Population dynamics of infectious diseases: A discrete time model

Oli, Madan K.; Venkataraman, Meenakshi; Klein, Paul; Wendland, Lori D.; Brown, Mary Bomberger

doi:10.1016/j.ecolmodel.2006.04.007

Cited by 46 publications

(50 citation statements)

References 60 publications

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“…However, determining wildlife disease dynamics including rates of infection, drivers of transmission, vector feeding preferences, and host mortality presents significant challenges (McCallum et al 2001, Wobeser 2008. The importance of these epizootiological parameters for understanding hostpathogen dynamics, population effects, and on host-pathogen evolution have long been recognized, but are infrequently addressed (Scott 1988, Oli et al 2006, Murray et al 2009, Lachish et al 2011a. Quantifying epizootiological parameters in wildlife populations is difficult because methods used in human epidemiology seldom apply (McCallum et al 2001, Caley and Hone 2004, Lachish et al 2011a; however, recent applications of multi-state mark-recapture models have provided an important tool to assess infection dynamics and population impacts (Faustino et al 2004, Senar and Conroy 2004, Conn and Cooch 2009, Atkinson and Samuel 2010 while accounting for differential capture heterogeneity (Jennelle et al 2007).…”

Section: Introductionmentioning

confidence: 99%

Avian malaria in Hawaiian forest birds: infection and population impacts across species and elevations

et al. 2015

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Abstract. Wildlife diseases can present significant threats to ecological systems and biological diversity, as well as domestic animal and human health. However, determining the dynamics of wildlife diseases and understanding the impact on host populations is a significant challenge. In Hawai'i, there is ample circumstantial evidence that introduced avian malaria (Plasmodium relictum) has played an important role in the decline and extinction of many native forest birds. However, few studies have attempted to estimate disease transmission and mortality, survival, and individual species impacts in this distinctive ecosystem. We combined multi-state capture-recapture (longitudinal) models with cumulative age-prevalence (crosssectional) models to evaluate these patterns in Apapane, Hawai'i Amakihi, and Iiwi in low-, mid-, and high-elevation forests on the island of Hawai'i based on four longitudinal studies of 3-7 years in length. We found species-specific patterns of malaria prevalence, transmission, and mortality rates that varied among elevations, likely in response to ecological factors that drive mosquito abundance. Malaria infection was highest at low elevations, moderate at mid elevations, and limited in high-elevation forests. Infection rates were highest for Iiwi and Apapane, likely contributing to the absence of these species in low-elevation forests. Adult malaria fatality rates were highest for Iiwi, intermediate for Amakihi at mid and high elevations, and lower for Apapane; low-elevation Amakihi had the lowest malaria fatality, providing strong evidence of malaria tolerance in this low-elevation population. Our study indicates that hatch-year birds may have greater malaria infection and/or fatality rates than adults. Our study also found that mosquitoes prefer feeding on Amakihi rather than Apapane, but Apapane are likely a more important reservoir for malaria transmission to mosquitoes. Our approach, based on host abundance and infection rates, may be an effective alternative to mosquito blood meal analysis for determining vector-host contacts when mosquito densities are low and collection of blood-fed mosquitoes is impractical. Our study supports the hypothesis that avian malaria has been a primary factor influencing the elevational distribution and abundance of these three species, and likely limits other native Hawaiian species that are susceptible to malaria.

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Section: Introductionmentioning

confidence: 99%

Avian malaria in Hawaiian forest birds: infection and population impacts across species and elevations

et al. 2015

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“…The two data sources (observation vectors) are coupled to an underlying process model, which can take the form of a classical matrix projection model (the structure of the model is arbitrary). As such, it would seem to be relatively straightforward to use point counts of individuals observed in a particular disease state to augment a discrete-time disease model (e.g., Oli et al 2006; see also ''Appendix A'') in a SSM. Recent SSM integration of multisite recruitment, census, and mark-recapture-recovery data (Borysiewicz et al 2009) could conceptually be extended to accommodate multiple disease states in the same way.…”

Section: Working With the Likelihoodmentioning

confidence: 99%

Disease dynamics in wild populations: modeling and estimation: a review

et al. 2010

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Models of infectious disease dynamics focus on describing the temporal and spatial variations in disease prevalence, and on understanding the factors that affect how many cases will occur in each time period and which individuals are likely to become infected. Classical methods for selecting and fitting models, mostly motivated by human diseases, are almost always based solely on raw counts of infected and uninfected individuals. We begin by reviewing the main classical approaches to parameter estimation, and some of their applications. We then review recently developed methods which enable representation of component processes such as infection and recovery, with observation models that acknowledge the complexities of the sampling and detection processes. We demonstrate the need to account for detectability in modeling disease dynamics, and explore a number of mark-recapture and occupancy study designs for estimating disease parameters while simultaneously accounting for variation in detectability. We highlight the utility of different modeling approaches and also consider the typically strong assumptions that may actually serve to limit their utility in general application to the study of disease dynamics (e.g., assignment of individuals to discrete disease states when underlying state space is more generally continuous; transitions assumed to be simple firstorder Markov; temporal separation of hazard and transition events).

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“…Parameter estimation and analysis of systems of discrete-time equations, also called matrix models, have seen broad application in population ecology (Caswell 1988). Their use to portray disease dynamics has been advocated (Dobson and Foufopoulos 2001, Oli et al 2006, Allen and van den Driessche 2008, Klepac and Caswell 2011, but matrix population models representing the influence of disease on host dynamics have rarely been fit with data (Cahn et al 2011, Muths et al 2011, Perez-Heydrich et al 2012. Assimilating matrix population models with data on diseases offers a major advance by applying welldeveloped tools in population ecology to questions in disease ecology.…”

Section: Data Assimilation For Models Of Infectious Diseasementioning

confidence: 99%

“…The deterministic model A (t) n (tÀ1) (Oli et al 2006) predicts the means of the eight element state vector n (t) ( Table 2) based on the true state of the population at t À 1 and parameters in the projection matrix A (t) ( Fig. 2; Appendix D).…”

Section: Process Modelmentioning

confidence: 99%

“…To do so, we used a modification of the method described by Allen and van den Driessche (2008) and Oli et al (2006) for computing R 0 from the matrix A. Estimating the reproductive ratio of the disease requires estimating the duration of the infectious period and the number of infections produced per unit duration. Details of procedures for estimating R 0 are provided in Appendix G.…”

Section: Computation Of Derived Quantitiesmentioning

confidence: 99%

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State‐space modeling to support management of brucellosis in the Yellowstone bison population

Hobbs

Geremia

Treanor

et al. 2015

Ecological Monographs

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Abstract. The bison (Bison bison) of the Yellowstone ecosystem, USA, exemplify the difficulty of conserving large mammals that migrate across the boundaries of conservation areas. Bison are infected with brucellosis (Brucella abortus) and their seasonal movements can expose livestock to infection. Yellowstone National Park has embarked on a program of adaptive management of bison, which requires a model that assimilates data to support management decisions. We constructed a Bayesian state-space model to reveal the influence of brucellosis on the Yellowstone bison population. A frequency-dependent model of brucellosis transmission was superior to a density-dependent model in predicting out-of-sample observations of horizontal transmission probability. A mixture model including both transmission mechanisms converged on frequency dependence. Conditional on the frequency-dependent model, brucellosis median transmission rate was 1.87 yr À1 . The median of the posterior distribution of the basic reproductive ratio (R 0 ) was 1.75. Seroprevalence of adult females varied around 60% over two decades, but only 9.6 of 100 adult females were infectious. Brucellosis depressed recruitment; estimated population growth rate k averaged 1.07 for an infected population and 1.11 for a healthy population. We used five-year forecasting to evaluate the ability of different actions to meet management goals relative to no action. Annually removing 200 seropositive female bison increased by 30-fold the probability of reducing seroprevalence below 40% and increased by a factor of 120 the probability of achieving a 50% reduction in transmission probability relative to no action. Annually vaccinating 200 seronegative animals increased the likelihood of a 50% reduction in transmission probability by fivefold over no action. However, including uncertainty in the ability to implement management by representing stochastic variation in the number of accessible bison dramatically reduced the probability of achieving goals using interventions relative to no action. Because the width of the posterior predictive distributions of future population states expands rapidly with increases in the forecast horizon, managers must accept high levels of uncertainty. These findings emphasize the necessity of iterative, adaptive management with relatively short-term commitment to action and frequent reevaluation in response to new data and model forecasts. We believe our approach has broad applications.

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Population dynamics of infectious diseases: A discrete time model

Cited by 46 publications

References 60 publications

Avian malaria in Hawaiian forest birds: infection and population impacts across species and elevations

Avian malaria in Hawaiian forest birds: infection and population impacts across species and elevations

Disease dynamics in wild populations: modeling and estimation: a review

State‐space modeling to support management of brucellosis in the Yellowstone bison population

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