I am also grateful for the support of the Stipendium Hungaricum Foundation, the Bolyai Institute and Doctoral School in Mathematics and Computer Science. My sincere thanks also go to the Dynamical Models in Biology team and the PhD students of Bolyai Institute, who encouraged me to go a long way.I would like to thank my parents and siblings for their continued support that started from my childhood and has been continuing until this moment. Also, I thank my wife and children for their patient for my long absent.Last but not least, I would like to thank my extended family and friends for their moral support throughout the writing of this thesis and my life in general.