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Comparison of random and structured movements for two complex movement networks. (A and B) Typical dynamics of unconstrained epidemics begun in Central London in a ward-scale metapopulation of Great Britain, for all random movements, all commuters, and the appropriate mix. Epidemiologic parameters are chosen to match pandemic influenza (A) and smallpox (B), with parameter values given in SI Text. (C and D) Mean number of infected cattle from an individual-based simulation of the British cattle population, either using the known pattern of movements or losing individual identity within a farm and moving a randomly selected animal. Each point corresponds to a unique initially infected farm and is the average of 100 simulations for each movement type; points are color coded as to whether the means are significantly different. Parameters are chosen to match (C) a slow infectious disease, such as bovine tuberculosis (simulated from 2002 to end 2007), and (D) a fast infection, such as foot-and-mouth disease (simulated for 2005 only).
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The theory of networks has had a huge impact in both the physical and life sciences, shaping our understanding of the interaction between multiple elements in complex systems. In particular, networks have been extensively used in predicting the spread of infectious diseases where individuals, or populations of individuals, interact with a limited s...
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... Model for Great Britain. We now extend these theoret- ical observations for the speed of spatial spread to two applied examples and consider the impact of movement patterns on ag- gregate epidemic dynamics (Fig. 2). We consider the meta- population of wards in Great Britain linked by both the commuter network and nonwork travel patterns (SI Text; see ref. 17 for details of this combined network structure) with infection pa- rameterized to match pandemic influenza and smallpox dynamics ( Fig. 2 A and B; parameters are given in SI Text). For both ...
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... impact of movement patterns on ag- gregate epidemic dynamics (Fig. 2). We consider the meta- population of wards in Great Britain linked by both the commuter network and nonwork travel patterns (SI Text; see ref. 17 for details of this combined network structure) with infection pa- rameterized to match pandemic influenza and smallpox dynamics ( Fig. 2 A and B; parameters are given in SI Text). For both infections we observe a far slower growth rate, with a later and lower peak, for a population of commuters compared with a population of random movers, in agreement with the 80% slower speed predicted by the simpler model; this pattern also holds independent of where the infection is ...
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... the individual identity of ani- mals on the farm. This loss of identity is analogous to the dif- ference between the commuter and random-mover formulations. We compare these two assumptions by simulating multiple epi- demics with the same initial individual cattle infected and com- paring the distributions of epidemic sizes that are predicted ( Fig. 2 C and D). Because of the vast heterogeneity in the number of cattle per farm, the specific structure of the movement network, and the relative rarity of movements between two given farms, it is not possible to produce an average or generic epidemic in the Keeling cattle population; instead we are forced to compare the distri- bution of ...
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... bution of simulation epidemic sizes while accounting for the extreme sensitivity of the expected epidemic to the initial seeding of infection. In general, we predict larger epidemics when mov- ing random cattle compared with moving cattle with a known identity, with the effects pronounced for both slow infections (such as bovine tuberculosis; Fig. 2C) and for short-lived highly transmissible infections (such as foot-and-mouth disease; Fig. 2D). We can therefore conclude that the normal duration of animal stays on farms (details given in SI Text) generally has a protective influence, limiting the spread of infection compared with more naïve assumptions about the network of animal ...
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... epidemic to the initial seeding of infection. In general, we predict larger epidemics when mov- ing random cattle compared with moving cattle with a known identity, with the effects pronounced for both slow infections (such as bovine tuberculosis; Fig. 2C) and for short-lived highly transmissible infections (such as foot-and-mouth disease; Fig. 2D). We can therefore conclude that the normal duration of animal stays on farms (details given in SI Text) generally has a protective influence, limiting the spread of infection compared with more naïve assumptions about the network of animal movements. This impact is generally greater for the more rapidly spreading infection (Fig. 2D); ...
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... disease; Fig. 2D). We can therefore conclude that the normal duration of animal stays on farms (details given in SI Text) generally has a protective influence, limiting the spread of infection compared with more naïve assumptions about the network of animal movements. This impact is generally greater for the more rapidly spreading infection (Fig. 2D); when individual identity is lost there are more frequent short stays on a farm (SI Text), and hence the infection is more likely to escape to new farms before recovery. In contrast, for the true pattern of movements, farms often act as bottle-necks for ...
Citations
... Besides the innate history and natural science of any disease, at-risk populations' demographic characteristics play a vital role in the type and intensity of interventive measures necessary to curb it [9][10][11]. Hence, disease knowledge is usually considered the first approach to any implementable health mitigation strategy [12,13], increasing public awareness of preventive measures to curb transmission. ...
Coronavirus disease 2019 (COVID-19) pandemic, caused by the Severe Acute Coronavirus 2 (SARS-CoV-2), is a global health threat with extensive misinformation and conspiracy theories. Therefore, this study investigated the knowledge, attitude and perception of sub-Saharan Africans (SSA) on COVID-19 during the exponential phase of the pandemic. In this cross-sectional survey, self-administered web-based questionnaires were distributed through several online platforms. A total of 1046 respondents from 35 SSA countries completed the survey. The median age was 33 years (18–76 years) and about half (50.5%) of them were males. More than 40% across all socio-demographic categories except the Central African region (21.2%), vocational/secondary education (28.6%), student/unemployed (35.5%), had high COVID-19 knowledge score. Socio-demographic factors and access to information were associated with COVID-19 knowledge. Bivariate analysis revealed that independent variables, including the region of origin, age, gender, education and occupation, were significantly (p < 0.05) associated with COVID-19 knowledge. Multivariate analysis showed that residing in East (odds ratio [OR]: 7.9, 95% confidence interval (CI): 4.7–14, p < 0.001), Southern (OR: 3.7, 95% CI: 2.1–6.5, p < 0.001) and West (OR: 3.9, 95% CI: 2.9–5.2, p < 0.001) Africa was associated with high COVID-19 knowledge level. Apart from East Africa (54.7%), willingness for vaccine acceptance across the other SSA regions was <40%. About 52%, across all socio-demographic categories, were undecided. Knowledge level, region of origin, age, gender, marital status and religion were significantly (p < 0.05) associated with COVID-19 vaccine acceptance. About 67.4% were worried about contracting SARS-CoV-2, while 65.9% indicated they would consult a health professional if exposed. More than one-third of the respondents reported that their governments had taken prompt measures to tackle the pandemic. Despite high COVID-19 knowledge in our study population, most participants were still undecided regarding vaccination, which is critical in eliminating the pandemic. Therefore, extensive, accurate, dynamic and timely education in this aspect is of ultimate priority.
... In a metapopulation network, nodes represent subpopulations such as communities, cities, or countries, whereas edges between nodes describe human mobility between two subpopulations and the edge weights characterize the scale or strength of human mobility 20 . Epidemic spreading among the subpopulations can be modeled as reaction-diffusion and reaction-commuting processes [21][22][23][24][25] , where the reaction process describes the infection dynamics within the subpopulations, diffusion and commuting represent the mobility of population among the nodes. In this type of model, infected populations move and carry pathogens between the nodes, leading to an outbreak of infectious disease at the scale of the whole system. ...
In our modern time, travel has become one of the most significant factors contributing to global epidemic spreading. A deficiency in the literature is that travel has largely been treated as a Markovian process: it occurs instantaneously without any memory effect. To provide informed policies such as determining the mandatory quarantine time, the non-Markovian nature of real-world traveling must be taken into account. We address this fundamental problem by constructing a network model in which travel takes a finite time and infections can occur during the travel. We find that the epidemic threshold can be maximized by a proper level of travel, implying that travel infections do not necessarily promote spreading. More importantly, the epidemic threshold can exhibit a two-threshold phenomenon in that it can increase abruptly and significantly as the travel time exceeds a critical value. This may provide a quantitative estimation of the minimally required quarantine time in a pandemic.
... The model predicts that a small rodent population can persist in the disease. The impact of the movement of workers from one ward to another and the permanent movement of cattle from one farm to another is investigated for infection dynamics, and it has been established that the commuters who create the network links may have a significant impact on the infection spreading [710]. This metapopulation formalism was used to infer the spatiotemporal spread of dengue cases reported in Santiago de Cali (Colombia) during 2015-2016 [711]. ...
... In this way, the virus could spread from one region to another, for example by an individual travelling from a susceptible location to an infected location, acquiring the infection, and then travelling back. We preferentially sent individuals back to their home location, keeping track of where they came from, in order not to overestimate the spread [26]. We moved individuals independently of their disease status (i.e. using a multinomial distribution with probabilities based on proportions of individuals in each state). ...
The COVID-19 pandemic is challenging nations with devastating health and economic consequences. The spread of the disease has revealed major geographical heterogeneity because of regionally varying individual behaviour and mobility patterns, unequal meteorological conditions, diverse viral variants, and locally implemented non-pharmaceutical interventions and vaccination roll-out. To support national and regional authorities in surveilling and controlling the pandemic in real-time as it unfolds, we here develop a new regional mathematical and statistical model. The model, which has been in use in Norway during the first two years of the pandemic, is informed by real-time mobility estimates from mobile phone data and laboratory-confirmed case and hospitalisation incidence. To estimate regional and time-varying transmissibility, case detection probabilities, and missed imported cases, we developed a novel sequential Approximate Bayesian Computation method allowing inference in useful time, despite the high parametric dimension. We test our approach on Norway and find that three-week-ahead predictions are precise and well-calibrated, enabling policy-relevant situational awareness at a local scale. By comparing the reproduction numbers before and after lockdowns, we identify spatially heterogeneous patterns in their effect on the transmissibility, with a stronger effect in the most populated regions compared to the national reduction estimated to be 85% (95% CI 78%-89%). Our approach is the first regional changepoint stochastic metapopulation model capable of real time spatially refined surveillance and forecasting during emergencies.
... While most frequently focused on parasites, analyses developed for food webs have also yielded profound insight into disease ecosystems (e.g., [12,[19][20][21]) and suggested ways to discover how targeted management might interrupt interspecies disease transmission networks (e.g., [22]). Methods from the study of metapopulations have also been leveraged with great success, looking at disease outbreaks among mostly isolated populations (re)introduced by migration and/or travel (e.g., [23][24][25]). Together, these perspectives have provided a more diverse and powerful toolkit for characterizing and predicting disease dynamics. ...
The realization that ecological principles play an important role in infectious disease dynamics has led to a renaissance in epidemiological theory. Ideas from ecological succession theory have begun to inform an understanding of the relationship between the individual microbiome and health but have not yet been applied to investigate broader, population-level epidemiological dynamics. We consider human hosts as habitat and apply ideas from succession to immune memory and multi-pathogen dynamics in populations. We demonstrate that ecologically meaningful life history characteristics of pathogens and parasites, rather than epidemiological features alone, are likely to play a meaningful role in determining the age at which people have the greatest probability of being infected. Our results indicate the potential importance of microbiome succession in determining disease incidence and highlight the need to explore how pathogen life history traits and host ecology influence successional dynamics. We conclude by exploring some of the implications that inclusion of successional theory might have for understanding the ecology of diseases and their hosts.
... In this subsection, we consider a meta-population model that takes into account groups of spatially separated 'island' populations with interactions. Such models are widely used in the context of spatiotemporal disease spread [21][22][23][24][25][26][27]. A system like this can be treated as a network in which the nodes represent the meta-populations while the weighted edges between them represent the intensity of their interaction. ...
The effective reproduction number, R ( t ) , plays a key role in the study of infectious diseases, indicating the current average number of new infections caused by an infected individual in an epidemic process. Estimation methods for the time evolution of R ( t ) , using incidence data, rely on the generation interval distribution, g ( τ ), which is usually obtained from empirical data or theoretical studies using simple epidemic models. However, for systems that present heterogeneity, either on the host population or in the expression of the disease, there is a lack of data and of a suitable general methodology to obtain g ( τ ). In this work, we use mathematical models to bridge this gap. We present a general methodology for obtaining explicit expressions of the reproduction numbers and the generation interval distributions, within and between model sub-compartments provided by an arbitrary compartmental model. Additionally, we present the appropriate expressions to evaluate those reproduction numbers using incidence data. To highlight the relevance of such methodology, we apply it to the spread of COVID-19 in municipalities of the state of Rio de Janeiro, Brazil. Using two meta-population models, we estimate the reproduction numbers and the contributions of each municipality in the generation of cases in all others.
... Shirley and Rushton (2005) tried to simulate the disease spreading in different four network structures: Erdős-Rényi, regular lattices, small-world, and scale-free [177]. In this context, many researchers worked on real networks for instance: Read et al. [178] used diary based survey of 3528 individuals for the spread of infectious disease, Christakis and Fowler [179] used 744 students' contact network at Harvard University to study the influenza outbreak in 2009, Salathé et al. [180] used wireless sensor to construct interaction network among students at an American high school, Kelling et al. [181] used meta-population networks on the basis of 10000 wards in the Great Britan. Rocha et al. [182] used SIR structure on networks to find out the sexual transmitted infection of 50,185 individuals based on data extracted from 12 cities from Brazilian Internet Community. ...
Background
Viral diseases are highly widespread infections caused by viruses. These viruses are passing from one human to other humans through a certain medium. The medium might be mosquito, animal, reservoir and food, etc. Here, the population of both human and mosquito vectors are important.
Main body of the abstract
The main objectives are here to introduce the historical perspective of mathematical modeling, enable the mathematical modeler to understand the basic mathematical theory behind this and present a systematic review on mathematical modeling for four vector-borne viral diseases using the deterministic approach. Furthermore, we also introduced other mathematical techniques to deal with vector-borne diseases. Mathematical models could help forecast the infectious population of humans and vectors during the outbreak.
Short conclusion
This study will be helpful for mathematical modelers in vector-borne diseases and ready-made material in the review for future advancement in the subject. This study will not only benefit vector-borne conditions but will enable ideas for other illnesses.
... 9: 211919 capture some aspects of population structure explicitly while treating others with homogeneous approximations. For example, the popular metapopulation approach treats discrete subpopulations as homogeneous entities that interact with one-another through coupling equations of various types [8][9][10][11][12]. Another approach, the degree-based mean-field approximation, attempts to incorporate heterogeneous contact patterns into continuum models by making assumptions about the relative timescales of social network dynamics and infectious disease spread [13]. ...
Computational models of infectious disease can be broadly categorized into two types: individual-based (agent-based) or compartmental models. While there are clear conceptual distinctions between these methodologies, a fair comparison of the approaches is difficult to achieve. Here, we carry out such a comparison by building a set of compartmental metapopulation models from an agent-based representation of a real population. By adjusting the compartmental model to approximately match the dynamics of the agent-based model, we identify two key qualitative properties of the individual-based dynamics which are lost upon aggregation into metapopulations. These are (i) the local depletion of susceptibility to infection and (ii) decoupling of different regional groups due to correlation between commuting behaviours and contact rates. The first of these effects is a general consequence of aggregating small, closely connected groups (i.e. families) into larger homogeneous metapopulations. The second can be interpreted as a consequence of aggregating two distinct types of individuals: school children, who travel short distances but have many potentially infectious contacts, and adults, who travel further but tend to have fewer contacts capable of transmitting infection. Our results could be generalized to other types of correlations between the characteristics of individuals and the behaviours that distinguish them.
... Besides the innate history and natural science of any disease, at-risk populations' demographic characteristics play a vital role in the type and intensity of interventive measures necessary to curb it [9][10][11]. Hence, disease knowledge is usually considered the rst approach to any implementable health mitigation strategy [12,13], increasing public awareness of preventive measures to curb transmission. ...
Coronavirus disease 2019 (COVID-19) pandemic, caused by the Severe Acute Coronavirus 2 (SARS-CoV-2), is a global health threat with extensive misinformation and conspiracy theories. Therefore, this study investigated the knowledge, attitude and perception of sub-Saharan Africans (SSA) on COVID-19 during the exponential phase of the pandemic. In this cross-sectional survey, self-administered web-based questionnaires were distributed through several online platforms. A total of 1046 respondents from 35 SSA countries completed the survey. The median age was 33 years (18–76 years) and about half (50.5%) of them were males. More than 40% across all socio-demographic categories except participants from the Central African region (21.2%), those with vocational/secondary education (28.6%), as well as student/unemployed (35.5%), had high COVID-19 knowledge scores. Socio-demographic factors and access to information were associated with COVID-19 knowledge. Bivariate analysis revealed that independent variables, including the region of origin, age, gender, education and occupation, were significantly (p < 0.05) associated with COVID-19 knowledge. Multivariate analysis showed that residing in East (odds ratio [OR]: 7.9, 95% confidence interval (CI): 4.7–14, p < 0.001), Southern (OR: 3.7, 95% CI: 2.1–6.5, p < 0.001) and West (OR: 3.9, 95% CI: 2.9–5.2, p < 0.001) Africa was associated with high COVID-19 knowledge level. Apart from East Africa (54.7%), willingness for vaccine acceptance across the other SSA regions was < 40%. About 52%, across all socio-demographic categories, were undecided. Knowledge level, region of origin, age, gender, marital status and religion were significantly (p < 0.05) associated with COVID-19 vaccine acceptance. About 67.4% were worried about contracting SARS-CoV-2, while 65.9% indicated they would consult a health professional if exposed. More than one-third of the respondents reported that their governments had taken prompt measures to tackle the pandemic. Despite high COVID-19 knowledge in our study population, most participants were still undecided regarding vaccination, which is critical in eliminating the pandemic. Therefore, extensive, accurate, dynamic and timely education in this aspect is of ultimate priority.
... The development of advanced metapopulation network models coincides with the pattern of increasingly frequent epidemics in recent years. Keeling et al. (2010) initiated the stream of network models for the spatial spreading of infectious disease in the commuter-to-work networks. They addressed that the infection dynamics in the recurrent commute networks were significantly different from their counterparts in the kernel and random mobility networks. ...
... These models assume that passengers follow certain movement distributions, such as random walks over the network. Nevertheless, prior work has revealed that recurring commute trips (i.e., individuals take the fixed routes back and forth) significantly impact the disease dynamics and the derived control policies (Keeling et al., 2010). Therefore, random mobility models are unsuitable for public transit applications and developing safe and effective transit control policies based on movement data. ...
During a pandemic such as COVID-19, managing public transit effectively becomes a critical policy decision. On the one hand, efficient transportation plays a pivotal role in enabling the movement of essential workers and keeping the economy moving. On the other hand, public transit can be a vector for disease propagation due to travelers’ proximity within shared and enclosed spaces. Without strategic preparedness, mass transit facilities are potential hotbeds for spreading infectious diseases. Thus, transportation agencies face a complex trade-off when developing context-specific operating strategies for public transit. This work provides a network-based analysis framework for understanding this trade-off, as well as tools for calculating targeted commute restrictions under different policy constraints, e.g., regarding public health considerations (limiting infection levels) and economic activity (limiting the reduction in travel). The resulting plans ensure that the traffic flow restrictions imposed on each route are adaptive to the time-varying epidemic dynamics. A case study based on the COVID-19 pandemic reveals that a well-planned subway system in New York City can sustain 88% of transit flow while reducing the risk of disease transmission by 50% relative to fully-loaded public transit systems. Transport policy-makers can exploit this optimization-based framework to address safety-and-mobility trade-offs and make proactive transit management plans during an epidemic outbreak.
