review, cholera was selected as a signature diarrheal disease and the role of natural disasters in triggering and transmitting cholera was analyzed.

RECENT FINDINGS

Key observations include identification of an inherent feedback loop that includes societal structure, prevailing climatic processes, and spatio-temporal seasonal variability of natural disasters. Data obtained from satellite-based remote sensing are concluded to have application, although limited, in predicting risks of a cholera outbreak(s). We argue that with the advent of new high spectral and spatial resolution data, earth observation systems should be seamlessly integrated in a decision support mechanism to be mobilize resources when a region suffers a natural disaster. A framework is proposed that can be used to assess the impact of natural disasters with response to outbreak of cholera, providing assessment of short- and long-term influence of climatic processes on disease outbreaks.

Threshold driven contagion on weighted networks

Weighted networks capture the structure of complex systems where interaction strength is meaningful. This information is essential to a large number of processes, such as threshold dynamics, where link weights reflect the amount of influence that neighbours have in determining a node's behaviour. Despite describing numerous cascading phenomena, such as neural firing or social contagion, the modelling of threshold dynamics on weighted networks has been largely overlooked. We fill this gap by studying a dynamical threshold model over synthetic and real weighted networks with numerical and analytical tools. We show that the time of cascade emergence depends non-monotonously on weight heterogeneities, which accelerate or decelerate the dynamics, and lead to non-trivial parameter spaces for various networks and weight distributions. Our methodology applies to arbitrary binary state processes and link properties, and may prove instrumental in understanding the role of edge heterogeneities in various natural and social phenomena.

Model distinguishability and inference robustness in mechanisms of cholera transmission and loss of immunity

Mathematical models of cholera and waterborne disease vary widely in their structures, in terms of transmission pathways, loss of immunity, and a range of other features. These differences can affect model dynamics, with different models potentially yielding different predictions and parameter estimates from the same data. Given the increasing use of mathematical models to inform public health decision-making, it is important to assess model distinguishability (whether models can be distinguished based on fit to data) and inference robustness (whether inferences from the model are robust to realistic variations in model structure). In this paper, we examined the effects of uncertainty in model structure in the context of epidemic cholera, testing a range of models with differences in transmission and loss of immunity structure, based on known features of cholera epidemiology. We fit these models to simulated epidemic and long-term data, as well as data from the 2006 Angola epidemic. We evaluated model distinguishability based on fit to data, and whether the parameter values, model behavior, and forecasting ability can accurately be inferred from incidence data. In general, all models were able to successfully fit to all data sets, both real and simulated, regardless of whether the model generating the simulated data matched the fitted model. However, in the long-term data, the best model fits were achieved when the loss of immunity structures matched those of the model that simulated the data. Two parameters, one representing person-to-person transmission and the other representing the reporting rate, were accurately estimated across all models, while the remaining parameters showed broad variation across the different models and data sets. The basic reproduction number (R₀) was often poorly estimated even using the correct model, due to practical unidentifiability issues in the waterborne transmission pathway which were consistent across all models. Forecasting efforts using noisy data were not successful early in the outbreaks, but once the epidemic peak had been achieved, most models were able to capture the downward incidence trajectory with similar accuracy. Forecasting from noise-free data was generally successful for all outbreak stages using any model. Our results suggest that we are unlikely to be able to infer mechanistic details from epidemic case data alone, underscoring the need for broader data collection, such as immunity/serology status, pathogen dose response curves, and environmental pathogen data. Nonetheless, with sufficient data, conclusions from forecasting and some parameter estimates were robust to variations in the model structure, and comparative modeling can help to determine how realistic variations in model structure may affect the conclusions drawn from models and data.

How Behaviour and the Environment Influence Transmission in Mobile Groups

The movement of individuals living in groups leads to the formation of physical interaction networks over which signals such as information or disease can be transmitted. Direct contacts represent the most obvious opportunities for a signal to be transmitted. However, because signals that persist after being deposited into the environment may later be acquired by other group members, indirect environmentally-mediated transmission is also possible. To date, studies of signal transmission within groups have focused on direct physical interactions and ignored the role of indirect pathways. Here, we use an agent-based model to study how the movement of individuals and characteristics of the signal being transmitted modulate transmission. By analysing the dynamic interaction networks generated from these simulations, we show that the addition of indirect pathways speeds up signal transmission, while the addition of physically-realistic collisions between individuals in densely packed environments hampers it. Furthermore, the inclusion of spatial biases that induce the formation of individual territories, reveals the existence of a trade-off such that optimal signal transmission at the group level is only achieved when territories are of intermediate sizes. Our findings provide insight into the selective pressures guiding the evolution of behavioural traits in natural groups, and offer a means by which multi-agent systems can be engineered to achieve desired transmission capabilities.

Relevance of Indirect Transmission for Wildlife Disease Surveillance

Epidemiological models of infectious diseases are essential tools in support of risk assessment, surveillance design, and contingency planning in public and animal health. Direct pathogen transmission from host to host is an essential process of each host–pathogen system and respective epidemiological modeling concepts. It is widely accepted that numerous diseases involve indirect transmission (IT) through pathogens shed by infectious hosts to their environment. However, epidemiological models largely do not represent pathogen persistence outside the host explicitly. We hypothesize that this simplification might bias management-related model predictions for disease agents that can persist outside their host for a certain time span. We adapted an individual-based, spatially explicit epidemiological model that can mimic both transmission processes. One version explicitly simulated indirect pathogen transmission through a contaminated environment. The second version simulated direct host-to-host transmission only. We aligned the model variants by the transmission potential per infectious host (i.e., basic reproductive number R₀) and the spatial transmission kernel of the infection to allow unbiased comparison of predictions. The quantitative model results are provided for the example of surveillance plans for early detection of foot-and-mouth disease in wild boar, a social host. We applied systematic sampling strategies on the serological status of randomly selected host individuals in both models. We compared between the model variants the time to detection and the area affected prior to detection, measures that strongly influence mitigation costs. Moreover, the ideal sampling strategy to detect the infection in a given time frame was compared between both models. We found the simplified, direct transmission model to underestimate necessary sample size by up to one order of magnitude but to overestimate the area put under control measures. Thus, the model predictions underestimated surveillance efforts but overestimated mitigation costs. We discuss parameterization of IT models and related knowledge gaps. We conclude that the explicit incorporation of IT mechanisms in epidemiological modeling may reward by adapting surveillance and mitigation efforts.

Lethal exposure: An integrated approach to pathogen transmission via environmental reservoirs

To mitigate the effects of zoonotic diseases on human and animal populations, it is critical to understand what factors alter transmission dynamics. Here we assess the risk of exposure to lethal concentrations of the anthrax bacterium, Bacillus anthracis, for grazing animals in a natural system over time through different transmission mechanisms. We follow pathogen concentrations at anthrax carcass sites and waterholes for five years and estimate infection risk as a function of grass, soil or water intake, age of carcass sites, and the exposure required for a lethal infection. Grazing, not drinking, seems the dominant transmission route, and transmission is more probable from grazing at carcass sites 1-2 years of age. Unlike most studies of virulent pathogens that are conducted under controlled conditions for extrapolation to real situations, we evaluate exposure risk under field conditions to estimate the probability of a lethal dose, showing that not all reservoirs with detectable pathogens are significant transmission pathways.

Emerging Tuberculosis Pathogen Hijacks Social Communication Behavior in the Group-Living Banded Mongoose (Mungos mungo)

An emerging Mycobacterium tuberculosis complex (MTC) pathogen, M. mungi, infects wild banded mongooses (Mungos mungo) in Northern Botswana, causing significant mortality. This MTC pathogen did not appear to be transmitted through a primary aerosol or oral route. We utilized histopathology, spoligotyping, mycobacterial interspersed repetitive units-variable number of tandem repeats (MIRU-VNTR), quantitative PCR (qPCR), and molecular markers (regions of difference [RDs] from various MTC members, including region of difference 1 [RD1] from M. bovis BCG [RD1^BCG], M. microti [RD1^mic], and M. pinnipedii [RD1^seal], genes Rv1510 [RD4], Rv1970 [RD7], Rv3877/8 [RD1], and Rv3120 [RD12], insertion element IS1561, the 16S RNA gene, and gene Rv0577 [cfp32]), including the newly characterized mongoose-specific deletion in RD1 (RD1^mon), in order to demonstrate the presence of M. mungi DNA in infected mongooses and investigate pathogen invasion and exposure mechanisms. M. mungi DNA was identified in 29% of nasal planum samples (n = 52), 56% of nasal rinses and swabs (n = 9), 53% of oral swabs (n = 19), 22% of urine samples (n = 23), 33% of anal gland tissue (n = 18), and 39% of anal gland secretions (n = 44). The occurrence of extremely low cycle threshold values obtained with qPCR in anal gland and nasal planum samples indicates that high levels of M. mungi can be found in these tissue types. Histological data were consistent with these results, suggesting that pathogen invasion occurs through breaks in the nasal planum and/or skin of the mongoose host, which are in frequent contact with anal gland secretions and urine during olfactory communication behavior. Lesions in the lung, when present, occurred only with disseminated disease. No environmental sources of M. mungi DNA could be found. We report primary environmental transmission of an MTC pathogen that occurs in association with social communication behavior.

Organisms causing infectious disease evolve modes of transmission that exploit environmental and host conditions favoring pathogen spread and persistence. We report a novel mode of environmental infectious disease transmission that occurs in association with olfactory secretions (e.g., urine and anal gland secretions), allowing pathogen exposure to occur within and between social groups through intricate social communication behaviors of the banded mongoose host. The presence of M. mungi in these environmentally deposited secretions would effectively circumvent natural social barriers (e.g., territoriality), facilitating between-group pathogen transmission in the absence of direct physical contact, a rare occurrence in this highly territorial species. This work identifies an important potential mechanism of pathogen transmission of epidemiological significance in social species. We also provide evidence of a novel mechanism of pathogen transmission for the MTC complex, where pathogen movement in the environment and host exposure dynamics are driven by social behavior.

Environmentally transmitted parasites: Host-jumping in a heterogeneous environment

Groups of chronically infected reservoir-hosts contaminate resource patches by shedding a parasite׳s free-living stage. Novel-host groups visit the same patches, where they are exposed to infection. We treat arrival at patches, levels of parasite deposition, and infection of the novel host as stochastic processes, and derive the expected time elapsing until a host-jump (initial infection of a novel host) occurs. At stationarity, mean parasite densities are independent of reservoir-host group size. But within-patch parasite-density variances increase with reservoir group size. The probability of infecting a novel host declines with parasite-density variance; consequently larger reservoir groups extend the mean waiting time for host-jumping. Larger novel-host groups increase the probability of a host-jump during any single patch visit, but also reduce the total number of visits per unit time. Interaction of these effects implies that the waiting time for the first infection increases with the novel-host group size. If the reservoir-host uses resource patches in any non-uniform manner, reduced spatial overlap between host species increases the waiting time for host-jumping.

Environmental Variation Generates Environmental Opportunist Pathogen Outbreaks

Many socio-economically important pathogens persist and grow in the outside host environment and opportunistically invade host individuals. The environmental growth and opportunistic nature of these pathogens has received only little attention in epidemiology. Environmental reservoirs are, however, an important source of novel diseases. Thus, attempts to control these diseases require different approaches than in traditional epidemiology focusing on obligatory parasites. Conditions in the outside-host environment are prone to fluctuate over time. This variation is a potentially important driver of epidemiological dynamics and affect the evolution of novel diseases. Using a modelling approach combining the traditional SIRS models to environmental opportunist pathogens and environmental variability, we show that epidemiological dynamics of opportunist diseases are profoundly driven by the quality of environmental variability, such as the long-term predictability and magnitude of fluctuations. When comparing periodic and stochastic environmental factors, for a given variance, stochastic variation is more likely to cause outbreaks than periodic variation. This is due to the extreme values being further away from the mean. Moreover, the effects of variability depend on the underlying biology of the epidemiological system, and which part of the system is being affected. Variation in host susceptibility leads to more severe pathogen outbreaks than variation in pathogen growth rate in the environment. Positive correlation in variation on both targets can cancel the effect of variation altogether. Moreover, the severity of outbreaks is significantly reduced by increase in the duration of immunity. Uncovering these issues helps in understanding and controlling diseases caused by environmental pathogens.

A multigroup model for cholera dynamics and control

We propose a general multigroup model for cholera dynamics that involves both direct and indirect transmission pathways and that incorporates spatial heterogeneity. Under biologically feasible conditions, we show that the basic reproduction number R0 remains a sharp threshold for cholera dynamics in multigroup settings. We verify the analysis by numerical simulation results. We also perform an optimal control study to explore optimal vaccination strategy for cholera outbreaks.

Dynamics of history-dependent epidemics in temporal networks

The structural properties of temporal networks often influence the dynamical processes that occur on these networks, e.g., bursty interaction patterns have been shown to slow down epidemics. In this paper, we investigate the effect of link lifetimes on the spread of history-dependent epidemics. We formulate an analytically tractable activity-driven temporal network model that explicitly incorporates link lifetimes. For Markovian link lifetimes, we use mean-field analysis for computing the epidemic threshold, while the effect of non-Markovian link lifetimes is studied using simulations. Furthermore, we also study the effect of negative correlation between the number of links spawned by an individual and the lifetimes of those links. Such negative correlations may arise due to the finite cognitive capacity of the individuals. Our investigations reveal that heavy-tailed link lifetimes slow down the epidemic, while negative correlations can reduce epidemic prevalence. We believe that our results help shed light on the role of link lifetimes in modulating diffusion processes on temporal networks.

Analyzing transmission dynamics of cholera with public health interventions

Cholera continues to be a serious public health concern in developing countries and the global increase in the number of reported outbreaks suggests that activities to control the diseases and surveillance programs to identify or predict the occurrence of the next outbreaks are not adequate. These outbreaks have increased in frequency, severity, duration and endemicity in recent years. Mathematical models for infectious diseases play a critical role in predicting and understanding disease mechanisms, and have long provided basic insights in the possible ways to control infectious diseases. In this paper, we present a new deterministic cholera epidemiological model with three types of control measures incorporated into a cholera epidemic setting: treatment, vaccination and sanitation. Essential dynamical properties of the model with constant intervention controls which include local and global stabilities for the equilibria are carefully analyzed. Further, using optimal control techniques, we perform a study to investigate cost-effective solutions for time-dependent public health interventions in order to curb disease transmission in epidemic settings. Our results show that the basic reproductive number (R0) remains the model's epidemic threshold despite the inclusion of a package of cholera interventions. For time-dependent controls, the results suggest that these interventions closely interplay with each other, and the costs of controls directly affect the length and strength of each control in an optimal strategy.

Analysis of cholera epidemics with bacterial growth and spatial movement

In this work, we propose novel epidemic models (named, susceptible-infected-recovered-susceptible-bacteria) for cholera dynamics by incorporating a general formulation of bacteria growth and spatial variation. In the first part, a generalized ordinary differential equation (ODE) model is presented and it is found that bacterial growth contributes to the increase in the basic reproduction number, [Formula: see text]. With the derived basic reproduction number, we analyse the local and global dynamics of the model. Particularly, we give a rigorous proof on the endemic global stability by employing the geometric approach. In the second part, we extend the ODE model to a partial differential equation (PDE) model with the inclusion of diffusion to capture the movement of human hosts and bacteria in a heterogeneous environment. The disease threshold of this PDE model is studied again by using the basic reproduction number. The results on the threshold dynamics of the ODE and PDE models are compared, and verified through numerical simulation. Additionally, our analysis shows that incorporating diffusive spatial spread does not produce a Turing instability when [Formula: see text] associated with the ODE model is less than the unity.

An experimental model to analyse the risk of introduction of a duck-originated H5 low-pathogenic avian influenza virus in poultry through close contact and contaminative transmission

Aquatic wild birds are often carriers of low-pathogenic avian influenza viruses (LPAIVs). If H5 and H7 LPAIVs are transmitted to poultry and have the opportunity to circulate, a highly pathogenic AIV may arise. Contact with aquatic wild birds is one of the most important ways in which these LPAIVs can be introduced into poultry flocks. In this study, the transmissibility of a duck-originated H5 LPAIV between ducks and chickens was analysed in a series of animal experiments, using different transmission routes. Results indicate that the outcome of virus intake by chickens exposed to infectious ducks depends on the way the virus is presented. Faecally contaminated drinking water proved to be the most efficient route by which the virus can be transmitted to chickens. The results from this study also suggest that some duck-originated H5 LPAIVs may be introduced to poultry but do not have the potential to become established in poultry populations.

Loss of competition in the outside host environment generates outbreaks of environmental opportunist pathogens

Environmentally transmitted pathogens face ecological interactions (e.g., competition, predation, parasitism) in the outside-host environment and host immune system during infection. Despite the ubiquitousness of environmental opportunist pathogens, traditional epidemiology focuses on obligatory pathogens incapable of environmental growth. Here we ask how competitive interactions in the outside-host environment affect the dynamics of an opportunist pathogen. We present a model coupling the classical SI and Lotka–Volterra competition models. In this model we compare a linear infectivity response and a sigmoidal infectivity response. An important assumption is that pathogen virulence is traded off with competitive ability in the environment. Removing this trade-off easily results in host extinction. The sigmoidal response is associated with catastrophic appearances of disease outbreaks when outside-host species richness, or overall competition pressure, decreases. This indicates that alleviating outside-host competition with antibacterial substances that also target the competitors can have unexpected outcomes by providing benefits for opportunist pathogens. These findings may help in developing alternative ways of controlling environmental opportunist pathogens.

Bursty communication patterns facilitate spreading in a threshold-based epidemic dynamics

Records of social interactions provide us with new sources of data for understanding how interaction patterns affect collective dynamics. Such human activity patterns are often bursty, i.e., they consist of short periods of intense activity followed by long periods of silence. This burstiness has been shown to affect spreading phenomena; it accelerates epidemic spreading in some cases and slows it down in other cases. We investigate a model of history-dependent contagion. In our model, repeated interactions between susceptible and infected individuals in a short period of time is needed for a susceptible individual to contract infection. We carry out numerical simulations on real temporal network data to find that bursty activity patterns facilitate epidemic spreading in our model.

Taming wildlife disease: bridging the gap between science and management

Parasites and pathogens of wildlife can threaten biodiversity, infect humans and domestic animals, and cause significant economic losses, providing incentives to manage wildlife diseases. Recent insights from disease ecology have helped transform our understanding of infectious disease dynamics and yielded new strategies to better manage wildlife diseases. Simultaneously, wildlife disease management (WDM) presents opportunities for large‐scale empirical tests of disease ecology theory in diverse natural systems.

To assess whether the potential complementarity between WDM and disease ecology theory has been realized, we evaluate the extent to which specific concepts in disease ecology theory have been explicitly applied in peer‐reviewed WDM literature.

While only half of WDM articles published in the past decade incorporated disease ecology theory, theory has been incorporated with increasing frequency over the past 40 years. Contrary to expectations, articles authored by academics were no more likely to apply disease ecology theory, but articles that explain unsuccessful management often do so in terms of theory.

Some theoretical concepts such as density‐dependent transmission have been commonly applied, whereas emerging concepts such as pathogen evolutionary responses to management, biodiversity–disease relationships and within‐host parasite interactions have not yet been fully integrated as management considerations.

Synthesis and applications. Theory‐based disease management can meet the needs of both academics and managers by testing disease ecology theory and improving disease interventions. Theoretical concepts that have received limited attention to date in wildlife disease management could provide a basis for improving management and advancing disease ecology in the future.

Theory‐based disease management can meet the needs of both academics and managers by testing disease ecology theory and improving disease interventions. Theoretical concepts that have received limited attention to date in wildlife disease management could provide a basis for improving management and advancing disease ecology in the future.

A multi-scale analysis of influenza A virus fitness trade-offs due to temperature-dependent virus persistence

Successful replication within an infected host and successful transmission between hosts are key to the continued spread of most pathogens. Competing selection pressures exerted at these different scales can lead to evolutionary trade-offs between the determinants of fitness within and between hosts. Here, we examine such a trade-off in the context of influenza A viruses and the differential pressures exerted by temperature-dependent virus persistence. For a panel of avian influenza A virus strains, we find evidence for a trade-off between the persistence at high versus low temperatures. Combining a within-host model of influenza infection dynamics with a between-host transmission model, we study how such a trade-off affects virus fitness on the host population level. We show that conclusions regarding overall fitness are affected by the type of link assumed between the within- and between-host levels and the main route of transmission (direct or environmental). The relative importance of virulence and immune response mediated virus clearance are also found to influence the fitness impacts of virus persistence at low versus high temperatures. Based on our results, we predict that if transmission occurs mainly directly and scales linearly with virus load, and virulence or immune responses are negligible, the evolutionary pressure for influenza viruses to evolve toward good persistence at high within-host temperatures dominates. For all other scenarios, influenza viruses with good environmental persistence at low temperatures seem to be favored.

It has recently been suggested that for avian influenza viruses, prolonged persistence in the environment plays an important role in the transmission between birds. In such situations, influenza virus strains may face a trade-off: they need to persist well in the environment at low temperatures, but they also need to do well inside an infected bird at higher temperatures. Here, we analyze how potential trade-offs on these two scales interact to determine overall fitness of the virus. We find that the link between infection dynamics within a host and virus shedding and transmission is crucial in determining the relative advantage of good low-temperature versus high-temperature persistence. We also find that the role of virus-induced mortality, the immune response and the route of transmission affect the balance between optimal low-temperature and high-temperature persistence.

Indirect transmission and the effect of seasonal pathogen inactivation on infectious disease periodicity

The annual occurrence of many infectious diseases remains a constant burden to public health systems. The seasonal patterns in respiratory disease incidence observed in temperate regions have been attributed to the impact of environmental conditions on pathogen survival. A model describing the transmission of an infectious disease by means of a pathogenic state capable of surviving in an environmental reservoir outside of its host organism is presented in this paper. The ratio of pathogen lifespan to the duration of the infectious disease state is found to be a critical parameter in determining disease dynamics. The introduction of a seasonally forced pathogen inactivation rate identifies a time delay between peak pathogen survival and peak disease incidence. The delay is dependent on specific disease parameters and, for influenza, decreases with increasing reproduction number. The observed seasonal oscillations are found to have a period identical to that of the seasonally forced inactivation rate and which is independent of the duration of infection acquired immunity.