Mathematical models for predicting human mobility in the context of infectious disease spread: introducing the impedance model

Informing policy via dynamic models: Cholera in Haiti

Public health decisions must be made about when and how to implement interventions to control an infectious disease epidemic. These decisions should be informed by data on the epidemic as well as current understanding about the transmission dynamics. Such decisions can be posed as statistical questions about scientifically motivated dynamic models. Thus, we encounter the methodological task of building credible, data-informed decisions based on stochastic, partially observed, nonlinear dynamic models. This necessitates addressing the tradeoff between biological fidelity and model simplicity, and the reality of misspecification for models at all levels of complexity. We assess current methodological approaches to these issues via a case study of the 2010-2019 cholera epidemic in Haiti. We consider three dynamic models developed by expert teams to advise on vaccination policies. We evaluate previous methods used for fitting these models, and we demonstrate modified data analysis strategies leading to improved statistical fit. Specifically, we present approaches for diagnosing model misspecification and the consequent development of improved models. Additionally, we demonstrate the utility of recent advances in likelihood maximization for high-dimensional nonlinear dynamic models, enabling likelihood-based inference for spatiotemporal incidence data using this class of models. Our workflow is reproducible and extendable, facilitating future investigations of this disease system.

Comparative Analysis of Geolocation Information through Mobile-Devices under Different COVID-19 Mobility Restriction Patterns in Spain

The COVID-19 pandemic is changing the world in unprecedented and unpredictable ways. Human mobility, being the greatest facilitator for the spread of the virus, is at the epicenter of this change. In order to study mobility under COVID-19, to evaluate the efficiency of mobility restriction policies, and to facilitate a better response to future crisis, we need to understand all possible mobility data sources at our disposal. Our work studies private mobility sources, gathered from mobile-phones and released by large technological companies. These data are of special interest because, unlike most public sources, it is focused on individuals rather than on transportation means. Furthermore, the sample of society they cover is large and representative. On the other hand, these data are not directly accessible for anonymity reasons. Thus, properly interpreting its patterns demands caution. Aware of that, we explore the behavior and inter-relations of private sources of mobility data in the context of Spain. This country represents a good experimental setting due to both its large and fast pandemic peak and its implementation of a sustained, generalized lockdown. Our work illustrates how a direct and naive comparison between sources can be misleading, as certain days (e.g., Sundays) exhibit a directly adverse behavior. After understanding their particularities, we find them to be partially correlated and, what is more important, complementary under a proper interpretation. Finally, we confirm that mobile-data can be used to evaluate the efficiency of implemented policies, detect changes in mobility trends, and provide insights into what new normality means in Spain.

Kernel-based formulation of intervening opportunities for spatial interaction modelling

Understanding spatial interactions such as human mobility has been one of the main analytical themes in geography, spatial economics, and traffic engineering for a long time. The intervening opportunities models, including the radiation model, provide a framework to elucidate spatial interactions generated by an individual's distance-ordered decision-making process. However, such classical definitions of intervening opportunities have often failed to predict realistic flow volumes, particularly for short-distance flows. To overcome this problem, we have proposed a new formulation of intervening opportunities with a kernel function to introduce a fuzziness in spatial search behaviours of destinations, to develop a new variant of the radiation model. The mobility patterns resulting from the modified radiation model that included kernel-based intervening opportunities outperformed the original radiation model when fitted to four datasets of inter-regional flows.

Geo-Epidemiology of Malaria at the Health Area Level, Dire Health District, Mali, 2013-2017

Background: According to the World Health Organization, there were more than 228 million cases of malaria globally in 2018, with 93% of cases occurring in Africa; in Mali, a 13% increase in the number of cases was observed between 2015 and 2018; this study aimed to evaluate the impact of meteorological and environmental factors on the geo-epidemiology of malaria in the health district of Dire, Mali. Methods: Meteorological and environmental variables were synthesized using principal component analysis and multiple correspondence analysis, the relationship between malaria incidence and synthetic indicators was determined using a multivariate general additive model; hotspots were detected by SaTScan. Results: Malaria incidence showed high inter and intra-annual variability; the period of high transmission lasted from September to February; health areas characterized by proximity to the river, propensity for flooding and high agricultural yield were the most at risk, with an incidence rate ratio of 2.21 with confidence intervals (95% CI: 1.85-2.58); malaria incidence in Dire declined from 120 to 20 cases per 10,000 person-weeks between 2013 and 2017. Conclusion: The identification of areas and periods of high transmission can help improve malaria control strategies.

Impact of human mobility on the transmission dynamics of infectious diseases

Spatial heterogeneity is an important aspect to be studied in infectious disease models. It takes two forms: one is local, namely diffusion in space, and other is related to travel. With the advancement of transportation system, it is possible for diseases to move from one place to an entirely separate place very quickly. In a developing country like India, the mass movement of large numbers of individuals creates the possibility of spread of common infectious diseases. This has led to the study of infectious disease model to describe the infection during transport. An SIRS-type epidemic model is formulated to illustrate the dynamics of such infectious disease propagation between two cities due to population dispersal. The most important threshold parameter, namely the basic reproduction number, is derived, and the possibility of existence of backward bifurcation is examined, as the existence of backward bifurcation is very unsettling for disease control and it is vital to know from modeling analysis when it can occur. It is shown that dispersal of populations would make the disease control difficult in comparison with nondispersal case. Optimal vaccination and treatment controls are determined. Further to find the best cost-effective strategy, cost-effectiveness analysis is also performed. Though it is not a case study, simulation work suggests that the proposed model can also be used in studying the SARS epidemic in Hong Kong, 2003.

Replacement, Refinement, and Reduction in Animal Studies With Biohazardous Agents

Animal models are critical to the advancement of our knowledge of infectious disease pathogenesis, diagnostics, therapeutics, and prevention strategies. The use of animal models requires thoughtful consideration for their well-being, as infections can significantly impact the general health of an animal and impair their welfare. Application of the 3Rs—replacement, refinement, and reduction—to animal models using biohazardous agents can improve the scientific merit and animal welfare. Replacement of animal models can use in vitro techniques such as cell culture systems, mathematical models, and engineered tissues or invertebrate animal hosts such as amoeba, worms, fruit flies, and cockroaches. Refinements can use a variety of techniques to more closely monitor the course of disease. These include the use of biomarkers, body temperature, behavioral observations, and clinical scoring systems. Reduction is possible using advanced technologies such as in vivo telemetry and imaging, allowing longitudinal assessment of animals during the course of disease. While there is no single method to universally replace, refine, or reduce animal models, the alternatives and techniques discussed are broadly applicable and they should be considered when infectious disease animal models are developed.

Hosts mobility and spatial spread of Rickettsia rickettsii

There are a huge number of pathogens with multi-component transmission cycles, involving amplifier hosts, vectors or complex pathogen life cycles. These complex systems present challenges in terms of modeling and policy development. A lethal tick-borne infectious disease, the Brazilian Spotted Fever (BSF), is a relevant example of that. The current increase of human cases of BSF has been associated with the presence and expansion of the capybara Hydrochoerus hydrochaeris, amplifier host for the agent Rickettsia rickettsii and primary host for the tick vector Amblyomma sculptum. We introduce a stochastic dynamical model that captures the spatial distribution of capybaras and ticks to gain a better understanding of the spatial spread of the R. rickettsii and potentially predict future epidemic outcomes. We implemented a reaction-diffusion process in which individuals were divided into classes denoting their state with respect to the disease. The model considered bidirectional movements between base and destination locations limited by the carrying capacity of the environment. We performed systematic stochastic simulations and numerical analysis of the model and investigate the impact of potential interventions to mitigate the spatial spread of the disease. The mobility of capybaras and their attached ticks was significantly influenced by the birth rate of capybaras and therefore, disease propagation velocity was higher in places with higher carrying capacity. Some geographical barriers, generated for example by riparian reforesting, can impede the spatial spread of BSF. The results of this work will allow the formulation of public actions focused on the prevention of BSF human cases.

Complex systems as the Brazilian Spotted Fever (BSF), present challenges in terms of modeling and policy development. BSF human cases have been associated with the presence and expansion of the capybara Hydrochoerus hydrochaeris, amplifier host for the agent Rickettsia rickettsii and primary host for the tick vector Amblyomma sculptum. We developed a reaction-diffusion system for the spread of BSF by considering the spatial structure and migration of amplifier hosts to gain a better understanding of the spatial spread of the R. rickettsii and potentially predict future epidemic outcomes. We performed stochastic simulations and numerical analysis to investigate the impact of potential interventions to mitigate the spatial spread of the disease. Our results indicate that as we vary the amount of capybaras’ food sources, the velocity at which the disease advances is roughly proportional to the carrying capacity, hence proportional to the local risk of zoonotic infection. Some geographical barriers, generated for example by riparian reforesting, can generate positive ecological impacts and can impede the spread of BSF to humans.

Infectious disease implications of large-scale migration of Venezuelan nationals

Background

The ongoing economic and political crisis in Venezuela has resulted in a collapse of the healthcare system and the re-emergence of previously controlled or eliminated infectious diseases. There has also been an exodus of Venezuelan international migrants in response to the crisis. We sought to describe the infectious disease risks faced by Venezuelan nationals and assess the international mobility patterns of the migrant population.

Methods

We synthesized data on recent infectious disease events in Venezuela and among international migrants from Venezuela, as well as on current country of residence among the migrant population. We used passenger-level itinerary data from the International Air Transport Association to evaluate trends in outbound air travel from Venezuela over time. We used two parameter-free mobility models, the radiation and impedance models, to estimate the expected population flows from Venezuelan cities to other major Latin American and Caribbean cities.

Results

Outbreaks of measles, diphtheria and malaria have been reported across Venezuela and other diseases, such as HIV and tuberculosis, are resurgent. Changes in migration in response to the crisis are apparent, with an increase in Venezuelan nationals living abroad, despite an overall decline in the number of outbound air passengers. The two models predicted different mobility patterns, but both highlighted the importance of Colombian cities as destinations for migrants and also showed that some migrants are expected to travel large distances. Despite the large distances that migrants may travel internationally, outbreaks associated with Venezuelan migrants have occurred primarily in countries proximate to Venezuela.

Conclusions

Understanding where international migrants are relocating is critical, given the association between human mobility and the spread of infectious diseases. In data-limited situations, simple models can be useful for providing insights into population mobility and may help identify areas likely to receive a large number of migrants.