Stochastic Models of Emerging Infectious Disease Transmission on Adaptive Random Networks

Inference of latent event times and transmission networks in individual level infectious disease models

Transmission networks indicate who-infected-whom in epidemics. Reconstruction of transmission networks is invaluable in applying and developing effective control strategies for infectious diseases. We introduce transmission network individual level models (TN-ILMs), a competing-risk, continuous time extension to individual level model framework for infectious diseases of Deardon et al. (2010). Through simulation study using a Julia language software package, Pathogen.jl, we explore the models with respect to their ability to jointly infer latent event times, latent disease transmission networks, and the TN-ILM parameters. We find good parameter, event time, and transmission network inference, with enhanced performance for inference of transmission networks in epidemic simulations that have higher spatial signals in their infectivity kernel. Finally, an application of a TN-ILM to data from a greenhouse experiment on the spread of tomato spotted wilt virus is presented.

A Mathematical Description of the Dynamics of Coronavirus Disease 2019 (COVID-19): A Case Study of Brazil

This paper deals with the mathematical modeling and numerical simulations related to the coronavirus dynamics. A description is developed based on the framework of the susceptible-exposed-infectious-removed model. Initially, a model verification is carried out calibrating system parameters with data from China, Italy, Iran, and Brazil. Results show the model capability to predict infectious evolution. Afterward, numerical simulations are performed in order to analyze different scenarios of COVID-19 in Brazil. Results show the importance of the governmental and individual actions to control the number and the period of the critical situations related to the pandemic.