Balancing economic and epidemiological interventions in the early stages of pathogen emergence.

The global pandemic of COVID-19 has underlined the need for more coordinated responses to emergent pathogens. These responses need to balance epidemic control in ways that concomitantly minimize hospitalizations and economic damages. We develop a hybrid economic-epidemiological modeling framework that allows us to examine the interaction between economic and health impacts over the first period of pathogen emergence when lockdown, testing, and isolation are the only means of containing the epidemic. This operational mathematical setting allows us to determine the optimal policy interventions under a variety of scenarios that might prevail in the first period of a large-scale epidemic outbreak. Combining testing with isolation emerges as a more effective policy than lockdowns, substantially reducing deaths and the number of infected hosts, at lower economic cost. If a lockdown is put in place early in the course of the epidemic, it always dominates the "laissez-faire" policy of doing nothing.

The Mathematical modeling of Cancer growth and angiogenesis by an individual based interacting system.

We present a mathematical model for the complex system for the growth of a solid tumor. The system embeds proliferation of cells depending on the surrounding oxygen field, hypoxia caused by insufficient oxygen when the tumor reaches a certain size, consequent VEGF release and angiogenic new vasculature growth, re-oxygenation of the tumor and subsequent tumor growth restart. Specifically cancerous cells are represented by individual units, interacting as proliferating particles of a solid body, oxygen, and VEGF are fields with a source and a sink, and new angiogenic vasculature is described by a network of growing curves. The model, as shown by numerical simulations, captures both the time-evolution of the tumor growth before and after angiogenesis and its spatial properties, with different distribution of proliferating and hypoxic cells in the external and deep layers of the tumor, and the spatial structure of the angiogenic network. The microscopic description of the growth opens the possibility of tuning the model to patient-specific scenarios.