Narrow Results

Studying different theoretical properties of epidemiological models has been widely addressed, while numerical studies and especially the calibration of models, which are often complicated and loaded with a high number of unknown parameters, against measured data have received less attention. In this paper, we describe how a combination of simulated data and Markov Chain Monte Carlo (MCMC) methods can be used to study the identifiability of model parameters with different type of measurements. Three known models are used as case studies to illustrate the importance of parameter identifiability: a basic SIR model, an influenza model with vaccination and treatment and a HIV–Malaria co-infection model. The analysis reveals that calibration of complex models commonly studied in mathematical epidemiology, such as the HIV–Malaria co-dynamics model, can be difficult or impossible, even if the system would be fully observed. The presented approach provides a tool for design and optimization of real-life field campaigns of collecting data, as well as for model selection.

In this paper, we formulate and analyze a mathematical model to investigate the transmission dynamics of tomato bacterial wilt disease (TBWD) in Mukono district, Uganda. We derive the basic reproduction number $R_0$ and prove the existence of a disease-free equilibrium point which is globally stable if $R_0<1$ and an endemic equilibrium which exists if $R_0>1$. Model parameters are estimated using the Markov Chain Monte Carlo (MCMC) methods and robustness tested. The model parameters were observed to be identifiable. Numerical simulations show that soil solarization and sensitization of farmers can help to eliminate the disease in Uganda. A modified tomato bacterial wilt model with control terms is formulated.