Modeling the spread of vector-borne diseases on bipartite networks

Complexity in the dengue spreading: A network analysis approach

In an increasingly interconnected society, preventing epidemics has become a major challenge. Numerous infectious diseases spread between individuals by a vector, creating bipartite networks of infection with the characteristics of complex networks. In the case of dengue, a mosquito-borne disease, these infection networks include a vector-the Aedes aegypti mosquito-which has expanded its endemic area due to climate change. In this scenario, innovative approaches are essential to help public agents in the fight against the disease. Using an agent-based model, we investigated the network morphology of a dengue endemic region considering four different serotypes and a small population. The degree, betweenness, and closeness distributions are evaluated for the bipartite networks, considering the interactions up to the second order for each serotype. We observed scale-free features and heavy tails in the degree distribution and betweenness and quantified the decay of the degree distribution with a q-Gaussian fit function. The simulation results indicate that the spread of dengue is primarily driven by human-to-human and human-to-mosquito interaction, reinforcing the importance of controlling the vector to prevent episodes of epidemic outbreaks.

Host movement, transmission hot spots, and vector-borne disease dynamics on spatial networks

We examine how spatial heterogeneity combines with mobility network structure to influence vector-borne disease dynamics. Specifically, we consider a Ross-Macdonald-type disease model on n spatial locations that are coupled by host movement on a strongly connected, weighted, directed graph. We derive a closed form approximation to the domain reproduction number using a Laurent series expansion, and use this approximation to compute sensitivities of the basic reproduction number to model parameters. To illustrate how these results can be used to help inform mitigation strategies, as a case study we apply these results to malaria dynamics in Namibia, using published cell phone data and estimates for local disease transmission. Our analytical results are particularly useful for understanding drivers of transmission when mobility sinks and transmission hot spots do not coincide.

Predictive Model of Lyme Disease Epidemic Process Using Machine Learning Approach

Lyme disease is the most prevalent tick-borne disease in Eastern Europe. This study focuses on the development of a machine learning model based on a neural network for predicting the dynamics of the Lyme disease epidemic process. A retrospective analysis of the Lyme disease cases reported in the Kharkiv region, East Ukraine, between 2010 and 2017 was performed. To develop the neural network model of the Lyme disease epidemic process, a multilayered neural network was used, and the backpropagation algorithm or the generalized delta rule was used for its learning. The adequacy of the constructed forecast was tested on real statistical data on the incidence of Lyme disease. The learning of the model took 22.14 s, and the mean absolute percentage error is 3.79%. A software package for prediction of the Lyme disease incidence on the basis of machine learning has been developed. Results of the simulation have shown an unstable epidemiological situation of Lyme disease, which requires preventive measures at both the population level and individual protection. Forecasting is of particular importance in the conditions of hostilities that are currently taking place in Ukraine, including endemic territories.

Spreader events and the limitations of projected networks for capturing dynamics on multipartite networks

Many systems of scientific interest can be conceptualized as multipartite networks. Examples include the spread of sexually transmitted infections, scientific collaborations, human friendships, product recommendation systems, and metabolic networks. In practice, these systems are often studied after projection onto a single class of nodes, losing crucial information. Here, we address a significant knowledge gap by comparing transmission dynamics on temporal multipartite networks and on their time-aggregated unipartite projections to determine the impact of the lost information on our ability to predict the systems' dynamics. We show that the dynamics of transmission models can be dramatically dissimilar on multipartite networks and on their projections at three levels: final outcome, the magnitude of the variability from realization to realization, and overall shape of the temporal trajectory. We find that the ratio of the number of nodes to the number of active edges over the time-aggregation scale determines the ability of projected networks to capture the dynamics on the multipartite network. Finally, we explore which properties of a multipartite network are crucial in generating synthetic networks that better reproduce the dynamical behavior observed in real multipartite networks.

Dynamical analysis of a mean-field vector-borne diseases model on complex networks: An edge based compartmental approach

In this paper, we propose a concise method to investigate the global dynamics of a mean-field vector-borne diseases model on complex networks. We obtain an explicit formula of the basic reproduction number by a renewal equation. We show that the model exhibits a threshold dynamics in terms of the basic reproduction number by constructing subtle Lyapunov functions. Roughly speaking, if the basic reproduction number R₀<1, the vector-borne diseases die out; otherwise, it persists. Moreover, numerical simulations show that vector-control is an effective measure for slowing down the spread of vector-borne diseases.

Incorporating tick feeding behaviour into R0 for tick-borne pathogens

Tick-borne pathogens pose a considerable disease burden in Europe and North America, where increasing numbers of human cases and the emergence of new tick-borne pathogens has renewed interest in resolving the mechanisms underpinning their geographical distribution and abundance. For Borrelia burgdorferi and tick-borne encephalitis (TBE) virus, transmission of infection from one generation of ticks to another occurs when older nymphal ticks infect younger larval ticks feeding on the same host, either indirectly via systemic infection of the vertebrate host or directly when feeding in close proximity. Here, expressions for the basic reproduction number, R₀, and the related tick type-reproduction number, T, are derived that account for the observation that larval and nymphal ticks tend to aggregate on the same minority of hosts, a tick feeding behaviour known as co-aggregation. The pattern of tick blood meals is represented as a directed, acyclic, bipartite contact network, with individual vertebrate hosts having in-degree, k_in, and out-degree, k_out, that respectively represent cumulative counts of nymphal and larval ticks fed over the lifetime of the host. The in- and out-degree are not independent when co-aggregation occurs such that [Formula: see text] where 〈.〉 indicates expected value. When systemic infection in the vertebrate host is the dominant transmission route R₀²=T, whereas when direct transmission between ticks co-feeding on the same host is dominant then R₀=T and the effect of co-aggregation on R₀ is more pronounced. Simulations of B. burgdorferi and TBE virus transmission on theoretical tick-mouse contact networks revealed that aggregation and co-aggregation have a synergistic effect on R₀ and T, that co-aggregation always increases R₀ and T, and that aggregation only increases R₀ and T when larvae and nymphs also co-aggregate. Co-aggregation has the greatest absolute effect on R₀ and T when the mean larval burden of hosts is high, and the largest relative effect on R₀ for pathogens sustained by co-feeding transmission, e.g. TBE virus in Europe, compared with those predominantly spread by systemic infection, e.g. B. burgdorferi. For both pathogens, though, co-aggregation increases the mean number of ticks infected per infectious tick, T, and so too the likelihood of pathogen persistence.

Pareto rules for malaria super-spreaders and super-spreading

Heterogeneity in transmission is a challenge for infectious disease dynamics and control. An 80-20 "Pareto" rule has been proposed to describe this heterogeneity whereby 80% of transmission is accounted for by 20% of individuals, herein called super-spreaders. It is unclear, however, whether super-spreading can be attributed to certain individuals or whether it is an unpredictable and unavoidable feature of epidemics. Here, we investigate heterogeneous malaria transmission at three sites in Uganda and find that super-spreading is negatively correlated with overall malaria transmission intensity. Mosquito biting among humans is 90-10 at the lowest transmission intensities declining to less than 70-30 at the highest intensities. For super-spreaders, biting ranges from 70-30 down to 60-40. The difference, approximately half the total variance, is due to environmental stochasticity. Super-spreading is thus partly due to super-spreaders, but modest gains are expected from targeting super-spreaders.

Bipartite graphs in systems biology and medicine: a survey of methods and applications

The latest advances in high-throughput techniques during the past decade allowed the systems biology field to expand significantly. Today, the focus of biologists has shifted from the study of individual biological components to the study of complex biological systems and their dynamics at a larger scale. Through the discovery of novel bioentity relationships, researchers reveal new information about biological functions and processes. Graphs are widely used to represent bioentities such as proteins, genes, small molecules, ligands, and others such as nodes and their connections as edges within a network. In this review, special focus is given to the usability of bipartite graphs and their impact on the field of network biology and medicine. Furthermore, their topological properties and how these can be applied to certain biological case studies are discussed. Finally, available methodologies and software are presented, and useful insights on how bipartite graphs can shape the path toward the solution of challenging biological problems are provided.

Dynamics of Zika virus outbreaks: an overview of mathematical modeling approaches

BACKGROUND

The Zika virus was first discovered in 1947. It was neglected until a major outbreak occurred on Yap Island, Micronesia, in 2007. Teratogenic effects resulting in microcephaly in newborn infants is the greatest public health threat. In 2016, the Zika virus epidemic was declared as a Public Health Emergency of International Concern (PHEIC). Consequently, mathematical models were constructed to explicitly elucidate related transmission dynamics.

SURVEY METHODOLOGY

In this review article, two steps of journal article searching were performed. First, we attempted to identify mathematical models previously applied to the study of vector-borne diseases using the search terms "dynamics," "mathematical model," "modeling," and "vector-borne" together with the names of vector-borne diseases including chikungunya, dengue, malaria, West Nile, and Zika. Then the identified types of model were further investigated. Second, we narrowed down our survey to focus on only Zika virus research. The terms we searched for were "compartmental," "spatial," "metapopulation," "network," "individual-based," "agent-based" AND "Zika." All relevant studies were included regardless of the year of publication. We have collected research articles that were published before August 2017 based on our search criteria. In this publication survey, we explored the Google Scholar and PubMed databases.

RESULTS

We found five basic model architectures previously applied to vector-borne virus studies, particularly in Zika virus simulations. These include compartmental, spatial, metapopulation, network, and individual-based models. We found that Zika models carried out for early epidemics were mostly fit into compartmental structures and were less complicated compared to the more recent ones. Simple models are still commonly used for the timely assessment of epidemics. Nevertheless, due to the availability of large-scale real-world data and computational power, recently there has been growing interest in more complex modeling frameworks.

DISCUSSION

Mathematical models are employed to explore and predict how an infectious disease spreads in the real world, evaluate the disease importation risk, and assess the effectiveness of intervention strategies. As the trends in modeling of infectious diseases have been shifting towards data-driven approaches, simple and complex models should be exploited differently. Simple models can be produced in a timely fashion to provide an estimation of the possible impacts. In contrast, complex models integrating real-world data require more time to develop but are far more realistic. The preparation of complicated modeling frameworks prior to the outbreaks is recommended, including the case of future Zika epidemic preparation.

Identifying Causes of Patterns in Ecological Networks: Opportunities and Limitations

Ecological networks depict the interactions between species, mainly based on observations in the field. The information contained in such interaction matrices depends on the sampling design, and typically, compounds preferences (specialization) and abundances (activity). Null models are the primary vehicles to disentangle the effects of specialization from those of sampling and abundance, but they ignore the feedback of network structure on abundances. Hence, network structure, as exemplified here by modularity, is difficult to link to specific causes. Indeed, various processes lead to modularity and to specific interaction patterns more generally. Inferring (co)evolutionary dynamics is even more challenging, as competition and trait matching yield identical patterns of interactions. A satisfactory resolution of the underlying factors determining network structure will require substantial additional information, not only on independently assessed abundances, but also on traits, and ideally on fitness consequences as measured in experimental setups.

Pattern of tick aggregation on mice: larger than expected distribution tail enhances the spread of tick-borne pathogens

The spread of tick-borne pathogens represents an important threat to human and animal health in many parts of Eurasia. Here, we analysed a 9-year time series of Ixodes ricinus ticks feeding on Apodemus flavicollis mice (main reservoir-competent host for tick-borne encephalitis, TBE) sampled in Trentino (Northern Italy). The tail of the distribution of the number of ticks per host was fitted by three theoretical distributions: Negative Binomial (NB), Poisson-LogNormal (PoiLN), and Power-Law (PL). The fit with theoretical distributions indicated that the tail of the tick infestation pattern on mice is better described by the PL distribution. Moreover, we found that the tail of the distribution significantly changes with seasonal variations in host abundance. In order to investigate the effect of different tails of tick distribution on the invasion of a non-systemically transmitted pathogen, we simulated the transmission of a TBE-like virus between susceptible and infective ticks using a stochastic model. Model simulations indicated different outcomes of disease spreading when considering different distribution laws of ticks among hosts. Specifically, we found that the epidemic threshold and the prevalence equilibria obtained in epidemiological simulations with PL distribution are a good approximation of those observed in simulations feed by the empirical distribution. Moreover, we also found that the epidemic threshold for disease invasion was lower when considering the seasonal variation of tick aggregation.

Our work analyses a 9-year time series of tick co-feeding patterns on Yellow-necked mice. Our data shows a strong heterogeneity, where most mice are parasitised by a small number of ticks while few host a much larger number. We describe the number of ticks per host by the commonly used Negative Binomial model, by the Poisson-LogNormal model, and we propose the Power Law model as an alternative. In our data, the last model seems to better describe the strong heterogeneity. In order to understand the epidemiological consequences, we use a computational model to reproduce a peculiar way of transmission, observed in some cases in nature, where uninfected ticks acquire an infection by feeding on a host where infected ticks are present, without any remarkable epidemiological involvement of the host itself. In particular, we are interested in determining the conditions leading to pathogen spread. We observe that the effective transmission of this infection in nature is highly dependent on the capability of the implemented model to describe the tick burden. In addition, we also consider seasonal changes in tick aggregation on mice, showing its influence on the spread of the infection.