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Bayesian compartmental models and associated reproductive numbers for an infection with multiple transmission modes.

ABSTRACT: Zoonotic visceral leishmaniasis (ZVL) is a serious neglected tropical disease that is endemic in 98 countries. ZVL is primarily transmitted via a sand fly vector. In the United States, it is enzootic in some canine populations; it is transmitted from infectious mother to pup transplacentally, and vector-borne transmission is absent. This absence affords a unique opportunity to study (1) vertical transmission dynamics in dogs and (2) the importance of vertical transmission in maintaining an infectious reservoir in the presence of a vector. In this paper, we present Bayesian compartmental models and reproductive number formulations to examine (1) and (2), providing a mechanism to plan and evaluate interventions in regions where both transmission modes are present. First, we propose an individual-level susceptible, infectious, removed (SIR) model to study the effect of maternal infection status during pregnancy on pup infection progression. We provide evidence that pups born to diagnostically positive mothers during pregnancy are more likely to become diagnostically positive both earlier in life, and at some point during their lifetime, than those born to diagnostically negative mothers. Second, we propose a population-level SIR model to study the impact of a vertically maintained reservoir on propagating infection in a naive canine population through emergent vector transmission using simulation studies. We also present reproductive numbers to quantify contributions of vertically infected and vector-infected dogs to maintaining infection in the population. We show that a vertically maintained canine reservoir can propagate infection in a theoretical naive population in the presence of a vector.

SUBMITTER: Ozanne MV

PROVIDER: S-EPMC7673222 | biostudies-literature | 2020 Sep

REPOSITORIES: biostudies-literature

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Bayesian compartmental models and associated reproductive numbers for an infection with multiple transmission modes.

Ozanne Marie V MV Brown Grant D GD Toepp Angela J AJ Scorza Breanna M BM Oleson Jacob J JJ Wilson Mary E ME Petersen Christine A CA

Biometrics 20191216 3

Zoonotic visceral leishmaniasis (ZVL) is a serious neglected tropical disease that is endemic in 98 countries. ZVL is primarily transmitted via a sand fly vector. In the United States, it is enzootic in some canine populations; it is transmitted from infectious mother to pup transplacentally, and vector-borne transmission is absent. This absence affords a unique opportunity to study (1) vertical transmission dynamics in dogs and (2) the importance of vertical transmission in maintaining an infec ...[more]

PMID: 31785149

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Project description:BackgroundMathematical modeling is now frequently used in outbreak investigations to understand underlying mechanisms of infectious disease dynamics, assess patterns in epidemiological data, and forecast the trajectory of epidemics. However, the successful application of mathematical models to guide public health interventions lies in the ability to reliably estimate model parameters and their corresponding uncertainty. Here, we present and illustrate a simple computational method for assessing parameter identifiability in compartmental epidemic models.MethodsWe describe a parametric bootstrap approach to generate simulated data from dynamical systems to quantify parameter uncertainty and identifiability. We calculate confidence intervals and mean squared error of estimated parameter distributions to assess parameter identifiability. To demonstrate this approach, we begin with a low-complexity SEIR model and work through examples of increasingly more complex compartmental models that correspond with applications to pandemic influenza, Ebola, and Zika.ResultsOverall, parameter identifiability issues are more likely to arise with more complex models (based on number of equations/states and parameters). As the number of parameters being jointly estimated increases, the uncertainty surrounding estimated parameters tends to increase, on average, as well. We found that, in most cases, R0 is often robust to parameter identifiability issues affecting individual parameters in the model. Despite large confidence intervals and higher mean squared error of other individual model parameters, R0 can still be estimated with precision and accuracy.ConclusionsBecause public health policies can be influenced by results of mathematical modeling studies, it is important to conduct parameter identifiability analyses prior to fitting the models to available data and to report parameter estimates with quantified uncertainty. The method described is helpful in these regards and enhances the essential toolkit for conducting model-based inferences using compartmental dynamic models.

Project description:The effective reproduction number (ℜt) is a theoretical indicator of the course of an infectious disease that allows policymakers to evaluate whether current or previous control efforts have been successful or whether additional interventions are necessary. This metric, however, cannot be directly observed and must be inferred from available data. One approach to obtaining such estimates is fitting compartmental models to incidence data. We can envision these dynamic models as the ensemble of structures that describe the disease's natural history and individuals' behavioural patterns. In the context of the response to the COVID-19 pandemic, the assumption of a constant transmission rate is rendered unrealistic, and it is critical to identify a mathematical formulation that accounts for changes in contact patterns. In this work, we leverage existing approaches to propose three complementary formulations that yield similar estimates for ℜt based on data from Ireland's first COVID-19 wave. We describe these Data Generating Processes (DGP) in terms of State-Space models. Two (DGP1 and DGP2) correspond to stochastic process models whose transmission rate is modelled as Brownian motion processes (Geometric and Cox-Ingersoll-Ross). These DGPs share a measurement model that accounts for incidence and transmission rates, where mobility data is assumed as a proxy of the transmission rate. We perform inference on these structures using Iterated Filtering and the Particle Filter. The final DGP (DGP3) is built from a pool of deterministic models that describe the transmission rate as information delays. We calibrate this pool of models to incidence reports using Hamiltonian Monte Carlo. By following this complementary approach, we assess the tradeoffs associated with each formulation and reflect on the benefits/risks of incorporating proxy data into the inference process. We anticipate this work will help evaluate the implications of choosing a particular formulation for the dynamics and observation of the time-varying transmission rate.

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Bayesian compartmental models and associated reproductive numbers for an infection with multiple transmission modes.

Publications

Bayesian compartmental models and associated reproductive numbers for an infection with multiple transmission modes.

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