My primary research interests focus on the following topics: A) Applied and computational mathematics, mathematical modeling, theoretical computer science, scientific computing, symbolic computation, computational algebra, algebraic geometry B) Chaos theory, chaos detection techniques, theoretical and numerical aspects of bifurcation theory and stability analysis in differential equations and polynomial system
Bioinformatics
Biology of interactions
Biology of Organisms
Biomathematics
Biophysics
Conservation Biology
Ecology
Marine Biology
Population Biology
Understanding and predicting the spread of disease outbreaks can be achieved through the examination of nonlinear biochemical and population dynamics models. These models depict the interplay between individuals who are susceptible, infected, and immune within population. By studying these models, we gain valuable insights into the complex dynamics of disease transmission and better understand how outbreaks occur and spread. In our research, we specifically focus on the stability of limit cycles for the bilinear incidence SIR and SIRS models. By studying the stability of limit cycles, we can determine the long-term behavior of the disease dynamics and make predictions about the future course of an outbreak. We can also analyze the stability of limit cycles at two steady-state points in the SIR and SIRS models. To validate our findings, we can perform both algebraic analyses and numerical simulations. The algebraic analyses can provide theoretical insights into the stability of limit cycles, while the numerical simulations allowed us to test the robustness of our results under different scenarios and parameter settings. Our simulations absolutely meet the criteria for both free and endemic states, ensuring the reliability and accuracy of our conclusions. We can develop more effective strategies to control and mitigate outbreaks. This knowledge can inform public health interventions, such as vaccination campaigns, quarantine measures, and targeted treatment protocols.
applied and computational mathematics, dynamical systems, computational algebra, population interaction, mathematical modeling, scientific computing, symbolic computation, theoretical and numerical aspects of bifurcation theory and stability analysis in differential equat