Holly Gaff

Estimating the reproductive numbers for the 2008–2009 cholera outbreaks in Zimbabwe

Cholera remains an important global cause of morbidity and mortality, capable of causing periodic epidemic disease. Beginning in August 2008, a major cholera epidemic occurred in Zimbabwe, with 98,585 reported cases and 4,287 deaths. The dynamics of such outbreaks, particularly in nonestuarine regions, are not well understood. We explored the utility of mathematical models in understanding transmission dynamics of cholera and in assessing the magnitude of interventions necessary to control epidemic disease. Weekly data on reported cholera cases were obtained from the Zimbabwe Ministry of Health and Child Welfare (MoHCW) for the period from November 13, 2008 to July 31, 2009. A mathematical model was formulated and fitted to cumulative cholera cases to estimate the basic reproductive numbers R0 and the partial reproductive numbers from all 10 provinces for the 2008–2009 Zimbabwe cholera epidemic. Estimated basic reproductive numbers were highly heterogeneous, ranging from a low value of just above unity to 2.72. Partial reproductive numbers were also highly heterogeneous, suggesting that the transmission routes varied by province; human-to-human transmission accounted for 41–95% of all transmission. Our models suggest that the underlying patterns of cholera transmission varied widely from province to province, with a corresponding variation in the amenability of outbreaks in different provinces to control measures such as immunization. These data underscore the heterogeneity of cholera transmission dynamics, potentially linked to differences in environment, socio-economic conditions, and cultural practices. The lack of traditional estuarine reservoirs combined with these estimates of R0 suggest that mass vaccination against cholera deployed strategically in Zimbabwe and surrounding regions could prevent future cholera epidemics and eventually eliminate cholera from the region.

Modeling optimal intervention strategies for cholera.

While cholera has been a recognized disease for two centuries, there is no strategy for its effective control. We formulate a mathematical model to include essential components such as a hyperinfectious, short-lived bacterial state, a separate class for mild human infections, and waning disease immunity. A new result quantifies contributions to the basic reproductive number from multiple infectious classes. Using optimal control theory, parameter sensitivity analysis, and numerical simulations, a cost-effective balance of multiple intervention methods is compared for two endemic populations. Results provide a framework for designing cost-effective strategies for diseases with multiple intervention methods.

Climate, environmental and socio-economic change: weighing up the balance in vector-borne disease transmission

Arguably one of the most important effects of climate change is the potential impact on human health. While this is likely to take many forms, the implications for future transmission of vector-borne diseases (VBDs), given their ongoing contribution to global disease burden, are both extremely important and highly uncertain. In part, this is owing not only to data limitations and methodological challenges when integrating climate-driven VBD models and climate change projections, but also, perhaps most crucially, to the multitude of epidemiological, ecological and socio-economic factors that drive VBD transmission, and this complexity has generated considerable debate over the past 10–15 years. In this review, we seek to elucidate current knowledge around this topic, identify key themes and uncertainties, evaluate ongoing challenges and open research questions and, crucially, offer some solutions for the field. Although many of these challenges are ubiquitous across multiple VBDs, more specific issues also arise in different vector–pathogen systems.

A dynamic landscape model for fish in the Everglades and its application to restoration

Abstract A model (ALFISH) for fish functional groups in freshwater marshes of the greater Everglades area of southern Florida has been developed. Its main objective is to assess the spatial pattern of fish densities through time across freshwater marshes. This model has the capability of providing a dynamic measure of the spatially-explicit food resources available to wading birds. ALFISH simulates two functional groups, large and small fish, where the larger ones can prey on the small fish type. Both functional groups are size-structured. The marsh landscape is modeled as 500×500 m spatial cells on a grid across southern Florida. A hydrology model predicts water levels in the spatial cells on 5-day time steps. Fish populations spread across the marsh during flooded conditions and either retreat into refugia (alligator ponds), move to other spatial cells, or die if their cell dries out. ALFISH has been applied to the evaluation of alternative water regulation scenarios under the Central and South Florida Comprehensive Project Review Study. The objective of this Review Study is to compare alternative methods for restoring historical ecological conditions in southern Florida. ALFISH has provided information on which plans are most are likely to increase fish biomass and its availability to wading bird populations.

Effects of Temperature on Emergence and Seasonality of West Nile Virus in California

Temperature has played a critical role in the spatiotemporal dynamics of West Nile virus transmission throughout California from its introduction in 2003 through establishment by 2009. We compared two novel mechanistic measures of transmission risk, the temperature-dependent ratio of virus extrinsic incubation period to the mosquito gonotrophic period (BT), and the fundamental reproductive ratio (R(0)) based on a mathematical model, to analyze spatiotemporal patterns of receptivity to viral amplification. Maps of BT and R(0) were created at 20-km scale and compared throughout California to seroconversions in sentinel chicken flocks at half-month intervals. Overall, estimates of BT and R(0) agreed with intensity of transmission measured by the frequency of sentinel chicken seroconversions. Mechanistic measures such as these are important for understanding how temperature affects the spatiotemporal dynamics of West Nile virus transmission and for delineating risk estimates useful to inform vector control agency intervention decisions and communicate outbreak potential.

Rickettsia parkeri in gulf coast ticks, southeastern Virginia, USA.

We report evidence that Amblyomma maculatum tick populations are well established in southeastern Virginia. We found that 43.1% of the adult Gulf Coast ticks collected in the summer of 2010 carried Rickettsia parkeri, suggesting that persons living in or visiting southeastern Virginia are at risk for infection with this pathogen.

Ticks and spotted fever group rickettsiae of southeastern Virginia.

The incidence of tick-borne rickettsial disease in the southeastern United States has been rising steadily through the past decade, and the range expansions of tick species and tick-borne infectious agents, new and old, has resulted in an unprecedented mix of vectors and pathogens. The results of an ongoing 4-year surveillance project describe the relative abundance of questing tick populations in southeastern Virginia. Since 2009, more than 66,000 questing ticks of 7 species have been collected from vegetation in a variety of habitats, with Amblyomma americanum constituting over 95% of ticks collected. Other species represented included Ixodes scapularis, Dermacentor variabilis, Amblyomma maculatum, Ixodes affinis, Haemaphysalis leporispalustris, and Ixodes brunneus. We found that 26.9-54.9% of A. americanum ticks tested were positive for Rickettsia amblyommii, a non-pathogenic symbiont of this tick species. We also found no evidence of R. rickettsii in D. variabilis ticks, although they did show low infection rates of R. montanensis (1.5-2.0%). Rickettsia parkeri and Candidatus R. andeanae were found in 41.8-55.7% and 0-1.5% A. maculatum ticks, respectively. The rate of R. parkeri in A. maculatum ticks is among the highest in the literature and has increased in the 2 years since R. parkeri and A. maculatum were first reported in southeastern Virginia. We conclude that tick populations in southeastern Virginia have recently undergone dramatic changes in species and abundance and that these populations support a variety of rickettsial agents with the potential for increased risk to human health.

Defining the Risk of Zika and Chikungunya Virus Transmission in Human Population Centers of the Eastern United States.

The recent spread of mosquito-transmitted viruses and associated disease to the Americas motivates a new, data-driven evaluation of risk in temperate population centers. Temperate regions are generally expected to pose low risk for significant mosquito-borne disease; however, the spread of the Asian tiger mosquito (Aedes albopictus) across densely populated urban areas has established a new landscape of risk. We use a model informed by field data to assess the conditions likely to facilitate local transmission of chikungunya and Zika viruses from an infected traveler to Ae. albopictus and then to other humans in USA cities with variable human densities and seasonality. Mosquito-borne disease occurs when specific combinations of conditions maximize virus-to-mosquito and mosquito-to-human contact rates. We develop a mathematical model that captures the epidemiology and is informed by current data on vector ecology from urban sites. The model demonstrates that under specific but realistic conditions, fifty-percent of introductions by infectious travelers to a high human, high mosquito density city could initiate local transmission and 10% of the introductions could result in 100 or more people infected. Despite the propensity for Ae. albopictus to bite non-human vertebrates, we also demonstrate that local virus transmission and human outbreaks may occur when vectors feed from humans even just 40% of the time. Inclusion of human behavioral changes and mitigations were not incorporated into the models and would likely reduce predicted infections. This work demonstrates how a conditional series of non-average events can result in local arbovirus transmission and outbreaks of human disease, even in temperate cities.

An Epidemiological Model of Rift Valley Fever with Spatial Dynamics

As a category A agent in the Center for Disease Control bioterrorism list, Rift Valley fever (RVF) is considered a major threat to the United States (USA). Should the pathogen be intentionally or unintentionally introduced to the continental USA, there is tremendous potential for economic damages due to loss of livestock, trade restrictions, and subsequent food supply chain disruptions. We have incorporated the effects of space into a mathematical model of RVF in order to study the dynamics of the pathogen spread as affected by the movement of humans, livestock, and mosquitoes. The model accounts for the horizontal transmission of Rift Valley fever virus (RVFV) between two mosquito and one livestock species, and mother-to-offspring transmission of virus in one of the mosquito species. Space effects are introduced by dividing geographic space into smaller patches and considering the patch-to-patch movement of species. For each patch, a system of ordinary differential equations models fractions of populations susceptible to, incubating, infectious with, or immune to RVFV. The main contribution of this work is a methodology for analyzing the likelihood of pathogen establishment should an introduction occur into an area devoid of RVF. Examples are provided for general and specific cases to illustrate the methodology.

Mathematical Model to Assess the Relative Effectiveness of Rift Valley Fever Countermeasures

Mathematical modeling of infectious diseases is increasingly used to explicate the mechanics of disease propagation, impact of controls, and sensitivity of countermeasures. The authors demonstrate use of a Rift Valley Fever (RVF) model to study efficacy of countermeasures to disease transmission parameters. RVF is a viral infectious disease that propagates through infected mosquitoes and primarily affects animals but also humans. Vaccines exist to protect against the disease but there is lack of data comparing efficacy of vaccination with alternative countermeasures such as managing mosquito population or destroying infected livestock. This paper presents a compartmentalized multispecies deterministic ordinary differential equation model of RVF propagation among livestock through infected Aedes and Culex mosquitoes and exercises the model to study the efficacy of vector adulticide, vector larvicide, livestock vaccination, and livestock culling on livestock population. Results suggest that livestock vaccination and culling offer the greatest benefit in terms of reducing livestock morbidity and mortality.