Mathematical models for prediction and optimal mitigation of epidemics

Abstract

Early detection of livestock diseases and development of cost optimal mitigation strategies are becoming a global necessity. Foot and Mouth Disease (FMD) is considered one of the most serious livestock diseases owing to its high rate of transmission and extreme economic consequences. Thus, it is imperative to improve parameterized mathematical models for predictive and preventive purposes. In this work, a meta-population based stochastic model is implemented to assess the FMD infection dynamics and to curb economic losses in countries with underdeveloped livestock disease surveillance databases. Our model predicts the spatio-temporal evolution of FMD over a weighted contact network where the weights are characterized by the effect of wind and movement of animals and humans. FMD incidence data from countries such as Turkey, Iran and Thailand are used to calibrate and validate our model, and the predictive performance of our model is compared with that of baseline models as well. Additionally, learning-based prediction models can be utilized to detect the time of onset of an epidemic outbreak. Such models are computationally simple and they may be trained to predict infection in the absence of background data representing the dynamics of disease transmission, which is otherwise necessary for predictions using spatio-temporal models. Thus, we comparatively study the predictive performance of our spatio-temporal against neural networks and autoregressive models. Also, Bayesian networks combined with Monte-Carlo simulations are used to determine the gold standard by approximation.

Next, cost-effective mitigation strategies are simulated using the theoretical concept of infection network fragmentation. Based on the theoretical reduction in the total number of infected animals, several simulative mitigation strategies are proposed and their cost-effectiveness measures specified by the percentage reduction in the total number of infected animals per million US dollars, are also analyzed. We infer that the cost-effectiveness measures of mitigation strategies implemented using our spatio-temporal predictive model have a narrower range and higher granularity than those for mitigation strategies formulated using learning-based prediction models.

Finally, we coin optimal mitigation strategies using Fuzzy Dominance Genetic Algorithms (FDGA). We use the concept of hierarchical fuzzy dominance to minimize the total number of infected animals, the direct cost incurred due to the implementation of mitigation strategies, the number of animals culled, and the number of animals vaccinated to mitigate an epidemic. This method has the potential to aid in economic policy development for countries that have lost their FMD-free status.