Individual-Based Models for Public Health

To give an overview of the recent history of publications on mathematical modelling of infectious diseases in the Chinese literature, and a more detailed review of the models on severe acute respiratory syndrome (SARS). Literature review through the Chinese CAJ full-text database. The number of Chinese publications on mathematical modelling has at least quadrupled since the SARS epidemic in 2003. This increase not only included papers on SARS, but also on various other infectious diseases, indicating a substantial expansion of modelling experience in China. Typical problems of most studies were poor availability of data and lack of involvement of disease experts and decision-makers rendering the studies less useful for policies on control. We expect that the recent experience on modelling and current better access to and exchange of epidemiological data have paved the way for a more substantial role of this discipline during possible future outbreaks of infectious diseases. By making Chinese modelling initiatives more visible to non-Chinese readers, we hope to attract more international collaborators.

Bats (order Chiroptera) are known as natural reservoir hosts of many emerging zoonotic diseases. The increasing trend in outbreaks of bat-borne emerging zoonotic diseases in recent years poses serious risks to public health. Coronaviruses in bat populations have demonstrated their potential to bring about deadly pandemics, such as SARS (severe acute respiratory syndrome) and MERS (Middle East respiratory syndrome). Hendra virus in Pteropus spp. (fruit bats or flying foxes) is a lethal zoonotic virus that has repeatedly emerged to infect horses, leading to fatal human infections in eastern Australia. However, more research has been needed on mechanisms how bats maintain zoonotic pathogens in their populations and on factors that stimulate the reservoir hosts to excrete the pathogens. This knowledge would help understand the spillover mechanism and manage the diseases effectively in their natural reservoir hosts before the diseases spillover. This thesis explores the transmission dynamics of bat-borne viruses (coronavirus and Hendra virus) in their natural reservoir hosts of bats, by employing mathematical epidemic models to simulate the dynamics. Chapter 1 commences with the story of the emergence of Hendra virus. From the story, particular questions are extracted. I review the knowledge previously available to answer those questions and explain how approaches for mathematical modelling of infectious diseases can be used to study these topics. Relevant information on bat biology and ecology is suggested. Management strategies for bat zoonotic diseases are also previewed. Finally, the aims and structure of the thesis are outlined. Chapter 2 analyses the effect of persistent infection on coronavirus maintenance in a population of Australian bats (Myotis macropus). By using a previously performed capture-mark-recapture (CMR) study, more intensive mathematical methods were employed. The multi-model selection processes supported the notion that it is appropriate to divide coronavirus infectious bats into two groups of persistently infectious and transiently infectious bats, based on the infectious period. The epidemic models predicted that the grouping of bats increases the probability of coronavirus maintenance in the bat population. Chapter 3 explores the effects of maternally-derived immunity in seasonally breeding wildlife on epidemic patterns by using a system of Hendra virus infection in black flying foxes (Pteropus alecto). Deterministic models were used to simulate epidemics, which were characterised by a variety of timings of viral introduction and a range of pre-existing herd immunities. Waning maternally-derived immunity dispersed the timing of supply of susceptible individuals from births and losses of maternally-derived immunity and thereby diluted the effect of seasonal breeding on epidemics. The dispersion of timing increased the probability of viral persistence and contributed to shifting the timing of epidemic peaks further away from the peak of a birth pulse. Chapter 4 numerically examines whether a metapopulation of flying foxes (Pteropus spp.) can support the maintenance of Hendra virus. The implications of metapopulation structure of flying foxes on Hendra virus dynamics needs more investigations. A single population of flying foxes in the context of a metapopulation structure was stochastically simulated to repeat the cycle of viral extinction and recolonisation in the population. The simulation results predicted that viral recolonisation should occur more frequently than extinction in a colony in a metapopulation, supporting the hypothesis that the metapopulation structure of flying foxes can maintain long-term persistence of Hendra virus. Chapter 5 examines the effects of culling and dispersal of flying foxes on the spillover risk of Hendra virus. Metapopulation models were simulated stochastically using various culling and dispersal scenarios. The models used the most favourable possible assumptions about Hendra virus epidemiology for the application of these management strategies. Nevertheless, many scenarios were predicted to be counter-productive in reducing the spillover risk of Hendra virus. Even though the scenarios expected positive effects on decreasing the spillover risk, the degree of benefits was not realistic if the cost was considered. I, therefore, concluded that culling or dispersal were not effective strategies to manage Hendra virus spillover. Chapter 6 describes the findings provided in each chapter. Then, I discuss the findings, focusing on the viral dynamics in reservoir populations of emerging infectious diseases. Based on the dynamics, I suggest the disease management strategies. I discuss how to do proper modelling research using insufficient data on wildlife diseases. Finally, this chapter provides suggestions for further research.

Modeling individual and population dynamics in a consumer–resource system: Behavior under food limitation and crowding and the effect on population cycling in Daphnia

Individual-based model of population dynamics in a sea urchin of the Kerguelen Plateau (Southern Ocean), Abatus cordatus, under changing environmental conditions

Susceptible-infectious-recovered models revisited: From the individual level to the population level

Pandemic influenza has the epidemic potential to kill millions of people. While various preventive measures exist (i.a., vaccination and school closures), deciding on strategies that lead to their most effective and efficient use remains challenging. To this end, individual-based epidemiological models are essential to assist decision makers in determining the best strategy to curb epidemic spread. However, individual-based models are computationally intensive and it is therefore pivotal to identify the optimal strategy using a minimal amount of model evaluations. Additionally, as epidemiological modeling experiments need to be planned, a computational budget needs to be specified a priori. Consequently, we present a new sampling technique to optimize the evaluation of preventive strategies using fixed budget best-arm identification algorithms. We use epidemiological modeling theory to derive knowledge about the reward distribution which we exploit using Bayesian best-arm identification algorithms (i.e., Top-two Thompson sampling and BayesGap). We evaluate these algorithms in a realistic experimental setting and demonstrate that it is possible to identify the optimal strategy using only a limited number of model evaluations, i.e., 2-to-3 times faster compared to the uniform sampling method, the predominant technique used for epidemiological decision making in the literature. Finally, we contribute and evaluate a statistic for Top-two Thompson sampling to inform the decision makers about the confidence of an arm recommendation. Code related to this paper is available at: https://plibin-vub.github.io/epidemic-bandits.

Historical records of childhood disease incidence reveal complex dynamics. For measles, a simple model has indicated that epidemic patterns represent attractors of a nonlinear dynamic system and that transitions between different attractors are driven by slow changes in birth rates and vaccination levels. The same analysis can explain the main features of chickenpox dynamics, but fails for rubella and whooping cough. We show that an additional (perturbative) analysis of the model, together with knowledge of the population size in question, can account for all the observed incidence patterns by predicting how stochastically sustained transient dynamics should be manifested in these systems.

Nowadays, the interest in analyze and study the behavior of uncontrollable nature phenomena related to the impact of marketing campaigns is an action of prime importance to prevent chaotic dynamics. In this paper we assess the influence of Dynamical Systems theory and Mathematical Epidemiology on a real viral marketing campaign: Dove Real Beauty Sketches, based on a SIR epidemiological model. Motivated by the overwhelming success of this campaign, we study the mathematical properties and dynamics of the campaign real data - from the parameters estimation and its sensitivity to the stability of the mathematical model, simulated in Matlab. Mathematically, we show not only that the campaign was a viral epidemic, but also that it can be leveraged and optimized by epidemiological and mathematical modeling, which offer important guidelines to maximize the impact of a viral message and minimize the uncertainty related to the conception and outcome of new marketing campaigns.

BackgroundIndividual-based modeling is a growing technique in the HIV transmission and prevention literature, but insufficient attention has been paid to formally evaluate the quality of reporting in this field. We present reporting recommendations for individual-based models for HIV treatment and prevention, assess the quality of reporting in the existing literature, and comment on the contribution of this model type to HIV policy and prediction.MethodsWe developed reporting recommendations for individual-based HIV transmission mathematical models, and through a systematic search, used them to evaluate the reporting in the existing literature. We identified papers that employed individual-based simulation models and were published in English prior to December 31, 2012. Articles were included if the models they employed simulated and tracked individuals, simulated HIV transmission between individuals in a particular population, and considered a particular treatment or prevention intervention. The papers were assessed with the reporting recommendations.FindingsOf 214 full text articles examined, 32 were included in the evaluation, representing 20 independent individual-based HIV treatment and prevention mathematical models. Manuscripts universally reported the objectives, context, and modeling conclusions in the context of the modeling assumptions and the model’s predictive capabilities, but the reporting of individual-based modeling methods, parameterization and calibration was variable. Six papers discussed the time step used and one discussed efforts to maintain internal validity in coding.ConclusionIndividual-based models represent detailed HIV transmission processes with the potential to contribute to inference and policy making for many different regions and populations. The rigor in reporting of assumptions, methods, and calibration of individual-based models focused on HIV transmission and prevention varies greatly. Higher standards for reporting of statistically rigorous calibration and model assumption testing need to be implemented to increase confidence in existing and future modeling results.

Crowds are a feature of large cities, occurring not only at mass gatherings but also at routine events such as the journey to work. To address extreme crowding, various computer models for crowd movement have been developed in the past decade, and we review these and show how they can be used to identify health and safety issues. State-of-the-art models that simulate the spread of epidemics operate on a population level, but the collection of fine-scale data might enable the development of models for epidemics that operate on a microscopic scale, similar to models for crowd movement. We provide an example of such simulations, showing how an individual-based crowd model can mirror aggregate susceptible-infected-recovered models that have been the main models for epidemics so far.

Coordination of cell behaviour is key to a myriad of biological processes including tissue morphogenesis, wound healing, and tumour growth. As such, individual-based computational models, which explicitly describe inter-cellular interactions, are commonly used to model collective cell dynamics. However, when using individual-based models, it is unclear how descriptions of cell boundaries affect overall population dynamics. In order to investigate this we define three cell boundary descriptions of varying complexities for each of three widely used off-lattice individual-based models: overlapping spheres, Voronoi tessellation, and vertex models. We apply our models to multiple biological scenarios to investigate how cell boundary description can influence tissue-scale behaviour. We find that the Voronoi tessellation model is most sensitive to changes in the cell boundary description with basic models being inappropriate in many cases. The timescale of tissue evolution when using an overlapping spheres model is coupled to the boundary description. The vertex model is demonstrated to be the most stable to changes in boundary description, though still exhibits timescale sensitivity. When using individual-based computational models one should carefully consider how cell boundaries are defined. To inform future work, we provide an exploration of common individual-based models and cell boundary descriptions in frequently studied biological scenarios and discuss their benefits and disadvantages.

Heterogeneity of infectious disease transmission can be generated by individual differences in the frequency of contacts with susceptible individuals, in the ability to transmit the infectious agent or in the duration of infection, and by spatial variation in the distribution, density or movements of hosts. Identifying spatial and individual heterogeneity can help improving management strategies to eradicate or mitigate infectious diseases, by targeting the individuals or areas that are responsible for most transmissions. Individual-based models allow quantifying the respective role of these sources of heterogeneity by integrating potential mechanisms that generate heterogeneity and then by tracking transmissions caused by each infected individual. In this study, we provide an individual-based model of endemic brucellosis Brucella melitensis transmission in the population of Alpine ibex (Capra ibex) of the Bargy massif (France) by taking advantage of detailed information available on ibex population dynamics, behaviour, and habitat use, and on epidemiological surveys. This host-pathogen system is expected to be subject of both individual and spatial heterogeneity. We first estimated the transmission probabilities, hitherto unknown, of the two main transmission routes of the infection (i.e., exposure to infectious births/abortions and venereal transmission). Then, we quantified heterogeneity at both individual and spatial levels. We found that both transmission routes are not negligible to explain the data, and that there is a high amount of heterogeneity of the host-pathogen system at the individual level, with females generating around 90% of the new cases of brucellosis infection. Males transmit infection at a lesser extent but still play a non-negligible role because they move between subpopulations and thereby create opportunities for spreading the infection spatially by venereal transmission. Two particular socio-spatial units are hotspots of transmission, and act as sources of transmission for the other units. These results may have important implications for disease management strategies.

An Individual-Based Model (IBM) was developed by employing natural and toxic survival rates of individuals to elucidate the community responses of benthic macroinvertebrates to anthropogenic disturbance in the streams. Experimental models (doseresponse and relative sensitivity) and mathematical models (power law and negative exponential distribution) were applied to determinate the individual survival rates due to acute toxicity in stressful conditions. A power law was additionally used to present the natural survival rate. Life events, covering movement, exposure to contaminants, death and reproduction, were simulated in the IBM at the individual level in small (1 m) and short (1 week) scales to produce species abundance distributions (SADs) at the community level in large (5 km) and long (1~~2 years) scales. Consequently, the SADs, such as geometric series, log-series, and log-normal distribution, were accordingly observed at severely (Biological Monitoring Working Party (BMWP□10), intermediately (BMWP□40) and weakly (BMWP□50) polluted sites. The results from a power law and negative exponential distribution were suitably fitted to the field data across the different levels of pollution, according to the Kolmogorov-Smirnov test. The IBMs incorporating natural and toxic survival rates in individuals were useful for presenting community responses to disturbances and could be utilized as an integrative tool to elucidate community establishment processes in benthic macroinvertebrates in the streams.

Rabies is a viral disease that is transmitted by bite and is fatal after the onset of symptoms. All warm blooded animals are susceptible to rabies and a wide range of species including foxes, wolves, jackals, raccoons, mongooses and bats act as reservoir hosts. Approximately 60,000 people die of rabies every year, mainly in Africa and Asia. The main source of human rabies is the domestic dog. Rabies in humans is preventable by timely administration of post-exposure prophylaxis, with a reduced schedule of administration if the person was protected by pre-exposure prophylaxis. Mass vaccination of dogs is considered effective in preventing human exposure and oral vaccine baits were used to eliminate rabies from foxes in central and western Europe. In N’Djamena, the capital of Chad, rabies is endemic with approximately one confirmed case of dog rabies per week. Each dog exposes on average two humans. In 2012 and 2013 two mass vaccination campaigns of dogs were conducted, reaching a coverage of more than 70% in both years. The campaigns interrupted transmission for nine months, but a resurgence of cases led to re-establishment of rabies at the pre-intervention endemic state. To better understand the movement and contact behaviour of dogs, 300 geo-located contact sensors were deployed on dogs in three different quarters of N’Djamena in 2016. We developed three mathematical models of rabies transmission, calibrated to the incidence data and coverage levels from the campaigns and data on dog movement and contacts from the geo-located contact sensors. We used an ordinary differential equation model to assess the effect of the vaccination campaigns and found that after the campaigns, the effective reproductive ratio dropped below one. Implementing a stochastic version of the model with the Gillespie algorithm confirmed the interruption of transmission. We found that population turnover contributed more to the decrease of vaccination coverage after the campaigns than individual immunity loss. Possible reasons for the resurgence of cases after the campaigns include spatial heterogeneity of vaccination coverage and dog density, underreporting and importation of latent dogs from the surroundings of N’Djamena. We developed a deterministic metapopulation model with importation of latent dogs to investigate the potential reasons for the resurgence seen in 2014. Our results indicate that importation of latently infected dogs better explains the incidence data than heterogeneity or underreporting. Because importation seems to be the most likely reason for the resurgence in cases, we investigated the chains of transmission triggered by imported cases. In order to realistically reproduce the contact heterogeneity at individual level, we used data from 300 geo-located contact sensors to build a network of 5000 dogs. Since there is no established method for expanding a network to a network with more nodes, we have developed and validated a network construction algorithm. We developed an individual based model and calibrated the transmission rate such that the simulation results correspond to outbreak data from two quarters in N’Djamena. We have shown that 70% coverage prevents major but not minor outbreaks. Since highly connected dogs hold a critical role in rabies transmission, vaccinating such dogs could increase the effect of vaccination strategies. Vaccinating dogs is an effective and equitable way of reducing human exposure and should therefore be an inherent of part rabies control programmes in endemic settings. However, in the absence of dog population management, population turnover quickly reduces vaccination coverage and reintroduction from surrounding areas or spillovers from wildlife reservoirs threaten the gains of mass dog vaccination campaigns. This suggests that maintaining high vaccination coverage by either repeated mass vaccination campaigns or continuous vaccination of dogs as well as oral vaccination of reservoirs (which was not investigated here) might be part of the best intervention package for settings like N’Djamena.

Mathematical modeling plays a crucial role in understanding and combating infectious diseases, offering predictive insights into disease spread and the impact of vaccination strategies. This paper explored the significance of mathematical modeling in epidemic control efforts, focusing on the interplay between vaccination strategies, disease transmission rates, and population immunity. To facilitate meaningful comparisons of vaccination strategies, we maintained a consistent framework by fixing the vaccination capacity to vary from 10 to 100% of the total population. As an example, at a 50% vaccination capacity, the pulse strategy averted approximately 45.61% of deaths, while continuous and hybrid strategies averted around 45.18 and 45.69%, respectively. Sensitivity analysis further indicated that continuous vaccination has a more direct impact on reducing the basic reproduction number $ R_0 $ compared to pulse vaccination. By analyzing key parameters such as $ R_0 $, pulse vaccination coefficients, and continuous vaccination parameters, the study underscores the value of mathematical modeling in shaping public health policies and guiding decision-making during disease outbreaks.