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Tuberculosis (TB) is caused by Mycobacterium tuberculosis (Mtb) bacteria. This disease is still a worldwide threat as it remains one of the leading causes of death in the world. Almost one-third of the world population is still infected by the Mtb bacteria either causing Latent TB or Active TB. In spite of huge progress in medical sciences with the latest prevention and treatment techniques, it is still a big threat to human beings. Possibly, there are several reasons behind the existence and survival of these Mtb bacteria depending upon the standard of living or the medical history of the person. Different people are treated in a different manner according to their conditions, which is strictly followed by the norms fixed by the government. Till date, there is limited research in the field of modeling clinical diagnosis path in TB; hence, it requires a full interplay between diagnosis and treatment. This motivated us to use a Discrete Event System (DES), Petri net, to model the diagnostic path as it helps to understand the structural and behavioral properties of the process. In this chapter, we are modeling the clinical diagnosis path of TB considering some important aspects within the process with the use of a graphical tool, Petri net. The modeling and analysis of the diagnostic path help to find and validate the longest and shortest methods to treat tuberculosis.

Mathematical modeling is playing a very important role in clarifying, analyzing, and drawing of qualitative and quantitative results. In almost every area of sciences, the complex system is being modeled using some mathematical modeling using a graphical approach, differential equation approach, statistical approach, and many more. In this chapter, we are focusing on the graphical approach using Petri Nets (PN). Petri net came in focus in the early ‘90s after Carl Adam introduced this method in his Ph.D. thesis. By then, it is being widely used to model the complex systems in engineering, computational, biological, and many more fields. Initially, it was accounted as a modeling tool in Computer Science (CS), but later, PN method started to model systems in Automatic Control (AC) too for automation after that it was being used in the background of Operations Research (OR). Therefore, this method recognized as the Discrete Event Dynamic Systems (DEDS) theory, at the intersection of CS, AC, and OR. Moreover, different kinds of hybrid PNs like Time Petri Net (TPN), Stochastic Petri Net (SPN) are being extensively studied today. PN is also being proved to be a useful tool to model the biological system like cell cycle, pathways in diseases to treat, and many more. It will help to find several structural and behavioral properties of the system.

Alcoholism is ranked as the third largest impact on human health and it leads to Alcohol-Related Brain Damage. However, in this study, we have used graph theory metrics in Igraph software to analyze the functional connectivity of the EEG network of 20 alcoholic and 20 healthy volunteers. The graph-theoretic analysis shows, compared with healthy control group, the brain network of an alcoholic has a smaller mean degree, larger degree centrality, smaller modularity, larger transitivity, larger global efficiency, larger assortativity, larger average path length, smaller network diameter but same small-world properties. The Alcoholic network lacks functionality, robustness, resilience and linear network. The alcoholic subject has disturbed connectivity in its brain network that leads to Alcohol-Related Brain Damage. This conclusion leads us to new perspective for Alcohol-Related Brain Damage.

Petroleum based synthetic plastics are an integral part of our daily life. However, their excessive usage has resulted in environmental pollution. The primary reason for this pollution is due to their non-biodegradable nature. On the other hand, polyhydroxyalkanoates (PHAs) are biodegradable polymers, which have been shown to be produced by a wide range of bacteria. The unique feature of this bioplastic production is that they can be produced from renewable substrate materials through a unique metabolic route. These PHAs have the potential to replace petroleum based synthetic plastics. PHAs have high commercial value which make them suitable agent for industrial and medical applications. Although simpler and monomeric forms of PHAs have limited biotechnological applications, however, modified forms of PHA can be used in various medical applications such as, drug delivery, biodegradable implants, anticancer agent, and tissue engineering etc. Among all, tissue engineering has emerged globally to improve the current therapeutic approaches, entailing a revolution in clinical practice. PHAs offer several benefits in tissue engineering. These chemically modified biopolymers can be used in tissue repair, regeneration of tissue, scaffolds preparation etc.