Using observed incidence to calibrate the transmission level of a mathematical model for Plasmodium vivax dynamics including case management and importation.

In this work, we present a simple and flexible model for Plasmodium vivax dynamics which can be easily combined with routinely collected data on local and imported case counts to quantify transmission intensity and simulate control strategies. This model extends the model from White et al. (2016) by including case management interventions targeting liver-stage or blood-stage parasites, as well as imported infections. The endemic steady state of the model is used to derive a relationship between the observed incidence and the transmission rate in order to calculate reproduction numbers and simulate intervention scenarios. To illustrate its potential applications, the model is used to calculate local reproduction numbers in Panama and identify areas of sustained malaria transmission that should be targeted by control interventions.

A mechanistic and data-driven reconstruction of the time-varying reproduction number: Application to the COVID-19 epidemic.

The effective reproduction number Reff is a critical epidemiological parameter that characterizes the transmissibility of a pathogen. However, this parameter is difficult to estimate in the presence of silent transmission and/or significant temporal variation in case reporting. This variation can occur due to the lack of timely or appropriate testing, public health interventions and/or changes in human behavior during an epidemic. This is exactly the situation we are confronted with during this COVID-19 pandemic. In this work, we propose to estimate Reff for the SARS-CoV-2 (the etiological agent of the COVID-19), based on a model of its propagation considering a time-varying transmission rate. This rate is modeled by a Brownian diffusion process embedded in a stochastic model. The model is then fitted by Bayesian inference (particle Markov Chain Monte Carlo method) using multiple well-documented hospital datasets from several regions in France and in Ireland. This mechanistic modeling framework enables us to reconstruct the temporal evolution of the transmission rate of the COVID-19 based only on the available data. Except for the specific model structure, it is non-specifically assumed that the transmission rate follows a basic stochastic process constrained by the observations. This approach allows us to follow both the course of the COVID-19 epidemic and the temporal evolution of its Reff(t). Besides, it allows to assess and to interpret the evolution of transmission with respect to the mitigation strategies implemented to control the epidemic waves in France and in Ireland. We can thus estimate a reduction of more than 80% for the first wave in all the studied regions but a smaller reduction for the second wave when the epidemic was less active, around 45% in France but just 20% in Ireland. For the third wave in Ireland the reduction was again significant (>70%).

Comparison of stochastic and deterministic frameworks in dengue modelling.

We perform estimations of compartment models for dengue transmission in rural Cambodia with increasing complexity regarding both model structure and the account for stochasticity. On the one hand, we successively account for three embedded sources of stochasticity: observation noise, demographic variability and environmental hazard. On the other hand, complexity in the model structure is increased by introducing vector-borne transmission, explicit asymptomatic infections and interacting virus serotypes. Using two sources of case data from dengue epidemics in Kampong Cham (Cambodia), models are estimated in the bayesian framework, with Markov Chain Monte Carlo and Particle Markov Chain Monte Carlo. We highlight the advantages and drawbacks of the different formulations in a practical setting. Although in this case the deterministic models provide a good approximation of the mean trajectory for a low computational cost, the stochastic frameworks better reflect and account for parameter and simulation uncertainty.

Dengue modeling in rural Cambodia: Statistical performance versus epidemiological relevance.

Dengue dynamics are shaped by the complex interplay between several factors, including vector seasonality, interaction between four virus serotypes, and inapparent infections. However, paucity or quality of data do not allow for all of these to be taken into account in mathematical models. In order to explore separately the importance of these factors in models, we combined surveillance data with a local-scale cluster study in the rural province of Kampong Cham (Cambodia), in which serotypes and asymptomatic infections were documented. We formulate several mechanistic models, each one relying on a different set of hypotheses, such as explicit vector dynamics, transmission via asymptomatic infections and coexistence of several virus serotypes. Models are confronted with the observed time series using Bayesian inference, through Markov chain Monte Carlo. Model selection is then performed using statistical information criteria, and the coherence of epidemiological characteristics (reproduction numbers, incidence proportion, dynamics of the susceptible classes) is assessed in each model. Our analyses on transmission dynamics in a rural endemic setting highlight that two-strain models with interacting effects better reproduce the long term data, but they are difficult to parameterize when relying on incidence cases only. On the other hand, considering the available data, incorporating vector and asymptomatic components seems of limited added-value when seasonality and underreporting are already accounted for.