The Effects of Host Diversity on Vector-Borne Disease: The Conditions under Which Diversity Will Amplify or Dilute the Disease Risk

Multihost vector-borne infectious diseases form a significant fraction of the global infectious disease burden. In this study we explore the relationship between host diversity, vector behavior, and disease risk. To this end, we have developed a new dynamic model which includes two distinct host species and one vector species with variable preferences. With the aid of the model we were able to compute the basic reproductive rate, R ₀, a well-established measure of disease risk that serves as a threshold parameter for disease outbreak. The model analysis reveals that the system has two different qualitative behaviors: (i) the well-known dilution effect, where the maximal R₀ is obtained in a community which consists a single host (ii) a new amplification effect, denoted by us as diversity amplification, where the maximal R₀ is attained in a community which consists both hosts. The model analysis extends on previous results by underlining the mechanism of both, diversity amplification and the dilution, and specifies the exact conditions for their occurrence. We have found that diversity amplification occurs where the vector prefers the host with the highest transmission ability, and dilution is obtained when the vector does not show any preference, or it prefers to bite the host with the lower transmission ability. The mechanisms of dilution and diversity amplification are able to account for the different and contradictory patterns often observed in nature (i.e., in some cases disease risk is increased while in other is decreased when the diversity is increased). Implication of the diversity amplification mechanism also challenges current premises about the interaction between biodiversity, climate change, and disease risk and calls for retrospective thinking in planning intervention policies aimed at protecting the preferred host species.     

The effects of human movement on the persistence of vector-borne diseases

With the recent resurgence of vector-borne diseases due to urbanization and development there is an urgent need to understand the dynamics of vector-borne diseases in rapidly changing urban environments. For example, many empirical studies have produced the disturbing finding that diseases continue to persist in modern city centers with zero or low rates of transmission. We develop spatial models of vector-borne disease dynamics on a network of patches to examine how the movement of humans in heterogeneous environments affects transmission. We show that the movement of humans between patches is sufficient to maintain disease persistence in patches with zero transmission. We construct two classes of models using different approaches: (i) Lagrangian models that mimic human commuting behavior and (ii) Eulerian models that mimic human migration. We determine the basic reproduction number R₀ for both modeling approaches. We show that for both approaches that if the disease-free equilibrium is stable (R₀<1) then it is globally stable and if the disease-free equilibrium is unstable (R₀>1) then there exists a unique positive (endemic) equilibrium that is globally stable among positive solutions. Finally, we prove in general that Lagrangian and Eulerian modeling approaches are not equivalent. The modeling approaches presented provide a framework to explore spatial vector-borne disease dynamics and control in heterogeneous environments. As an example, we consider two patches in which the disease dies out in both patches when there is no movement between them. Numerical simulations demonstrate that the disease becomes endemic in both patches when humans move between the two patches.     

Two-Host,Two-Vector Basic Reproduction Ratio (R 0) for Bluetongue

Mathematical formulations for the basic reproduction ratio (R ₀) exist for several vector-borne diseases. Generally, these are based on models of one-host, one-vector systems or two-host, one-vector systems. For many vector borne diseases, however, two or more vector species often co-occur and, therefore, there is a need for more complex formulations. Here we derive a two-host, two-vector formulation for the R ₀ of bluetongue, a vector-borne infection of ruminants that can have serious economic consequences; since 1998 for example, it has led to the deaths of well over 1 million sheep in Europe alone. We illustrate our results by considering the situation in South Africa, where there are two major hosts (sheep, cattle) and two vector species with differing ecologies and competencies as vectors, for which good data exist. We investigate the effects on R ₀ of differences in vector abundance, vector competence and vector host preference between vector species. Our results indicate that R ₀ can be underestimated if we assume that there is only one vector transmitting the infection (when there are in fact two or more) and/or vector host preferences are overlooked (unless the preferred host is less beneficial or more abundant). The two-host, one-vector formula provides a good approximation when the level of cross-infection between vector species is very small. As this approaches the level of intraspecies infection, a combination of the two-host, one-vector R ₀ for each vector species becomes a better estimate. Otherwise, particularly when the level of cross-infection is high, the two-host, two-vector formula is required for accurate estimation of R ₀. Our results are equally relevant to Europe, where at least two vector species, which co-occur in parts of the south, have been implicated in the recent epizootic of bluetongue.     

Vector borne diseases on an urban environment: The effects of heterogeneity and human circulation

We study the effect of human circulation and host/vector heterogeneities on the onset of epidemics of arboviruses. From a meta-population dynamics based on the classical Bailey–Dietz model, we derive a multi-group model under three assumptions: (i) fast host sojourn time-scale; (ii) mosquitoes do not move; (iii) time homogeneity and strong connectivity of human circulation. Within this modelling framework, three different kinds of R₀ appear: (i) the “true” or “global” R₀—derived from the corresponding next generation matrix; (ii) the uniform R₀—obtained if the patches are taken homogeneous; (iii) the local R₀s—obtained if the patches are disconnected. We show that there is relevant epidemiological information associated to all of them. In particular, they can be used to understand the effects of changing the circulation on the value of the global R₀. We also present additional results on the effects on R₀ of different vector control policies, and a simulation with data from the city of Rio de Janeiro, Brazil.     

Bioeconomic management of invasive vector-borne diseases

Invasive insects, arthropods, and other invertebrates are of concern due to the role some play in introducing and transmitting pathogens via a pathogen–vector relationship. Indeed, vector-borne diseases represent a significant portion of emerging diseases. We compare and contrast three strategic approaches to managing a vector-borne pathogen: conventional strategies based on disease ecology without regard to economic tradeoffs and cost-effective strategies based on a bioeconomic framework. Conventional strategies entail managing the vector population below a threshold value based on R ₀—the basic reproductive ratio of the pathogen, which measures a pathogen’s ability to invade uninfected systems. This does not account for post-infection dynamics, nor does it balance ecological and economic tradeoffs. Thresholds take on a more profound role under a bioeconomic paradigm: rather than unilaterally determining vector control choices, thresholds inform control choices and are influenced by them. Simulation results show cost-effective strategies can lower overall program costs and may be less sensitive to parameter estimation.     

Modelling vertical transmission in vector-borne diseases with applications to Rift Valley fever

We present two ordinary differential equation models for Rift Valley fever (RVF) transmission in cattle and mosquitoes. We extend existing models for vector-borne diseases to include an asymptomatic host class and vertical transmission in vectors. We define the basic reproductive number, ₀, and analyse the existence and stability of equilibrium points. We compute sensitivity indices of ₀ and a reactivity index (that measures epidemicity) to parameters for baseline wet and dry season values. ₀ is most sensitive to the mosquito biting and death rates. The reactivity index is most sensitive to the mosquito biting rate and the infectivity of hosts to vectors. Numerical simulations show that even with low equilibrium prevalence, increases in mosquito densities through higher rainfall, in the presence of vertical transmission, can result in large epidemics. This suggests that vertical transmission is an important factor in the size and persistence of RVF epidemics.     

Urbanization,land tenure security and vector-borne Chagas disease

Modern cities represent one of the fastest growing ecosystems on the planet. Urbanization occurs in stages; each stage characterized by a distinct habitat that may be more or less susceptible to the establishment of disease vector populations and the transmission of vector-borne pathogens. We performed longitudinal entomological and epidemiological surveys in households along a 1900 × 125 m transect of Arequipa, Peru, a major city of nearly one million inhabitants, in which the transmission of Trypanosoma cruzi, the aetiological agent of Chagas disease, by the insect vector Triatoma infestans, is an ongoing problem. The transect spans a cline of urban development from established communities to land invasions. We find that the vector is tracking the development of the city, and the parasite, in turn, is tracking the dispersal of the vector. New urbanizations are free of vector infestation for decades. T. cruzi transmission is very recent and concentrated in more established communities. The increase in land tenure security during the course of urbanization, if not accompanied by reasonable and enforceable zoning codes, initiates an influx of construction materials, people and animals that creates fertile conditions for epidemics of some vector-borne diseases.     

Epidemics with partial immunity to reinfection

We obtain analytical results about epidemics generated by the partial immunity model of Gomes et al. [3], in which infection confers partial immunity to reinfection. When the demographic process is excluded, the behavior switches from epidemic to endemic as the basic reproduction number R₀ crosses the reinfection threshold . We derive formulas for two quantities characterizing the size of the epidemic below the reinfection threshold: the attack rate A, which is the fraction of the population infected at least once, and the final size Z, which is the average number of infections per individual. We also derive a system of differential equations which can be used to obtain more detailed information, such as the fraction of the population infected n times throughout the epidemic, for every n.     

The epidemic threshold of vector-borne diseases with seasonality

Cutaneous leishmaniasis is a vector-borne disease transmitted to humans by sandflies. In this paper, we develop a mathematical model which takes into account the seasonality of the vector population and the distribution of the latent period from infection to symptoms in humans. Parameters are fitted to real data from the province of Chichaoua, Morocco. We also introduce a generalization of the definition of the basic reproduction number R ₀ which is adapted to periodic environments. This R ₀ is estimated numerically for the epidemic in Chichaoua; 1.94. The model suggests that the epidemic could be stopped if the vector population were reduced by a factor 3.76.     

Modeling Relapsing Disease Dynamics in a Host-Vector Community

Vector-borne diseases represent a threat to human and wildlife populations and mathematical models provide a means to understand and control epidemics involved in complex host-vector systems. The disease model studied here is a host-vector system with a relapsing class of host individuals, used to investigate tick-borne relapsing fever (TBRF). Equilibrium analysis is performed for models with increasing numbers of relapses and multiple hosts and the disease reproduction number, R₀, is generalized to establish relationships with parameters that would result in the elimination of the disease. We show that host relapses in a single competent host-vector system is needed to maintain an endemic state. We show that the addition of an incompetent second host with no relapses increases the number of relapses needed for maintaining the pathogen in the first competent host system. Further, coupling of the system with hosts of differing competencies will always reduce R₀, making it more difficult for the system to reach an endemic state.     

Climate Change,Population Immunity,and Hyperendemicity in the Transmission Threshold of Dengue

Background

It has been suggested that the probability of dengue epidemics could increase because of climate change. The probability of epidemics is most commonly evaluated by the basic reproductive number (R₀), and in mosquito-borne diseases, mosquito density (the number of female mosquitoes per person [MPP]) is the critical determinant of the R₀ value. In dengue-endemic areas, 4 different serotypes of dengue virus coexist–a state known as hyperendemicity–and a certain proportion of the population is immune to one or more of these serotypes. Nevertheless, these factors are not included in the calculation of R₀. We aimed to investigate the effects of temperature change, population immunity, and hyperendemicity on the threshold MPP that triggers an epidemic.

Methods and Findings

We designed a mathematical model of dengue transmission dynamics. An epidemic was defined as a 10% increase in seroprevalence in a year, and the MPP that triggered an epidemic was defined as the threshold MPP. Simulations were conducted in Singapore based on the recorded temperatures from 1980 to 2009 The threshold MPP was estimated with the effect of (1) temperature only; (2) temperature and fluctuation of population immunity; and (3) temperature, fluctuation of immunity, and hyperendemicity. When only the effect of temperature was considered, the threshold MPP was estimated to be 0.53 in the 1980s and 0.46 in the 2000s, a decrease of 13.2%. When the fluctuation of population immunity and hyperendemicity were considered in the model, the threshold MPP decreased by 38.7%, from 0.93 to 0.57, from the 1980s to the 2000s.

Conclusions

The threshold MPP was underestimated if population immunity was not considered and overestimated if hyperendemicity was not included in the simulations. In addition to temperature, these factors are particularly important when quantifying the threshold MPP for the purpose of setting goals for vector control in dengue-endemic areas.     

Approximation of the Basic Reproduction Number <Emphasis Type="Italic">R</Emphasis><Subscript>0</Subscript> for Vector-Borne Diseases with a Periodic Vector Population

The main purpose of this paper is to give an approximate formula involving two terms for the basic reproduction number R ₀ of a vector-borne disease when the vector population has small seasonal fluctuations of the form p(t) = p ₀ (1+ε cos (ωt − φ)) with ε ≪ 1. The first term is similar to the case of a constant vector population p but with p replaced by the average vector population p ₀. The maximum correction due to the second term is (ε²/8)% and always tends to decrease R ₀. The basic reproduction number R ₀ is defined through the spectral radius of a linear integral operator. Four numerical methods for the computation of R ₀ are compared using as example a model for the 2005/2006 chikungunya epidemic in La Réunion. The approximate formula and the numerical methods can be used for many other epidemic models with seasonality. MSC 92D30 ⋅ 45C05 ⋅ 47A55     

Modeling Seasonal Rabies Epidemics in China

Human rabies, an infection of the nervous system, is a major public-health problem in China. In the last 60 years (1950–2010) there had been 124,255 reported human rabies cases, an average of 2,037 cases per year. However, the factors and mechanisms behind the persistence and prevalence of human rabies have not become well understood. The monthly data of human rabies cases reported by the Chinese Ministry of Health exhibits a periodic pattern on an annual base. The cases in the summer and autumn are significantly higher than in the spring and winter. Based on this observation, we propose a susceptible, exposed, infectious, and recovered (SEIRS) model with periodic transmission rates to investigate the seasonal rabies epidemics. We evaluate the basic reproduction number R ₀, analyze the dynamical behavior of the model, and use the model to simulate the monthly data of human rabies cases reported by the Chinese Ministry of Health. We also carry out some sensitivity analysis of the basic reproduction number R ₀ in terms of various model parameters. Moreover, we demonstrate that it is more reasonable to regard R ₀ rather than the average basic reproduction number [`(R)]₀\bar{R}_{0} or the basic reproduction number [^(R)]₀\hat{R}_{0} of the corresponding autonomous system as a threshold for the disease. Finally, our studies show that human rabies in China can be controlled by reducing the birth rate of dogs, increasing the immunization rate of dogs, enhancing public education and awareness about rabies, and strengthening supervision of pupils and children in the summer and autumn.     

Spatial Heterogeneity,Host Movement and Mosquito-Borne Disease Transmission

Mosquito-borne diseases are a global health priority disproportionately affecting low-income populations in tropical and sub-tropical countries. These pathogens live in mosquitoes and hosts that interact in spatially heterogeneous environments where hosts move between regions of varying transmission intensity. Although there is increasing interest in the implications of spatial processes for mosquito-borne disease dynamics, most of our understanding derives from models that assume spatially homogeneous transmission. Spatial variation in contact rates can influence transmission and the risk of epidemics, yet the interaction between spatial heterogeneity and movement of hosts remains relatively unexplored. Here we explore, analytically and through numerical simulations, how human mobility connects spatially heterogeneous mosquito populations, thereby influencing disease persistence (determined by the basic reproduction number R ₀), prevalence and their relationship. We show that, when local transmission rates are highly heterogeneous, R ₀ declines asymptotically as human mobility increases, but infection prevalence peaks at low to intermediate rates of movement and decreases asymptotically after this peak. Movement can reduce heterogeneity in exposure to mosquito biting. As a result, if biting intensity is high but uneven, infection prevalence increases with mobility despite reductions in R ₀. This increase in prevalence decreases with further increase in mobility because individuals do not spend enough time in high transmission patches, hence decreasing the number of new infections and overall prevalence. These results provide a better basis for understanding the interplay between spatial transmission heterogeneity and human mobility, and their combined influence on prevalence and R ₀.     

The effect of transmission route on plant virus epidemic development and disease control

A model for indirect vector transmission and epidemic development of plant viruses is extended to consider direct transmission through vector mating. A basic reproduction number is derived which is the sum of the R₀ values specific for three transmission routes. We analyse the model to determine the effect of direct transmission on plant disease control directed against indirect transmission. Increasing the rate of horizontal sexual transmission means that vector control rate or indirect transmission rate must be increased/decreased substantially to maintain R₀ at a value less than 1. By contrast, proportionately increasing the probability of transovarial transmission has little effect. Expressions are derived for the steady-state values of the viruliferous vector population. There is clear advantage for an insect virus in indirect transmission to plants, especially where the sexual and transovarial transmission rates are low; however information on virulence-transmissibility relationships is required to explain the evolution of a plant virus from an insect virus.     

Physiological analysis on oscillatory behavior of glucose-insulin regulation by model with delays

Despite temporally forced transmission driving many infectious diseases, analytical insight into its role when combined with stochastic disease processes and non-linear transmission has received little attention. During disease outbreaks, however, the absence of saturation effects early on in well-mixed populations mean that epidemic models may be linearised and we can calculate outbreak properties, including the effects of temporal forcing on fade-out, disease emergence and system dynamics, via analysis of the associated master equations. The approach is illustrated for the unforced and forced SIR and SEIR epidemic models. We demonstrate that in unforced models, initial conditions (and any uncertainty therein) play a stronger role in driving outbreak properties than the basic reproduction number R₀, while the same properties are highly sensitive to small amplitude temporal forcing, particularly when R₀ is small. Although illustrated for the SIR and SEIR models, the master equation framework may be applied to more realistic models, although analytical intractability scales rapidly with increasing system dimensionality. One application of these methods is obtaining a better understanding of the rate at which vector-borne and waterborne infectious diseases invade new regions given variability in environmental drivers, a particularly important question when addressing potential shifts in the global distribution and intensity of infectious diseases under climate change.     

Estimating the temporal and spatial risk of bluetongue related to the incursion of infected vectors into Switzerland

Background

The design of veterinary and public health surveillance systems has been improved by the ability to combine Geographical Information Systems (GIS), mathematical models and up to date epidemiological knowledge. In Switzerland, an early warning system was developed for detecting the incursion of the bluetongue disease virus (BT) and to monitor the frequency of its vectors. Based on data generated by this surveillance system, GIS and transmission models were used in order to determine suitable seasonal vector habitat locations and risk periods for a larger and more targeted surveillance program.

Results

Combined thematic maps of temperature, humidity and altitude were created to visualize the association with Culicoides vector habitat locations. Additional monthly maps of estimated basic reproduction number transmission rates (R₀) were created in order to highlight areas of Switzerland prone to higher BT outbreaks in relation to both vector activity and transmission levels. The maps revealed several foci of higher risk areas, especially in northern parts of Switzerland, suitable for both vector presence and vector activity for 2006.Results showed a variation of R₀ values comparing 2005 and 2006 yet suggested that Switzerland was at risk of an outbreak of BT, especially if the incursion arrived in a suitable vector activity period. Since the time of conducting these analyses, this suitability has proved to be the case with the recent outbreaks of BT in northern Switzerland.

Conclusion

Our results stress the importance of environmental factors and their effect on the dynamics of a vector-borne disease. In this case, results of this model were used as input parameters for creating a national targeted surveillance program tailored to both the spatial and the temporal aspect of the disease and its vectors. In this manner, financial and logistic resources can be used in an optimal way through seasonally and geographically adjusted surveillance efforts. This model can serve as a tool for other vector-borne diseases including human zoonotic vectors which are likely to spread into Europe.

     

Empirical Estimation of R 0 for Unknown Transmission Functions: The Case of Chronic Wasting Disease in Alberta

We consider the problem of estimating the basic reproduction number R ₀ from data on prevalence dynamics at the beginning of a disease outbreak. We derive discrete and continuous time models, some coefficients of which are to be fitted from data. We show that prevalence of the disease is sufficient to determine R ₀. We apply this method to chronic wasting disease spread in Alberta determining a range of possible R ₀ and their sensitivity to the probability of deer annual survival.     

West Nile virus epidemics in North America are driven by shifts in mosquito feeding behavior

West Nile virus (WNV) has caused repeated large-scale human epidemics in North America since it was first detected in 1999 and is now the dominant vector-borne disease in this continent. Understanding the factors that determine the intensity of the spillover of this zoonotic pathogen from birds to humans (via mosquitoes) is a prerequisite for predicting and preventing human epidemics. We integrated mosquito feeding behavior with data on the population dynamics and WNV epidemiology of mosquitoes, birds, and humans. We show that Culex pipiens, the dominant enzootic (bird-to-bird) and bridge (bird-to-human) vector of WNV in urbanized areas in the northeast and north-central United States, shifted its feeding preferences from birds to humans by 7-fold during late summer and early fall, coinciding with the dispersal of its preferred host (American robins, Turdus migratorius) and the rise in human WNV infections. We also show that feeding shifts in Cx. tarsalis amplify human WNV epidemics in Colorado and California and occur during periods of robin dispersal and migration. Our results provide a direct explanation for the timing and intensity of human WNV epidemics. Shifts in feeding from competent avian hosts early in an epidemic to incompetent humans after mosquito infection prevalences are high result in synergistic effects that greatly amplify the number of human infections of this and other pathogens. Our results underscore the dramatic effects of vector behavior in driving the transmission of zoonotic pathogens to humans.     

Modelling the epidemiology of hepatitis B in New Zealand

Hepatitis B is a vaccine preventable disease caused by the hepatitis B virus (HBV) that can induce potentially fatal liver damage. It has the second highest mortality rate of all vaccine preventable diseases in New Zealand. Vaccination against HBV was introduced in New Zealand in 1988, and the country is now categorised with overall low endemicity but with areas of both high and medium endemic levels. We present an SECIR compartmental mathematical model, with the population divided into age classes, for the transmission of HBV using local data on incidence of infection and vaccination coverage. We estimate the basic reproduction number, R₀, to be 1.53, and show that the vaccination campaign has substantially reduced this below one. However, a large number of carriers remain in the population acting as a source of infection.