In this work we explore the effects of human mobility on the dispersion of a vector borne disease. We combine an already presented stochastic model for dengue with a simple representation of the daily motion of humans on a schematic city of 20x20 blocks with 100 inhabitants in each block. The pattern of motion of the individuals is described in terms of complex networks in which links connect different blocks and the link length distribution is in accordance with recent findings on human mobility. It is shown that human mobility can turn out to be the main driving force of the disease dispersal.
We propose an SEIR model for the populations and an SEI model for the vector to describe the transmission dynamics of a four-strain model with both primary and secondary dengue infections. In order to accomplish this, we propose and obtain an analytic solution of a system of 47 coupled differential equations. This would be the most complete epidemic model proposed to describe the dengue epidemic.
In this work we analyze the post monsoon Dengue outbreaks by analyzing the transient and long term dynamics of Dengue incidences and its environmental correlates in Ahmedabad city in western India from 2005-2012. We calculate the reproduction number $R_p$ using the growth rate of post monsoon Dengue outbreaks and biological parameters like host and vector incubation periods and vector mortality rate, and its uncertainties are estimated through Monte-Carlo simulations by sampling parameters from their respective probability distributions. Reduction in Female Aedes mosquito density required for …
We introduce the use of fractional calculus, i.e., the use of integrals and derivatives of non-integer (arbitrary) order, in epidemiology. The proposed approach is illustrated with an outbreak of dengue disease, which is motivated by the first dengue epidemic ever recorded in the Cape Verde islands off the coast of west Africa, in 2009. Numerical simulations show that in some cases the fractional models fit better the reality when compared with the standard differential models. The classical results are obtained as particular cases by considering the order of the derivatives to take an integer…
The incidence of Dengue epidemiologic disease has grown in recent decades. In this paper an application of optimal control in Dengue epidemics is presented. The mathematical model includes the dynamic of Dengue mosquito, the affected persons, the people's motivation to combat the mosquito and the inherent social cost of the disease, such as cost with ill individuals, educations and sanitary campaigns. The dynamic model presents a set of nonlinear ordinary differential equations. The problem was discretized through Euler and Runge Kutta schemes, and solved using nonlinear optimization packages.…
In the last two decades dengue cases increased significantly throughout the world. In several regions dengue re-emerged, particularly in Latin America, where dengue cases not only increased but also occurred more frequently. It is therefore necessary to understand the mechanisms that drive epidemic outbreaks in non-endemic regions, to help in the design of control strategies. We develop a stochastic model that includes climate variables, social structure, and mobility between a non-endemic city and an endemic area. We choose as a case study the non-endemic city of San Ram{ó}n de la Nueva Or{á}…
Dengue is a vector borne disease transmitted to humans by {\it{Aedes Aegypti}} mosquitoes carrying Dengue virus of different serotypes. Primarily an urban epidemic, Dengue exhibits complex spatial and temporal dynamics, influenced by many biological, human and environmental factors. In this work, we study the Dengue spread for a single serotype including human mobility. We model the Dengue spreading by using PDE reaction-diffusion and stochastic Cellular Automata (CA) with human and vector dynamics and analyze the spatial and temporal spreading of the disease using parameters from field studie…
A model for the transmission of dengue disease is presented. It consists of eight mutually-exclusive compartments representing the human and vector dynamics. It also includes a control parameter (insecticide) in order to fight the mosquitoes. The main goal of this work is to investigate the best way to apply the control in order to effectively reduce the number of infected humans and mosquitoes. A case study, using data of the outbreak that occurred in 2009 in Cape Verde, is presented.
Dengue is one of the most important infectious diseases in the world, in terms of death and economic cost. Hence, the modeling of dengue is of great importance to help us understand the dynamics disease, and interfering with its spreading mathematical by the proposition of control methods. In this work, control strategies in an attempt to eliminate the Aedes aegypti mosquito, as well as proposals for the vaccination campaign are evaluated. In our mathematical model, the mechanical control is accomplished through the environmental support capacity affected by a discrete function that represents…
We present an application of optimal control theory to Dengue epidemics. This epidemiologic disease is an important theme in tropical countries due to the growing number of infected individuals. The dynamic model is described by a set of nonlinear ordinary differential equations, that depend on the dynamic of the Dengue mosquito, the number of infected individuals, and the people's motivation to combat the mosquito. The cost functional depends not only on the costs of medical treatment of the infected people but also on the costs related to educational and sanitary campaigns. Two approaches to…
We introduce a dengue model (SEIR) where the human individuals are treated on an individual basis (IBM) while the mosquito population, produced by an independent model, is treated by compartments (SEI). We study the spread of epidemics by the sole action of the mosquito. Exponential, deterministic and experimental distributions for the (human) exposed period are considered in two weather scenarios, one corresponding to temperate climate and the other to tropical climate. Virus circulation, final epidemic size and duration of outbreaks are considered showing that the results present little sens…
Metapopulation (multipatch) models are widely used to study the patterns of spatial spread of epidemics. In this paper we study the impact of inter-patch connection weights on the predictions of these models. We contrast arbitrary, uniform link weights with link weights predicted using a gravity model based on patch populations and distance. In a synthetic system with one large driver city and many small follower cities, we show that under uniform link weights, epidemics in the follower regions are perfectly synchronized. In contrast, gravity-based links allow a more realistic, less synchroniz…
Different extensions of the classical single-strain SIR model for the host population, motivated by modeling dengue fever epidemiology, have reported a rich dynamic structure including deterministic chaos which was able to explain the large fluctuations of disease incidences. A comparison between the basic two-strain dengue model, which already captures differences between primary and secondary infections, with the four-strain dengue model, that introduces the idea of competition of multiple strains in dengue epidemics shows that the difference between first and secondary infections drives the…
Quantifying the attack ratio of disease is key to epidemiological inference and Public Health planning. For multi-serotype pathogens, however, different levels of serotype-specific immunity make it difficult to assess the population at risk. In this paper we propose a Bayesian method for estimation of the attack ratio of an epidemic and the initial fraction of susceptibles using aggregated incidence data. We derive the probability distribution of the effective reproductive number, R t , and use MCMC to obtain posterior distributions of the parameters of a single-strain SIR transmission model w…
After their re-emergence in the last decades, dengue fever and other vector-borne diseases are a potential threat to the lives of millions of people. Based on a data set of dengue cases in the Brazilian city of Fortaleza, collected from 2011 to 2016, we study the spatio-temporal characteristics of dengue outbreaks to characterize epidemic and non-epidemic years. First, we identify regions that show a high prevalence of dengue cases and mosquito larvae in different years and also analyze their corresponding correlations. Our results show that the characteristic correlation length of the epidemi…
We use a stochastic Markovian dynamics approach to describe the spreading of vector-transmitted diseases, like dengue, and the threshold of the disease. The coexistence space is composed by two structures representing the human and mosquito populations. The human population follows a susceptible-infected-recovered (SIR) type dynamics and the mosquito population follows a susceptible-infected-susceptible (SIS) type dynamics. The human infection is caused by infected mosquitoes and vice-versa so that the SIS and SIR dynamics are interconnected. We develop a truncation scheme to solve the evoluti…
Modeling and analysis of a novel two-strain dengue epidemics model considering secondary infections with increased mortality
Johannes Gutenberg-Universität Mainz（约翰内斯·古腾堡美因茨大学）；Institute for Quantitative and Computational Biosciences (IQCB), Johannes Gutenberg University Mainz（约翰内斯·古腾堡美因茨大学定量与计算生物科学研究所）；Ordu University, Faculty of Science and Letters（奥尔杜大学理学院）；Escuela Superior Politécnica del Litoral（厄瓜多尔高等理工学院）；Center for Applied Dynamical Systems and Computational Methods (CADSCOM), Faculty of Natural Sciences and Mathematics, Escuela Superior Politécnica del Litoral（厄瓜多尔高等理工学院自然科学与数学学院应用动力系统与计算方法中心）；TU Dresden（德累斯顿工业大学）；University of Koblenz（科布伦茨大学）
There are nowadays a huge load of publications about dengue epidemic models, which mostly employ deterministic differential equations. The analytical properties of deterministic models are always of particular interest by many experts, but their validity - if they can indeed track some empirical data - is an increasing demand by many practitioners. In this view, the data can tell to which figure the solutions yielded from the models should be; they drift all the involving parameters towards the most appropriate values. By prior understanding of the population dynamics, some parameters with inh…
We construct an epidemic model for the transmission of dengue fever with an early-life stage in the vector dynamics and age-structure within hosts. The early-life stage of the vector is modeled via a general function that supports multiple vector densities. The {\it basic reproductive number} and {\it vector demographic threshold} are computed to study the local and global stability of the infection-free state. A numerical framework is implemented and simulations are performed.
A Mathematical Model of Dengue Transmission Incorporating Hospital Capacity and Threshold-Based Fogging Interventions
Universitas Indonesia（印度尼西亚大学）；Escuela Superior Politécnica del Litoral（沿海高等理工学院）；TU Dresden（德累斯顿工业大学）；Ordu University（奥尔杜大学）；University of Koblenz（科布伦茨大学）；Johannes–Gutenberg Universität Mainz（约翰内斯·古腾堡美因茨大学）；Institute for Quantitative and Computational Biosciences (IQCB), Johannes Gutenberg University Mainz（约翰内斯·古腾堡美因茨大学定量与计算生物科学研究所）
Urbanization drives the epidemiology of infectious diseases to many threats and new challenges. In this research, we study the interplay between human mobility and dengue outbreaks in the complex urban environment of the city-state of Singapore. We integrate both stylized and mobile phone data-driven mobility patterns in an agent-based transmission model in which humans and mosquitoes are represented as agents that go through the epidemic states of dengue. We monitor with numerical simulations the system-level response to the epidemic by comparing our results with the observed cases reported d…
Dengue is a vector-borne viral disease increasing dramatically over the past years due to improvement in human mobility. The movement of host individuals between and within the patches are captured via a residence-time matrix. A system of ordinary differential equations (ODEs) modeling the spatial spread of disease among the multiple patches is used to create a system of stochastic differential equations (SDEs). Numerical solutions of the system of SDEs are compared with the deterministic solutions obtained via ODEs.
The transmission of vector infectious diseases, which produces complex spatiotemporal patterns, is analyzed by a periodically forced two-dimensional cellular automata model. The system, which comprises three population levels, is introduced to describe complex features of the dynamics of the vector transmitted dengue epidemics, known to be very sensitive to seasonal variables. The three coupled levels represent the human, the adult and immature vector populations. The dynamics includes external seasonality forcing (rainfall intensity data), human and mosquito mobility, and vector control effec…
Climate change and human mobility will shape dengue emergence risk in Europe
University of Padua（帕多瓦大学）；Istituto Nazionale di Fisica Nucleare, Sez. Padova（意大利国家核物理研究所帕多瓦分部）；Istituto Nazionale di Fisica Nucleare, Sez. Milano Bicocca（意大利国家核物理研究所米兰比科卡分部）；University of Parma（帕尔马大学）；Padova Neuroscience Center, University of Padua（帕多瓦大学帕多瓦神经科学中心）；University of Genoa（热那亚大学）；Machine Learning Genoa Center, University of Genoa（热那亚大学机器学习热那亚中心）；Padua Center for Network Medicine, University of Padua（帕多瓦大学帕多瓦网络医学中心）
Vector-transmitted diseases such as dengue fever and chikungunya have been spreading rapidly in many parts of the world. The Zika virus has been known since 1947 and invaded South America in 2013. It can be transmitted not only by (mosquito) vectors but also directly through sexual contact. Zika has developed into a serious global health problem because, while most cases are asymptomatic or very light, babies born to Zika - infected mothers may develop microcephaly and other very serious birth defects. We formulate and analyze two epidemic models for vector-transmitted diseases, one appropriat…
This paper examines the interplay of the effect of cross immunity and antibody-dependent enhancement (ADE) in mutistrain diseases. Motivated by dengue fever, we study a model for the spreading of epidemics in a population with multistrain interactions mediated by both partial temporary cross immunity and ADE. Although ADE models have previously been observed to cause chaotic outbreaks, we show analytically that weak cross immunity has a stabilizing effect on the system. That is, the onset of disease fluctuations requires a larger value of ADE with small cross immunity than without. However, st…
Human mobility plays a key role on the transformation of local disease outbreaks into global pandemics. Thus, the inclusion of human movements into epidemic models has become mandatory for understanding current epidemic episodes and to design efficient prevention policies. Following this challenge, here we develop a Markovian framework which enables to address the impact of recurrent mobility patterns on the epidemic onset at different temporal scales. This formalism is validated by comparing their predictions with results from mechanistic simulations. The fair agreement between both theory an…
Mobility restrictions - travel advisories, trade and travel bans, border closures and, in extreme cases, area quarantines or cordons sanitaires - are among the most widely used measures to control infectious diseases. Restrictions of this kind were important in the response to epidemics of SARS (2003), H1N1 influenza (2009), and Ebola (2014). However, they do not always work as expected. The imposition of a cordon sanitaire to control the 2014 West African Ebola outbreak, for example, is argued to have led to a higher-than-expected number of cases in the quarantined area. To determine when mob…
Emerging marine infectious diseases pose a substantial threat to marine ecosystems and the conservation of their biodiversity. Compartmental models of epidemic transmission in marine sessile organisms, available only recently, are based on non-spatial descriptions in which space is homogenised and parasite mobility is not explicitly accounted for. However, in realistic scenarios epidemic transmission is conditioned by the spatial distribution of hosts and the parasites mobility patterns, calling for a explicit description of space. In this work we develop a spatially-explicit individual-based …
Vector-borne epidemics are the result of the combination of different factors such as the crossed contagions between humans and vectors, their demographic distribution and human mobility among others. The current availability of information about the former ingredients demands their incorporation to current mathematical models for vector-borne disease transmission. Here, relying on metapopulation dynamics, we propose a framework whose results are in fair agreement with those obtained from mechanistic simulations. This framework allows us to derive an expression of the epidemic threshold captur…
Various theoretical models have been proposed to understand the basic nature of epidemics. Recent studies focus on the effects of mobility to epidemic process. However, uncorrelated random walk is typically assumed as the type of movement. In our daily life, the movement of people sometimes tends to be limited to a certain direction, which can be described by biased random walk. Here, we developed an agent-based model of susceptible-infected-recovered (SIR) epidemic process in a 2D continuous space where agents tend to move in a certain direction in addition to random movement. Moreover, we ma…
International Institute of Information Technology Bangalore（班加罗尔国际信息技术学院）；Sorbonne University Abu Dhabi（索邦大学阿布扎比分校）；Sorbonne Center for Artificial Intelligence（索邦人工智能中心）；University of Georgia（佐治亚大学）；Duke-NUS Medical School（杜克-新加坡国立大学医学院）；National University of Singapore（新加坡国立大学）
Dengue fever is a virulent disease spreading over 100 tropical and subtropical countries in Africa, the Americas, and Asia. This arboviral disease affects around 400 million people globally, severely distressing the healthcare systems. The unavailability of a specific drug and ready-to-use vaccine makes the situation worse. Hence, policymakers must rely on early warning systems to control intervention-related decisions. Forecasts routinely provide critical information for dangerous epidemic events. However, the available forecasting models (e.g., weather-driven mechanistic, statistical time se…
The spreading of epidemics is very much determined by the structure of the contact network, which may be impacted by the mobility dynamics of the individuals themselves. In confined scenarios where a small, closed population spends most of its time in localized environments and has easily identifiable mobility patterns --such as workplaces, university campuses or schools-- it is of critical importance to identify the factors controlling the rate of disease spread. Here we present a discrete-time, metapopulation-based model to describe the transmission of SIS-like diseases that take place in co…
Human mobility is a key component of large-scale spatial-transmission models of infectious diseases. Correctly modeling and quantifying human mobility is critical for improving epidemic control policies, but may be hindered by incomplete data in some regions of the world. Here we explore the opportunity of using proxy data or models for individual mobility to describe commuting movements and predict the diffusion of infectious disease. We consider three European countries and the corresponding commuting networks at different resolution scales obtained from official census surveys, from proxy d…
Metapopulation models have been a popular tool for the study of epidemic spread over a network of highly populated nodes (cities, provinces, countries) and have been extensively used in the context of the ongoing COVID-19 pandemic. In the present work, we revisit such a model, bearing a particular case example in mind, namely that of the region of Andalusia in Spain during the period of the summer-fall of 2020 (i.e., between the first and second pandemic waves). Our aim is to consider the possibility of incorporation of mobility across the province nodes focusing on mobile-phone time dependent…
Understanding and predicting outbreaks of contagious diseases are crucial to the development of society and public health, especially for underdeveloped countries. However, challenging problems are encountered because of complex epidemic spreading dynamics influenced by spatial structure and human dynamics (including both human mobility and human interaction intensity). We propose a systematical model to depict nationwide epidemic spreading in Côte d'Ivoire, which integrates multiple factors, such as human mobility, human interaction intensity, and demographic features. We provide insights to …
Risk-mediated transmission dynamics govern epidemic trajectories beyond physical mobility
Hokkaido University（北海道大学）；Doshisha University（立命馆大学）；Weill Cornell Medicine-Qatar, Cornell University（康奈尔大学威尔医学院卡塔尔分校）；Weill Cornell Medicine, Cornell University（康奈尔大学威尔医学院）；College of Health Sciences, QU Health, Qatar University（卡塔尔大学健康科学学院）；College of Health and Life Sciences, Hamad bin Khalifa University（哈马德·本·哈利法大学健康与生命科学学院）；Kyushu University（九州大学）
We develop a multi-patch and multi-group model that captures the dynamics of an infectious disease when the host is structured into an arbitrary number of groups and interacts into an arbitrary number of patches where the infection takes place. In this framework, we model host mobility that depends on its epidemiological status, by a Lagrangian approach. This framework is applied to a general SEIRS model and the basic reproduction number $\mathcal{R_0}$ is derived. The effects of heterogeneity in groups, patches and mobility patterns on $\mathcal{R_0}$ and disease prevalence are explored. Our …
Inspired by dengue and yellow fever epidemics, we investigated the contact process (CP) in a multiscale network constituted by one-dimensional chains connected through a Barabási-Albert scale-free network. In addition to the CP dynamics inside the chains, the exchange of individuals between connected chains (travels) occurs at a constant rate. A finite epidemic threshold and an epidemic mean lifetime diverging exponentially in the subcritical phase, concomitantly with a power law divergence of the outbreak's duration, were found. A generalized scaling function involving both regular and SF com…
Host mobility plays a fundamental role in the spatial spread of infectious diseases. Previous theoretical works based on the integration of network theory into the metapopulation framework have shown that the heterogeneities that characterize real mobility networks favor the propagation of epidemics. Nevertheless, the studies conducted so far assumed the mobility process to be either Markovian or non-Markovian with a fixed traveling time scale. Available statistics however show that the time spent by travelers at destination is characterized by wide fluctuations, ranging between a single day u…
Large-scale human mobility data is a key resource in data-driven policy making and across many scientific fields. Most recently, mobility data was extensively used during the COVID-19 pandemic to study the effects of governmental policies and to inform epidemic models. Large-scale mobility is often measured using digital tools such as mobile phones. However, it remains an open question how truthfully these digital proxies represent the actual travel behavior of the general population. Here, we examine mobility datasets from multiple countries and identify two fundamentally different types of b…
In June 2020, Arizona, U.S., emerged as one of the world's worst coronavirus disease 2019(COVID-19) spots after the stay-at-home order was lifted in the middle of May. However, with the decisions to reimpose restrictions, the number of COVID-19 cases has been declining, and Arizona is considered to be a good model in slowing the epidemic. In this paper, we aimed to examine the COVID-19 situation in Arizona and assess the impact of human mobility change. We constructed the mobility integrated metapopulation susceptible-infectious-removed model and fitted to publicly available datasets on COVID-…
Human mobility, contact patterns, and their interplay are key aspects of our social behavior that shape the spread of infectious diseases across different regions. In the light of new evidence and data sets about these two elements, epidemic models should be refined to incorporate both the heterogeneity of human contacts and the complexity of mobility patterns. Here, we propose a theoretical framework that allows accommodating these two aspects in the form of a set of Markovian equations. We validate these equations with extensive mechanistic simulations and derive analytically the epidemic th…
Human mobility is a key factor in spatial disease dynamics and related phenomena. In computational models host mobility is typically modelled by diffusion in space or on metapolulation networks. Alternatively, an effective force of infection across distance has been introduced to capture spatial dispersal implicitly. Both approaches do not account for important aspects of natural human mobility, diffusion does not capture the high degree of predictability in natural human mobility patters, e.g. the high percentage of return movements to individuals' base location, the effective force of infect…
We propose a theoretical framework for the study of epidemics in structured metapopulations, with heterogeneous agents, subjected to recurrent mobility patterns. We propose to represent the heterogeneity in the composition of the metapopulations as layers in a multiplex network, where nodes would correspond to geographical areas and layers account for the mobility patterns of agents of the same class. We analyze both the classical Susceptible-Infected-Susceptible and the Susceptible-Infected-Removed epidemic models within this framework, and compare macroscopic and microscopic indicators of th…
Network science has increasingly become central to the field of epidemiology and our ability to respond to infectious disease threats. However, many networks derived from modern datasets are not just large, but dense, with a high ratio of edges to nodes. This includes human mobility networks where most locations have a large number of links to many other locations. Simulating large-scale epidemics requires substantial computational resources and in many cases is practically infeasible. One way to reduce the computational cost of simulating epidemics on these networks is sparsification, where a…
Given the growth of urbanization and emerging pandemic threats, more sophisticated models are required to understand disease propagation and investigate the impacts of intervention strategies across various city types. We introduce a fully mechanistic, activity-based and highly spatio-temporally resolved epidemiological model which leverages on person-trajectories obtained from integrated mobility demand and supply models in full-scale cities. Simulating COVID-19 evolution in two full-scale cities with representative synthetic populations and mobility patterns, we analyze activity-based contac…
Among the realistic ingredients to be considered in the computational modeling of infectious diseases, human mobility represents a crucial challenge both on the theoretical side and in view of the limited availability of empirical data. In order to study the interplay between small-scale commuting flows and long-range airline traffic in shaping the spatio-temporal pattern of a global epidemic we i) analyze mobility data from 29 countries around the world and find a gravity model able to provide a global description of commuting patterns up to 300 kms; ii) integrate in a worldwide structured me…
We investigate a model for spatial epidemics explicitly taking into account bi-directional movements between base and destination locations on individual mobility networks. We provide a systematic analysis of generic dynamical features of the model on regular and complex metapopulation network topologies and show that significant dynamical differences exist to ordinary reaction-diffusion and effective force of infection models. On a lattice we calculate an expression for the velocity of the propagating epidemic front and find that in contrast to the diffusive systems, our model predicts a satu…
Human movement decisions during Coronavirus Disease 2019
International Institute for Zoonosis Control, Hokkaido University（国际动物传染病控制研究所，北海道大学）；Faculty of Environmental Earth Science, Hokkaido University（环境地球科学学院，北海道大学）；Recruit Co., Ltd（recruit株式会社）；Department of Biology, Faculty of Science, Kyushu University（理学部生物学系，九州大学）
We study how international flights can facilitate the spread of an epidemic to a worldwide scale. We combine an infrastructure network of flight connections with a population density dataset to derive the mobility network, and then we define an epidemic framework to model the spread of the disease. Our approach combines a compartmental SEIRS model with a graph diffusion model to capture the clusteredness of the distribution of the population. The resulting model is characterised by the dynamics of a metapopulation SEIRS, with amplification or reduction of the infection rate which is determined…
