The theoretical approches I use are mainly given by differential equations. I also work on simulation computational models like cellular automata or bit-string systems to study quasispecies dynamics and evolution.

In my Ph.D. I investigated the hypercycle theory and the origin of life problem. I also explored the quasispecies theory, used as a theoretical tool to analyze the dynamics and evolution of RNA viruses. I have also analyzed several ecological models of replicator systems under several interactions as competition, predator-prey or symbiontic dynamics.

In my first postdoc I worked on theoretical and computational virology. More specifically, I studied RNA silencing and viral dynamics for plant RNA viruses such as Tobacco etch virus or Turnip mosaic potyvirus. During this period I colsely collaborated with experimentalists designing and studying the mathematical and computational models to study real data.

Now I am joining a research group working on both experiments and theory. The group is studying important human pathogens such as herpesviruses, HIV-1 and HCV. Viral diseases have taken an enormous impact on human health. For instance, HIV-1 has caused a worldwide pandemic that has killed over 25 million people. Herpesvirus, such as cytomegalovirus (CMV), infects a majority of the world's population causing tens of thousands of birth defects each year in the US and EU alone: hepatitis C virus (HCV) ifects over 200 million people worldwide and kills 10-20,000 people each year in the US. Influenza virus kills 250-500,000 people worldwide. The development of new theory to understand the behavior of these pathogens is extremely important, specially when one can combine theoretical and experimental scientific research. The use of applied mathematics to characterize these systems offers an excellent oportunity to shed light on possible therapies which may be tested with experimental research, opening new ways for medical research.

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