Impact of infectious diseases on wild bovidae populations in Thailand: insights from population modelling and disease dynamics.

The wildlife and livestock interface is vital for wildlife conservation and habitat management. Infectious diseases maintained by domestic species may impact threatened species such as Asian bovids, as they share natural resources and habitats. To predict the population impact of infectious diseases with different traits, we used stochastic mathematical models to simulate the population dynamics over 100 years for 100 times in a model gaur (Bos gaurus) population with and without disease. We simulated repeated introductions from a reservoir, such as domestic cattle. We selected six bovine infectious diseases; anthrax, bovine tuberculosis, haemorrhagic septicaemia, lumpy skin disease, foot and mouth disease and brucellosis, all of which have caused outbreaks in wildlife populations. From a starting population of 300, the disease-free population increased by an average of 228% over 100 years. Brucellosis with frequency-dependent transmission showed the highest average population declines (-97%), with population extinction occurring 16% of the time. Foot and mouth disease with frequency-dependent transmission showed the lowest impact, with an average population increase of 200%. Overall, acute infections with very high or low fatality had the lowest impact, whereas chronic infections produced the greatest population decline. These results may help disease management and surveillance strategies support wildlife conservation.

Phylogenetic inference of inter-population transmission rates for infectious diseases.

Estimating transmission rates is a challenging yet essential aspect of comprehending and controlling the spread of infectious diseases. Various methods exist for estimating transmission rates, each with distinct assumptions, data needs, and constraints. This study introduces a novel phylogenetic approach called transRate, which integrates genetic information with traditional epidemiological approaches to estimate inter-population transmission rates. The phylogenetic method is statistically consistent as the sample size (i.e. the number of pathogen genomes) approaches infinity under the multi-population susceptible-infected-recovered model. Simulation analyses indicate that transRate can accurately estimate the transmission rate with a sample size of 200 ~ 400 pathogen genomes. Using transRate, we analyzed 40,028 high-quality sequences of SARS-CoV-2 in human hosts during the early pandemic. Our analysis uncovered significant transmission between populations even before widespread travel restrictions were implemented. The development of transRate provides valuable insights for scientists and public health officials to enhance their understanding of the pandemic's progression and aiding in preparedness for future viral outbreaks. As public databases for genomic sequences continue to expand, transRate is increasingly vital for tracking and mitigating the spread of infectious diseases.

Approximating reproduction numbers: a general numerical method for age-structured models.

In this paper, we introduce a general numerical method to approximate the reproduction numbers of a large class of multi-group, age-structured, population models with a finite age span. To provide complete flexibility in the definition of the birth and transition processes, we propose an equivalent formulation for the age-integrated state within the extended space framework. Then, we discretize the birth and transition operators via pseudospectral collocation. We discuss applications to epidemic models with continuous and piecewise continuous rates, with different interpretations of the age variable (e.g., demographic age, infection age and disease age) and the transmission terms (e.g., horizontal and vertical transmission). The tests illustrate that the method can compute different reproduction numbers, including the basic and type reproduction numbers as special cases.

Threshold dynamics of a switching diffusion SIR model with logistic growth and healthcare resources.

In this article, we have constructed a stochastic SIR model with healthcare resources and logistic growth, aiming to explore the effect of random environment and healthcare resources on disease transmission dynamics. We have showed that under mild extra conditions, there exists a critical parameter, i.e., the basic reproduction number $ R_0/ $, which completely determines the dynamics of disease: when $ R_0/ < 1 $, the disease is eradicated; while when $ R_0/ > 1 $, the disease is persistent. To validate our theoretical findings, we conducted some numerical simulations using actual parameter values of COVID-19. Both our theoretical and simulation results indicated that (1) the white noise can significantly affect the dynamics of a disease, and importantly, it can shift the stability of the disease-free equilibrium; (2) infectious disease resurgence may be caused by random switching of the environment; and (3) it is vital to maintain adequate healthcare resources to control the spread of disease.

Modeling the transmission mitigation impact of testing for infectious diseases.

A fundamental question of any program focused on the testing and timely diagnosis of a communicable disease is its effectiveness in reducing transmission. Here, we introduce testing effectiveness (TE)-the fraction by which testing and post-diagnosis isolation reduce transmission at the population scale-and a model that incorporates test specifications and usage, within-host pathogen dynamics, and human behaviors to estimate TE. Using TE to guide recommendations, we show that today's rapid diagnostics should be used immediately upon symptom onset to control influenza A and respiratory syncytial virus but delayed by up to two days to control omicron-era severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Furthermore, while rapid tests are superior to reverse transcription quantitative polymerase chain reaction (RT-qPCR) to control founder-strain SARS-CoV-2, omicron-era changes in viral kinetics and rapid test sensitivity cause a reversal, with higher TE for RT-qPCR despite longer turnaround times. Last, we illustrate the model's flexibility by quantifying trade-offs in the use of post-diagnosis testing to shorten isolation times.

Infection patterns in simple and complex contagion processes on networks.

Contagion processes, representing the spread of infectious diseases, information, or social behaviors, are often schematized as taking place on networks, which encode for instance the interactions between individuals. The impact of the network structure on spreading process has been widely investigated, but not the reverse question: do different processes unfolding on a given network lead to different infection patterns? How do the infection patterns depend on a model's parameters or on the nature of the contagion processes? Here we address this issue by investigating the infection patterns for a variety of models. In simple contagion processes, where contagion events involve one connection at a time, we find that the infection patterns are extremely robust across models and parameters. In complex contagion models instead, in which multiple interactions are needed for a contagion event, non-trivial dependencies on models parameters emerge, as the infection pattern depends on the interplay between pairwise and group contagions. In models involving threshold mechanisms moreover, slight parameter changes can significantly impact the spreading paths. Our results show that it is possible to study crucial features of a spread from schematized models, and inform us on the variations between spreading patterns in processes of different nature.

Comprehensive profiling of social mixing patterns in resource poor countries: A mixed methods research protocol.

BACKGROUND: Low-and-middle-income countries (LMICs) bear a disproportionate burden of communicable diseases. Social interaction data inform infectious disease models and disease prevention strategies. The variations in demographics and contact patterns across ages, cultures, and locations significantly impact infectious disease dynamics and pathogen transmission. LMICs lack sufficient social interaction data for infectious disease modeling. METHODS: To address this gap, we will collect qualitative and quantitative data from eight study sites (encompassing both rural and urban settings) across Guatemala, India, Pakistan, and Mozambique. We will conduct focus group discussions and cognitive interviews to assess the feasibility and acceptability of our data collection tools at each site. Thematic and rapid analyses will help to identify key themes and categories through coding, guiding the design of quantitative data collection tools (enrollment survey, contact diaries, exit survey, and wearable proximity sensors) and the implementation of study procedures. We will create three age-specific contact matrices (physical, nonphysical, and both) at each study site using data from standardized contact diaries to characterize the patterns of social mixing. Regression analysis will be conducted to identify key drivers of contacts. We will comprehensively profile the frequency, duration, and intensity of infants' interactions with household members using high resolution data from the proximity sensors and calculating infants' proximity score (fraction of time spent by each household member in proximity with the infant, over the total infant contact time) for each household member. DISCUSSION: Our qualitative data yielded insights into the perceptions and acceptability of contact diaries and wearable proximity sensors for collecting social mixing data in LMICs. The quantitative data will allow a more accurate representation of human interactions that lead to the transmission of pathogens through close contact in LMICs. Our findings will provide more appropriate social mixing data for parameterizing mathematical models of LMIC populations. Our study tools could be adapted for other studies.

Optimal control of a fractional order SEIQR epidemic model with non-monotonic incidence and quarantine class.

During any infectious disease outbreak, effective and timely quarantine of infected individuals, along with preventive measures by the population, is vital for controlling the spread of infection in society. Therefore, this study attempts to provide a mathematically validated approach for managing the epidemic spread by incorporating the Monod-Haldane incidence rate, which accounts for psychological effects, and a saturated quarantine rate as Holling functional type III that considers the limitation in quarantining of infected individuals into the standard Susceptible-Exposed-Infected-Quarantine-Recovered (SEIQR) model. The rate of change of each subpopulation is considered as the Caputo form of fractional derivative where the order of derivative represents the memory effects in epidemic transmission dynamics and can enhance the accuracy of disease prediction by considering the experience of individuals with previously encountered. The mathematical study of the model reveals that the solutions are well-posed, ensuring nonnegativity and boundedness within an attractive region. Further, the study identifies two equilibria, namely, disease-free (DFE) and endemic (EE); and stability analysis of equilibria is performed for local as well as global behaviours for the same. The stability behaviours of equilibria mainly depend on the basic reproduction number R0 and its alternative threshold T0 which is computed using the Next-generation matrix method. It is investigated that DFE is locally and globally asymptotic stable when R0<1. Furthermore, we show the existence of EE and investigate that it is locally and globally asymptotic stable using the Routh-Hurwitz criterion and the Lyapunov stability theorem for fractional order systems with R0>1 under certain conditions. This study also addresses a fractional optimal control problem (FOCP) using Pontryagin's maximum principle aiming to minimize the spread of infection with minimal expenditure. This approach involves introducing a time-dependent control measure, u(t), representing the behavioural response of susceptible individuals. Finally, numerical simulations are presented to support the analytical findings using the Adams Bashforth Moulton scheme in MATLAB, providing a comprehensive understanding of the proposed SEIQR model.

An SEIR network epidemic model with manual and digital contact tracing allowing delays.

We consider an SEIR epidemic model on a network also allowing random contacts, where recovered individuals could either recover naturally or be diagnosed. Upon diagnosis, manual contact tracing is triggered such that each infected network contact is reported, tested and isolated with some probability and after a random delay. Additionally, digital tracing (based on a tracing app) is triggered if the diagnosed individual is an app-user, and then all of its app-using infectees are immediately notified and isolated. The early phase of the epidemic with manual and/or digital tracing is approximated by different multi-type branching processes, and three respective reproduction numbers are derived. The effectiveness of both contact tracing mechanisms is numerically quantified through the reduction of the reproduction number. This shows that app-using fraction plays an essential role in the overall effectiveness of contact tracing. The relative effectiveness of manual tracing compared to digital tracing increases if: more of the transmission occurs on the network, when the tracing delay is shortened, and when the network degree distribution is heavy-tailed. For realistic values, the combined tracing case can reduce R0 by 20%-30%, so other preventive measures are needed to reduce the reproduction number down to 1.2-1.4 for contact tracing to make it successful in avoiding big outbreaks.

Dynamics of simplicial SEIRS epidemic model: global asymptotic stability and neural Lyapunov functions.

The transmission of infectious diseases on a particular network is ubiquitous in the physical world. Here, we investigate the transmission mechanism of infectious diseases with an incubation period using a networked compartment model that contains simplicial interactions, a typical high-order structure. We establish a simplicial SEIRS model and find that the proportion of infected individuals in equilibrium increases due to the many-body connections, regardless of the type of connections used. We analyze the dynamics of the established model, including existence and local asymptotic stability, and highlight differences from existing models. Significantly, we demonstrate global asymptotic stability using the neural Lyapunov function, a machine learning technique, with both numerical simulations and rigorous analytical arguments. We believe that our model owns the potential to provide valuable insights into transmission mechanisms of infectious diseases on high-order network structures, and that our approach and theory of using neural Lyapunov functions to validate model asymptotic stability can significantly advance investigations on complex dynamics of infectious disease.

Spatial Interaction Analysis of Infectious Disease Import and Export between Regions.

Human travel plays a crucial role in the spread of infectious disease between regions. Travel of infected individuals from one region to another can transport a virus to places that were previously unaffected or may accelerate the spread of disease in places where the disease is not yet well established. We develop and apply models and metrics to analyze the role of inter-regional travel relative to the spread of disease, drawing from data on COVID-19 in the United States. To better understand how transportation affects disease transmission, we established a multi-regional time-varying compartmental disease model with spatial interaction. The compartmental model was integrated with statistical estimates of travel between regions. From the integrated model, we derived a transmission import index to assess the risk of COVID-19 transmission between states. Based on the index, we determined states with high risk for disease spreading to other states at the scale of months, and we analyzed how the index changed over time during 2020. Our model provides a tool for policymakers to evaluate the influence of travel between regions on disease transmission in support of strategies for epidemic control.

Modelling the impact of precaution on disease dynamics and its evolution.

In this paper, we introduce the notion of practically susceptible population, which is a fraction of the biologically susceptible population. Assuming that the fraction depends on the severity of the epidemic and the public's level of precaution (as a response of the public to the epidemic), we propose a general framework model with the response level evolving with the epidemic. We firstly verify the well-posedness and confirm the disease's eventual vanishing for the framework model under the assumption that the basic reproduction number R 0 < 1 . For R 0 > 1 , we study how the behavioural response evolves with epidemics and how such an evolution impacts the disease dynamics. More specifically, when the precaution level is taken to be the instantaneous best response function in literature, we show that the endemic dynamic is convergence to the endemic equilibrium; while when the precaution level is the delayed best response, the endemic dynamic can be either convergence to the endemic equilibrium, or convergence to a positive periodic solution. Our derivation offers a justification/explanation for the best response used in some literature. By replacing "adopting the best response" with "adapting toward the best response", we also explore the adaptive long-term dynamics.

Geography and health: role of human translocation and access to care.

Natural, geographical barriers have historically limited the spread of communicable diseases. This is no longer the case in today's interconnected world, paired with its unprecedented environmental and climate change, emphasising the intersection of evolutionary biology, epidemiology and geography (i.e. biogeography). A total of 14 articles of the special issue entitled "Geography and health: role of human translocation and access to care" document enhanced disease transmission of diseases, such as malaria, leishmaniasis, schistosomiasis, COVID-19 (Severe acute respiratory syndrome corona 2) and Oropouche fever in spite of spatiotemporal surveillance. High-resolution satellite images can be used to understand spatial distributions of transmission risks and disease spread and to highlight the major avenue increasing the incidence and geographic range of zoonoses represented by spill-over transmission of coronaviruses from bats to pigs or civets. Climate change and globalization have increased the spread and establishment of invasive mosquitoes in non-tropical areas leading to emerging outbreaks of infections warranting improved physical, chemical and biological vector control strategies. The translocation of pathogens and their vectors is closely connected with human mobility, migration and the global transport of goods. Other contributing factors are deforestation with urbanization encroaching into wildlife zones. The destruction of natural ecosystems, coupled with low income and socioeconomic status, increase transmission probability of neglected tropical and zoonotic diseases. The articles in this special issue document emerging or re-emerging diseases and surveillance of fever symptoms. Health equity is intricately connected to accessibility to health care and the targeting of healthcare resources, necessitating a spatial approach. Public health comprises successful disease management integrating spatial surveillance systems, including access to sanitation facilities. Antimicrobial resistance caused, e.g. by increased use of antibiotics in health, agriculture and aquaculture, or acquisition of resistance genes, can be spread by horizontal gene transfer. This editorial reviews the key findings of this 14-article special issue, identifies important gaps relevant to our interconnected world and makes a number of specific recommendations to mitigate the transmission risks of infectious diseases in the post-COVID-19 pandemic era.

A risk-induced dispersal strategy of the infected population for a disease-free state in the SIS epidemic model.

This article proposes a dispersal strategy for infected individuals in a spatial susceptible-infected-susceptible (SIS) epidemic model. The presence of spatial heterogeneity and the movement of individuals play crucial roles in determining the persistence and eradication of infectious diseases. To capture these dynamics, we introduce a moving strategy called risk-induced dispersal (RID) for infected individuals in a continuous-time patch model of the SIS epidemic. First, we establish a continuous-time n-patch model and verify that the RID strategy is an effective approach for attaining a disease-free state. This is substantiated through simulations conducted on 7-patch models and analytical results derived from 2-patch models. Second, we extend our analysis by adapting the patch model into a diffusive epidemic model. This extension allows us to explore further the impact of the RID movement strategy on disease transmission and control. We validate our results through simulations, which provide the effects of the RID dispersal strategy.

Contagion dynamics in time-varying metapopulation networks with node's activity and attractiveness.

The metapopulation network model is a mathematical framework used to study the spatial spread of epidemics with individuals' mobility. In this paper, we develop a time-varying network model in which the activity of a population is correlated with its attractiveness in mobility. By studying the spreading dynamics of the SIR (susceptible-infectious-recovered)-type disease in different correlated networks based on the proposed model, we theoretically derive the mobility threshold and numerically observe that increasing the correction between activity and attractiveness results in a reduced mobility threshold but suppresses the fraction of infected subpopulations. It also introduces greater heterogeneity in the spatial distribution of infected individuals. Additionally, we investigate the impact of nonpharmaceutical interventions on the spread of epidemics in different correlation networks. Our results show that the simultaneous implementation of self-isolation and self-protection is more effective in negatively correlated networks than that in positively correlated or non-correlated networks. Both self-isolation and self-protection strategies enhance the mobility threshold and, thus, slow down the spread of the epidemic. However, the effectiveness of each strategy in reducing the fraction of infected subpopulations varies in different correlated networks. Self-protection is more effective in positively correlated networks, whereas self-isolation is more effective in negatively correlated networks. Our study will provide insights into epidemic prevention and control in large-scale time-varying metapopulation networks.

Social contacts patterns relevant to the transmission of infectious diseases in Suzhou, China following the COVID-19 epidemic.

BACKGROUND: The COVID-19 pandemic has profoundly affected human social contact patterns, but there is limited understanding regarding the post-pandemic social contact patterns. Our objective is to quantitatively assess social contact patterns in Suzhou post-COVID-19. METHODS: We employed a diary design and conducted social contact surveys from June to October 2023, utilizing paper questionnaires. A generalized linear model was utilized to analyze the relationship between individual contacts and covariates. We examined the proportions of contact type, location, duration, and frequency. Additionally, age-related mixed matrices were established. RESULTS: The participants reported an average of 11.51 (SD 5.96) contact numbers and a total of 19.78 (SD 20.94) contact numbers per day, respectively. The number of contacts was significantly associated with age, household size, and the type of week. Compared to the 0-9 age group, those in the 10-19 age group reported a higher number of contacts (IRR = 1.12, CI: 1.01-1.24), while participants aged 20 and older reported fewer (IRR range: 0.54-0.67). Larger households (5 or more) reported more contacts (IRR = 1.09, CI: 1.01-1.18) and fewer contacts were reported on weekends (IRR = 0.95, CI: 0.90-0.99). School had the highest proportion of contact durations exceeding 4 h (49.5%) and daily frequencies (90.4%), followed by home and workplace. The contact patterns exhibited clear age-assortative mixing, with Q indices of 0.27 and 0.28. CONCLUSIONS: We assessed the characteristics of social contact patterns in Suzhou, which are essential for parameterizing models of infectious disease transmission. The high frequency and intensity of contacts among school-aged children should be given special attention, making school intervention policies a crucial component in controlling infectious disease transmission.

Temporal variations in international air travel: implications for modelling the spread of infectious diseases.

BACKGROUND: The international flight network creates multiple routes by which pathogens can quickly spread across the globe. In the early stages of infectious disease outbreaks, analyses using flight passenger data to identify countries at risk of importing the pathogen are common and can help inform disease control efforts. A challenge faced in this modelling is that the latest aviation statistics (referred to as contemporary data) are typically not immediately available. Therefore, flight patterns from a previous year are often used (referred to as historical data). We explored the suitability of historical data for predicting the spatial spread of emerging epidemics. METHODS: We analysed monthly flight passenger data from the International Air Transport Association to assess how baseline air travel patterns were affected by outbreaks of Middle East respiratory syndrome (MERS), Zika and severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) over the past decade. We then used a stochastic discrete time susceptible-exposed-infected-recovered (SEIR) metapopulation model to simulate the global spread of different pathogens, comparing how epidemic dynamics differed in simulations based on historical and contemporary data. RESULTS: We observed local, short-term disruptions to air travel from South Korea and Brazil for the MERS and Zika outbreaks we studied, whereas global and longer-term flight disruptions occurred during the SARS-CoV-2 pandemic. For outbreak events that were accompanied by local, small and short-term changes in air travel, epidemic models using historical flight data gave similar projections of the timing and locations of disease spread as when using contemporary flight data. However, historical data were less reliable to model the spread of an atypical outbreak such as SARS-CoV-2, in which there were durable and extensive levels of global travel disruption. CONCLUSION: The use of historical flight data as a proxy in epidemic models is an acceptable practice, except in rare, large epidemics that lead to substantial disruptions to international travel.

An immuno-epidemiological model with waning immunity after infection or vaccination.

In epidemics, waning immunity is common after infection or vaccination of individuals. Immunity levels are highly heterogeneous and dynamic. This work presents an immuno-epidemiological model that captures the fundamental dynamic features of immunity acquisition and wane after infection or vaccination and analyzes mathematically its dynamical properties. The model consists of a system of first order partial differential equations, involving nonlinear integral terms and different transfer velocities. Structurally, the equation may be interpreted as a Fokker-Planck equation for a piecewise deterministic process. However, unlike the usual models, our equation involves nonlocal effects, representing the infectivity of the whole environment. This, together with the presence of different transfer velocities, makes the proved existence of a solution novel and nontrivial. In addition, the asymptotic behavior of the model is analyzed based on the obtained qualitative properties of the solution. An optimal control problem with objective function including the total number of deaths and costs of vaccination is explored. Numerical results describe the dynamic relationship between contact rates and optimal solutions. The approach can contribute to the understanding of the dynamics of immune responses at population level and may guide public health policies.

Towards development of functional climate-driven early warning systems for climate-sensitive infectious diseases: Statistical models and recommendations.

Climate, weather and environmental change have significantly influenced patterns of infectious disease transmission, necessitating the development of early warning systems to anticipate potential impacts and respond in a timely and effective way. Statistical modelling plays a pivotal role in understanding the intricate relationships between climatic factors and infectious disease transmission. For example, time series regression modelling and spatial cluster analysis have been employed to identify risk factors and predict spatial and temporal patterns of infectious diseases. Recently advanced spatio-temporal models and machine learning offer an increasingly robust framework for modelling uncertainty, which is essential in climate-driven disease surveillance due to the dynamic and multifaceted nature of the data. Moreover, Artificial Intelligence (AI) techniques, including deep learning and neural networks, excel in capturing intricate patterns and hidden relationships within climate and environmental data sets. Web-based data has emerged as a powerful complement to other datasets encompassing climate variables and disease occurrences. However, given the complexity and non-linearity of climate-disease interactions, advanced techniques are required to integrate and analyse these diverse data to obtain more accurate predictions of impending outbreaks, epidemics or pandemics. This article presents an overview of an approach to creating climate-driven early warning systems with a focus on statistical model suitability and selection, along with recommendations for utilizing spatio-temporal and machine learning techniques. By addressing the limitations and embracing the recommendations for future research, we could enhance preparedness and response strategies, ultimately contributing to the safeguarding of public health in the face of evolving climate challenges.