Vector-borne diseases models with residence times – A Lagrangian perspective

Bichara, Derdei; Castillo‐Chavez, Carlos

doi:10.1016/j.mbs.2016.09.006

Cited by 52 publications

(56 citation statements)

References 55 publications

(127 reference statements)

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“…The effects of various forms of heterogeneity on the basic reproduction number has been explored in ref. 23, and we have found, for example, that the irreducibility of the residence time matrix P is no longer sufficient to ensure a sharp threshold property, albeit the irreducibility of the host-vector network configuration is necessary for such property (23).…”

Section: A Lagrangian Approach Of Modeling Mobility and Infectious DImentioning

confidence: 98%

“…3 and System 3 illustrate the approach. A Lagrangian model based on residence times has been proposed recently for vector-borne diseases like Dengue, malaria, and Zika (23). The appropriateness of the Lagrangian approach for the study of the dynamics of vector-borne diseases lies also in its assessment of the life-history specifics of the vector involved (75).…”

Section: A Lagrangian Approach Of Modeling Mobility and Infectious DImentioning

confidence: 99%

“…The model in ref. 23 The infectiousness of human to mosquitoes is β vh , whereas the infectiousness of mosquitoes to humans is given by β hv . The host recovery and natural mortality rates are given, respectively, by γ and µ.…”

Section: A Lagrangian Approach Of Modeling Mobility and Infectious DImentioning

confidence: 99%

“…Patches are connected by their ability to transfer relevant information between one another, which, in the context of disease dynamics, is modeled by the ability of individuals to move between patches. Patches may be constructed (defined) by species (human and mosquito) with movement explicitly modeled via patch-specific residence times and under a framework that sees disease dynamics as the result of location-dependent interactions (23,24).…”

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confidence: 99%

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Perspectives on the role of mobility, behavior, and time scales in the spread of diseases

Castillo‐Chavez

Bichara

Morin

2016

Proc. Natl. Acad. Sci. U.S.A.

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The dynamics, control, and evolution of communicable and vectorborne diseases are intimately connected to the joint dynamics of epidemiological, behavioral, and mobility processes that operate across multiple spatial, temporal, and organizational scales. The identification of a theoretical explanatory framework that accounts for the pattern regularity exhibited by a large number of host-parasite systems, including those sustained by host-vector epidemiological dynamics, is but one of the challenges facing the coevolving fields of computational, evolutionary, and theoretical epidemiology. Host-parasite epidemiological patterns, including epidemic outbreaks and endemic recurrent dynamics, are characteristic to well-identified regions of the world; the result of processes and constraints such as strain competition, host and vector mobility, and population structure operating over multiple scales in response to recurrent disturbances (like El Niño) and climatological and environmental perturbations over thousands of years. It is therefore important to identify and quantify the processes responsible for observed epidemiological macroscopic patterns: the result of individual interactions in changing social and ecological landscapes. In this perspective, we touch on some of the issues calling for the identification of an encompassing theoretical explanatory framework by identifying some of the limitations of existing theory, in the context of particular epidemiological systems. Fostering the reenergizing of research that aims at disentangling the role of epidemiological and socioeconomic forces on disease dynamics, better understood as complex adaptive systems, is a key aim of this perspective.infectious disease | risk | complex adaptive systems | mobility | behavior

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Section: A Lagrangian Approach Of Modeling Mobility and Infectious DImentioning

confidence: 98%

Section: A Lagrangian Approach Of Modeling Mobility and Infectious DImentioning

confidence: 99%

Section: A Lagrangian Approach Of Modeling Mobility and Infectious DImentioning

confidence: 99%

mentioning

confidence: 99%

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Perspectives on the role of mobility, behavior, and time scales in the spread of diseases

Castillo‐Chavez

Bichara

Morin

2016

Proc. Natl. Acad. Sci. U.S.A.

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“…We define a sink to be a community where transmission is not self-sustaining [16]; in this community, ℛ " < 1. To model mobility/travel, we use a generalized Lagrangian approach proposed by Castillo-Chavez and colleagues [17][18][19]. This modeling approach allows individuals to remain identifiable as residents of their home community when they are in other communities.…”

Section: Introductionmentioning

confidence: 99%

Source-sink dynamics could sustain HIV epidemics in rural communities in sub-Saharan Africa: the case of Malawi

Okano

Sharp

Palk

et al. 2018

Preprint

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Background: Approximately 25.5 million individuals are infected with HIV in sub-Saharan Africa (SSA).Epidemics in this region are generalized, show substantial geographic variation in prevalence, and are driven by heterosexual transmission; populations are highly mobile. We propose that generalized HIV epidemics should be viewed as a series of micro-epidemics occurring in multiple connected communities. Using a mathematical model, we test the hypothesis that travel can sustain HIV micro-epidemics in communities where transmission is too low to be self-sustaining. We use Malawi as a case study. Methods:We first conduct a mapping exercise to visualize geographic variation in HIV prevalence and population-level mobility. We construct maps by spatially interpolating georeferenced HIV-testing and mobility data from a nationally representative population-level survey: the 2015-16 Malawi Demographic and Health Survey. To test our hypothesis, we construct a novel HIV epidemic model that includes three transmission pathways: resident-to-resident, visitor-caused and travel-related. The model consists of communities functioning as "sources" and "sinks". A community is a source if transmission is high enough to be self-sustaining, and a sink if it is not.Results: HIV prevalence ranges from zero to 27%. Mobility is high, 27% of the population took a trip lasting at least a month in the previous year. Prevalence is higher in urban centers than rural areas, but long-duration travel is higher in rural areas than urban centers. We show that a source-community can sustain a micro-epidemic in a sink-community, but only if specific epidemiological and demographic threshold conditions are met. The threshold depends upon the level of transmission in the source-and sink-communities, as well as the relative sizes of the two communities. The larger the source than the sink, the lower transmission in the source-community needs to be for sustainability. Discussion:Our results support our hypothesis, and suggest that it may be rather easy for large urban communities to sustain HIV micro-epidemics in small rural communities; this may be occurring in northern Malawi. Visitor-generated and travel-related transmission may also be sustaining micro-epidemics in rural communities in other SSA countries with highly-mobile populations. It is essential to consider mobility when developing HIV elimination strategies.

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Epidemiological Models Incorporating Mobility, Behavior, and Time Scales

Brauer

Castillo‐Chavez

Feng

2019

Texts in Applied Mathematics

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The work of Eubank et al. [24], Sara del Valle et al. [44], Chowell et al. [7, 18], and Castillo-Chavez and Song [13] have highlighted the impact of modified modeling approaches that incorporate heterogeneous modes of mobility within variable environments in order to study their impact on the dynamics of infectious diseases. Castillo-Chavez and Song [13], for example, proceeded to highlight a Lagrangian perspective, that is, the use of models that keep track at all times of the identity of each individual. This approach was used to study the consequences of deliberate efforts to transmit smallpox in a highly populated city, involving transient subpopulations and the availability of massive modes of public transportation. Here, a multi-group epidemic Lagrangian framework where mobility and the risk of infection are functions of patch residence time and local environmental risk is introduced. This Lagrangian approach has been used within classical contact epidemiological (that is, transmission is due to "contacts" between individuals) formulations in the context of a possible deliberate release of biological agents [2, 13]. The Lagrangian approach is introduced here as a modeling approach that explicitly avoids the assignment of heterogeneous contact rates to individuals. The use of contacts or activity levels and the view that transmission is due to collisions between individuals has a long history and it is conceptually consistent with the way we envision disease transmission between susceptible and infectious individuals. However, contacts are hard to define and consequently, at least in the context of communicable diseases, impossible to measure in various settings. Is it possible to capture interactions of individual mathematically in a way different from the notion of contacts? The approach that is proposed focuses on the use of modeling frameworks that involve patches/environments defined or characterized by risks of infection that are functions of the time spent in each environment/patch. These patches/environments may or may not have permanent hosts and they may be used to account for places of "transitory" residence like mass transportation systems or

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Vector-borne diseases models with residence times – A Lagrangian perspective

Cited by 52 publications

References 55 publications

Perspectives on the role of mobility, behavior, and time scales in the spread of diseases

Perspectives on the role of mobility, behavior, and time scales in the spread of diseases

Source-sink dynamics could sustain HIV epidemics in rural communities in sub-Saharan Africa: the case of Malawi

Epidemiological Models Incorporating Mobility, Behavior, and Time Scales

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