Human movement, cooperation and the effectiveness of coordinated vector control strategies

A 'Portfolio of Model Approximations' approach to understanding invasion success with vector-borne disease

The central challenge of mathematical modeling of real-world systems is to strike an appropriate balance between insightful abstraction and detailed accuracy. Models in mathematical epidemiology frequently tend to either extreme, focusing on analytically provable boundaries in simplified, mass-action approximations, or else relying on calculated numerical solutions and computational simulation experiments to capture nuance and details specific to a particular host-disease system. We propose that there is value in an approach striking a slightly different compromise in which a detailed but analytically difficult system is modeled with careful detail, but then abstraction is applied to the results of numerical solutions to that system, rather than to the biological system itself. In this 'Portfolio of Model Approximations' approach, multiple levels of approximation are used to analyze the model at different scales of complexity. While this method has the potential to introduce error in the translation from model to model, it also has the potential to produce generalizable insight for the set of all similar systems, rather than isolated, tailored results that must be started anew for each next question. In this paper, we demonstrate this process and its value with a case study from evolutionary epidemiology. We consider a modified Susceptible-Infected-Recovered model for a vector-borne pathogen affecting two annually reproducing hosts. From observing patterns in simulations of the system and exploiting basic epidemiological properties, we construct two approximations of the model at different levels of complexity that can be treated as hypotheses about the behavior of the model. We compare the predictions of the approximations to the simulated results and discuss the trade-offs between accuracy and abstraction. We discuss the implications for this particular model, and in the context of mathematical biology in general.

A general modeling framework for exploring the impact of individual concern and personal protection on vector-borne disease dynamics

BACKGROUND

As climate variability and extreme weather events associated with climate change become more prevalent, public health authorities can expect to face an expanding spectrum of vector-borne diseases with increasing incidence and geographical spread. Common interventions include the use of larvicides and adulticides, as well as targeted communications to increase public awareness regarding the need for personal protective measures, such as mosquito repellant, protective clothing, and mosquito nets. Here, we propose a simplified compartmental model of mosquito-borne disease dynamics that incorporates the use of personal protection against mosquito bites influenced by two key individual-level behavioral drivers-concern for being bitten by mosquitos as a nuisance and concern for mosquito-borne disease transmission.

METHODS

We propose a modified compartmental model that describes the dynamics of vector-borne disease spread in a naïve population while considering the public demand for community-level control and, importantly, the effects of personal-level protection on population-level outbreak dynamics. We consider scenarios at low, medium, and high levels of community-level vector control, and at each level, we consider combinations of low, medium, and high levels of motivation to use personal protection, namely concern for disease transmission and concern for being bitten in general.

RESULTS

When there is very little community-level vector control, nearly the entire population is quickly infected, regardless of personal protection use. When vector control is at an intermediate level, both concerns that motivate the use of personal protection play an important role in reducing disease burden. When authorities have the capacity for high-level community vector control through pesticide use, the motivation to use personal protection to reduce disease transmission has little additional effect on the outbreak.

CONCLUSIONS

While results show that personal-level protection alone is not enough to significantly impact an outbreak, personal protective measures can significantly reduce the severity of an outbreak in conjunction with community-level control. Furthermore, the model provides insight for targeting public health messaging to increase the use of personal protection based on concerns related to being bitten by mosquitos or vector-borne disease transmission.

How public reaction to disease information across scales and the impacts of vector control methods influence disease prevalence and control efficacy

With the development of social media, the information about vector-borne disease incidence over broad spatial scales can cause demand for local vector control before local risk exists. Anticipatory intervention may still benefit local disease control efforts; however, infection risks are not the only focal concerns governing public demand for vector control. Concern for environmental contamination from pesticides and economic limitations on the frequency and magnitude of control measures also play key roles. Further, public concern may be focused more on ecological factors (i.e., controlling mosquito populations) or on epidemiological factors (i.e., controlling infection-carrying mosquitoes), which may lead to very different control outcomes. Here we introduced a generic Ross-MacDonald model, incorporating these factors under three spatial scales of disease information: local, regional, and global. We tailored and parameterized the model for Zika virus transmitted by Aedes aegypti mosquito. We found that sensitive reactivity caused by larger-scale incidence information could decrease average human infections per patch breeding capacity, however, the associated increase in total control effort plays a larger role, which leads to an overall decrease in control efficacy. The shift of focal concerns from epidemiological to ecological risk could relax the negative effect of the sensitive reactivity on control efficacy when mosquito breeding capacity populations are expected to be large. This work demonstrates that, depending on expected total mosquito breeding capacity population size, and weights of different focal concerns, large-scale disease information can reduce disease infections without lowering control efficacy. Our findings provide guidance for vector-control strategies by considering public reaction through social media.

The dynamics of evolutionary rescue from a novel pathogen threat in a host metapopulation

When a novel disease strikes a naïve host population, there is evidence that the most immediate response can involve host evolution while the pathogen remains relatively unchanged. When hosts also live in metapopulations, there may be critical differences in the dynamics that emerge from the synergy among evolutionary, ecological, and epidemiological factors. Here we used a Susceptible-Infected-Recovery model to explore how spatial and temporal ecological factors may drive the epidemiological and rapid-evolutionary dynamics of host metapopulations. For simplicity, we assumed two host genotypes: wild type, which has a positive intrinsic growth rate in the absence of disease, and robust type, which is less likely to catch the infection given exposure but has a lower intrinsic growth rate in the absence of infection. We found that the robust-type host would be strongly selected for in the presence of disease when transmission differences between the two types is large. The growth rate of the wild type had dual but opposite effects on host composition: a smaller increase in wild-type growth increased wild-type competition and lead to periodical disease outbreaks over the first generations after pathogen introduction, while larger growth increased disease by providing more susceptibles, which increased robust host density but decreased periodical outbreaks. Increased migration had a similar impact as the increased differential susceptibility, both of which led to an increase in robust hosts and a decrease in periodical outbreaks. Our study provided a comprehensive understanding of the combined effects among migration, disease epidemiology, and host demography on host evolution with an unchanging pathogen. The findings have important implications for wildlife conservation and zoonotic disease control.

Coordination among neighbors improves the efficacy of Zika control despite economic costs

Emerging mosquito-borne viruses like Zika, dengue, and chikungunya pose a major threat to public health, especially in low-income regions of Central and South America, southeast Asia, and the Caribbean. Outbreaks of these diseases are likely to have long-term social and economic consequences due to Zika-induced congenital microcephaly and other complications. Larval control of the container-inhabiting mosquitoes that transmit these infections is an important tool for mitigating outbreaks. However, metapopulation theory suggests that spatiotemporally uneven larvicide treatment can impede control effectiveness, as recolonization compensates for mortality within patches. Coordinating the timing of treatment among patches could therefore substantially improve epidemic control, but we must also consider economic constraints, since coordination may have costs that divert resources from treatment. To inform practical disease management strategies, we ask how coordination among neighbors in the timing of mosquito control efforts influences the size of a mosquito-borne infectious disease outbreak under the realistic assumption that coordination has costs. Using an SIR (Susceptible-Infectious-Recovered)/metapopulation model of mosquito and disease dynamics, we examine whether sharing surveillance information and coordinating larvicide treatment among neighboring patches reduces human infections when incorporating coordination costs. We examine how different types of coordination costs and different surveillance methods jointly influence the effectiveness of larval control. We find that the effect of coordination depends on both costs and the type of surveillance used to inform treatment. With epidemiological surveillance, coordination improves disease outcomes, even when costly. With demographic surveillance, coordination either improves or hampers disease control, depending on the type of costs and surveillance sensitivity. Our results suggest coordination among neighbors can improve management of mosquito-borne epidemics under many, but not all, assumptions about costs. Therefore, estimating coordination costs is an important step for most effectively applying metapopulation theory to strategies for managing outbreaks of mosquito-borne viral infections.

A generic arboviral model framework for exploring trade-offs between vector control and environmental concerns

Effective public health measures must balance potentially conflicting demands from populations they serve. In the case of infectious disease risks from mosquito-borne infections, such as Zika virus, public concern about the pathogen may be counterbalanced by public concern about environmental contamination from chemical agents used for vector control. Here we introduce a generic framework for modeling how the spread of an infectious pathogen might lead to varying public perceptions, and therefore tolerance, of both disease risk and pesticide use. We consider how these dynamics might impact the spread of a vector-borne disease. We tailor and parameterize our model for direct application to Zika virus as spread by Aedes aegypti mosquitoes, though the framework itself has broad applicability to any arboviral infection. We demonstrate how public risk perception of both disease and pesticides may drastically impact the spread of a mosquito-borne disease in a susceptible population. We conclude that models hoping to inform public health decision making about how best to mitigate arboviral disease risks should explicitly consider the potential public demand for, or rejection of, chemical control of mosquito populations.

Correlation of the basic reproduction number (R0) and eco-environmental variables in Colombian municipalities with chikungunya outbreaks during 2014-2016

Chikungunya virus (CHIKV) emerged in Colombia in 2014 into a population presumed fully susceptible. This resulted in a quick and intense spread across Colombia, resulting in an epidemic that affected an estimated 450,000 people. The reported Colombian cases accounted for over 49% of all the cases reported to the PAHO. Eco-environmental factors are known to be associated with the spread of arboviruses such as CHIKV, and likely contribute to the differences in transmission profiles that were observed across several municipalities. To determine the association of eco-environmental factors and CHIKV, the basic reproduction number (R₀) in 85 municipalities, which accounted for 65.6% of reported CHIKV cases in Colombia, was estimated. Estimates of R₀ ranged from 1 to 9, where over 76% of municipalities had R₀ values between 1 and 2. When we looked at the distribution of R₀, the cumulative proportions were 20% with R₀>2, 14% with R₀>3, and 9% with R₀>4. Next, we determined that there were different patterns of correlation between environmental and/or ecological variables and R₀ when we considered different R₀ lower-thresholds. Broadly, we found that temperature-related variables are significantly and positively correlated to R₀ regardless of the lower threshold, while other variables like duration of outbreak and size of the urban area are inversely related to R₀. Specifically, we conclude that high values of temperature-related variables where R₀ > 1 will result in a fast growth of cases in a shorter time period (with faster cessation of outbreak transmission) but will result overall in a fewer total cases compared to outbreak areas (R₀ > 1, but classified as lower). Thus, in the absence of vector control, a less explosive outbreak may be more advantageous for the virus in terms of transmission.

Chikungunya virus emerged in Colombia in 2014 into a presumed fully susceptible population and rapidly spread in the country. Numerous municipalities were differently affected by this virus across the country. The main purpose of this work was understanding why those differences were produced and, in turn, what are the variables addressing such differences. For this purpose, we estimated for 85 municipalities the basic reproduction number (R₀), a crucial parameter to understand epidemics that is expressed as the number of secondary cases produced by a primary case. Such parameter was correlated with numerous variables resulting evident a crucial role of temperature in the increase of R₀. Interestingly, other variables like size of the urban area and cases showed to be negatively correlated with R₀. Results shows that high temperatures produce high R₀, but those municipalities that showed high R₀ showed an explosive epidemic with faster increase of cases that ceased equally fast, so the duration of epidemic is short producing small amount of cases. In this way, more cases are expected with municipalities with lower values of R₀, which is suitably explained by the tortoise-hare model, where the less explosive outbreak results to be more advantageous for the virus.

Contrasting the value of targeted versus area-wide mosquito control scenarios to limit arbovirus transmission with human mobility patterns based on different tropical urban population centers

Vector control is still our primary intervention for both prevention and mitigation of epidemics of many vector-borne diseases. Efficiently targeting control measures is important since control can involve substantial economic costs. Targeting is not always straightforward, as transmission of vector-borne diseases is affected by various types of host movement. Here we assess how taking daily commuting patterns into consideration can help improve vector control efforts. We examine three tropical urban centers (San Juan, Recife, and Jakarta) that have recently been exposed to Zika and/or dengue infections and consider whether the distribution of human populations and resulting commuting flows affects the optimal scale at which control interventions should be implemented. We developed a stochastic, spatial model and investigated four control scenarios. The scenarios differed in the spatial extent of their implementation and were: 1) a response at the level of an individual neighborhood; 2) a response targeted at a neighborhood in which infected humans were detected and the one with which it was most strongly connected by human movement; 3) a limited area-wide response where all neighborhoods within a certain radius of the focal area were included; and 4) a collective response where all participating neighborhoods implemented control. The relative effectiveness of the scenarios varied only slightly between different settings, with the number of infections averted over time increasing with the scale of implementation. This difference depended on the efficacy of control at the neighborhood level. At low levels of efficacy, the scenarios mirrored each other in infections averted. At high levels of efficacy, impact increased with the scale of the intervention. As a result, the choice between scenarios will not only be a function of the amount of effort decision-makers are willing to invest, but largely epend on the overall effectiveness of vector control approaches.

Control and prevention of Aedes-transmitted viruses, such as dengue, chikungunya, or Zika relies heavily on vector control approaches. Given the effort and cost involved in implementation of vector control, targeting of control measures is highly desirable. However, it is unclear to what extent the effectiveness of highly focal and reactive control measures depends on the commuting and movement patterns of humans. To investigate this question, we developed a model and four control scenarios that ranged from highly focal to area-wide larval control. The distribution of humans and their commuting patterns were modelled after three major tropical urban centers, San Juan, Recife, and Jakarta. We show that as implementation is applied across a wider area, a greater number of infections is averted. Critically, this only occurs if the efficacy of control at the neighborhood level is sufficiently high. A consistent outcome across the three settings was that the focal strategy was most likely to provide the best outcome at lower levels of effort, and when the efficacy of control was low. These outcomes suggest that optimal control strategies will likely have to be tailored to individual settings by decision makers and would benefit from localized cost-effectiveness modelling studies.

(Meta)population dynamics determine effective spatial distributions of mosquito-borne disease control

Recent epidemics of mosquito-borne dengue and Zika viruses demonstrate the urgent need for effective measures to control these diseases. The best method currently available to prevent or reduce the size of outbreaks is to reduce the abundance of their mosquito vectors, but there is little consensus on which mechanisms of control are most effective, or when and where they should be implemented. Although the optimal methods are likely context dependent, broadly applicable strategies for mosquito control, such as how to distribute limited resources across a landscape in times of high epidemic risk, can mitigate (re)emerging outbreaks. We used mathematical simulations to examine how the spatial distribution of larval mosquito control affects the size of disease outbreaks, and how mosquito metapopulation dynamics and demography might impact the efficacy of different spatial distributions of control. We found that the birth rate and mechanism of density-dependent regulation of mosquito populations affected the average outbreak size across all control distributions. These factors also determined whether control distributions favoring the interior or the edges of the landscape most effectively reduced human infections. Thus, understanding local mosquito population regulation and dispersion can lead to more effective control strategies.

Assessing the effects of daily commuting in two-patch dengue dynamics: A case study of Cali, Colombia

There are many infectious diseases that can be spread by daily commuting of people and dengue fever is one of them. The absence of vaccine and irregularities in ongoing vector control programs make this disease the most frequent and persistent in many tropical and subtropical regions of the world. This paper targets to access the effects of daily commuting on dengue transmission dynamics by using a deterministic two-patch model fitted to observed data gathered in Cali, Colombia where dengue fever is highly persistent and exhibits endemo-epidemic patterns. The two-patch dengue transmission model with daily communing of human residents between patches (that is, between the city and its suburban areas) is presented using the concept of residence times, which certainly affect the disease transmission rates by inducing variability in human population sizes and vectorial densities at each patch. The same modeling framework is applied to two primary scenarios (epidemic outbreaks and endemic persistence of the disease) and for each scenario two coupling cases (one-way and asymmetric commuting) with different inflow and outflow intensities are analyzed. The concept of effective vectorial density, introduced in this paper, allows to explain in very simple terms why the daily commuting affects quite differently the dengue morbidity among human residents in both patches. In particular, residents of the patch with a greater share of incoming than outgoing commuters may actually "benefit" from inflow of daily commuter by avoiding a considerable number of infections. However, residents of the patch with a greater share of outgoing than incoming commuters, especially those who stay at home patch, incur more risk of getting infected. Additionally, the model shows that daily commuting enhance the total number of human infections acquired in both patches and may even provoke an epidemic outbreak in one patch while moderately lowering the level of the disease persistence in another patch.

Human movement, cooperation and the effectiveness of coordinated vector control strategies

Vector-borne disease transmission is often typified by highly focal transmission and influenced by movement of hosts and vectors across different scales. The ecological and environmental conditions (including those created by humans through vector control programmes) that result in metapopulation dynamics remain poorly understood. The development of control strategies that would most effectively limit outbreaks given such dynamics is particularly urgent given the recent epidemics of dengue, chikungunya and Zika viruses. We developed a stochastic, spatial model of vector-borne disease transmission, allowing for movement of hosts between patches. Our model is applicable to arbovirus transmission by Aedes aegypti in urban settings and was parametrized to capture Zika virus transmission in particular. Using simulations, we investigated the extent to which two aspects of vector control strategies are affected by human commuting patterns: the extent of coordination and cooperation between neighbouring communities. We find that transmission intensity is highest at intermediate levels of host movement. The extent to which coordination of control activities among neighbouring patches decreases the prevalence of infection is affected by both how frequently humans commute and the proportion of neighbouring patches that commits to vector surveillance and control activities. At high levels of host movement, patches that do not contribute to vector control may act as sources of infection in the landscape, yet have comparable levels of prevalence as patches that do cooperate. This result suggests that real cooperation among neighbours will be critical to the development of effective pro-active strategies for vector-borne disease control in today's commuter-linked communities.