Selecting the Best Model for Complex Interplay Between HIV and Nutrition

Abstract HIV is a serious infectious disease. The role of nutrition in HIV progression has long been recognized. However, no mathematical models exist to describe the interplay of HIV with the nutritional components. In this paper, we present a family of models of HIV and the two protein components albumin and globulin. We use data from SIV-infected monkeys to perform model selection on the family of models. We discover that the simplest model accurately and uniquely describes the data. The selection of the simplest model leads to the observation that albumin and globulin do not impact the infection rate of target cells by the virus and the clearance of the infected target cells by the immune system. Furthermore, we obtain that the recruitment of target cells and immune cells do not depend on the globulin. Mathematical analysis of the selected model reveals that the model has an infection-free equilibrium and a unique infected equilibrium when the reproduction number is above one. The infection-free equilibrium is locally stable when the reproduction number is below one, and unstable when the reproduction number is greater than one. The infection equilibrium is locally stable whenever it exists. To determine the parameters of the best fitted model we perform structural and practical identifiability analysis. The structural identifiability analysis reveals that the model is identifiable when the immune cell infection rate is fixed at a value obtained from the literature. Practical identifiability reveals that only seven of the sixteen parameters are practically identifiable with the given data. Practical identifiability of parameters performed with synthetic data sampled a lot more frequently reveals that only two parameters are practically unidentifiable. We conclude that experiments that will improve the quality of the data can help improve the parameter estimates and lead to better understanding of the interplay of HIV and nutrition.