Mathematical Modeling and Optimal Control for Two Biological Systems

Global development post industrialization has accelerated industrial production, improved the economy, ushered in technological innovation, and improved the quality of life for many. Conversely, it has caused rising emissions, loss of biodiversity, increasing infertility, and an overall unsustainable world. This research evaluates two such effects namely, infertility and unsustainable development. Mathematical models for two biological systems i.e, In-vitro fertilization and global sustainability are proposed, and optimal control techniques are utilized to provide tailored solutions. Firstly, a mathematical method is proposed for the In-vitro fertilization (IVF) process to reduce the overall cost of the process and maintain patient success. This method improves accessibility to infertility treatment by providing customized dosage protocols for each patient thereby reducing the need for daily diagnostic testing. Personalized patient specific dosing profiles are derived using optimal control methods with two models for two widely used IVF dosing protocols. Clinical trials validated the results from this method corroborating the success of this study. Secondly, a global model is developed to represent the dynamics of our planet focusing on the food-energy-water (FEW) nexus with ecological, economic and techno-socio-economic dimensions. This model includes a simplified food-web model in a macroeconomic framework and a rudimentary legal system with the capability to predict the temporal progression of global indicators. Global scale data for stocks and flows of food, energy and water is used to develop and validate the model. Yearly historical data is used to validate global indicators such as human population, gross domestic product (GDP), carbon dioxide (CO2) emissions, Nitrous Oxide (NOx) emissions and global water stress. The model results show that current levels of consumption with the accelerated human population growth will lead to an unsustainable world in the future. Thus, an optimal control method based approach is applied to attain a sustainable world by maintaining the ecological systems, reducing emissions while maintaining the rate of economic growth. This work is an attempt to propose science based policy measures targeted towards improved female infertility healthcare, improved health of the ecosystem with sustainable economic growth.