Online ISSN: 2515-8260

### Author : Balamuralitharan, S.

##### Stability and Hopf Bifurcation Analysis of Hepatitis B Infection Model with CTL Response Delay

M. Aniji; N. Kavitha; S. Balamuralitharan

European Journal of Molecular & Clinical Medicine, 2020, Volume 7, Issue 6, Pages 74-90

In this paper, the Hepatitis B Virus (HBV) infectious model with Cytotoxic T-Lymphocyte (CTL) response delay and its effect on the stability of equilibrium has been investigated. The boundedness and non-negativity solutions of the proposed model were verified. The local stability of virus-free equilibrium and the infected equilibrium were determined by the basic reproduction number R0. Further, the existence of Hopf bifurcation at the infected equilibrium of CTL response was also observed. Using different set of parameters, the empirical findings in the study are shown with numerical simulations.

##### Current Mathematical Models and Numerical Simulation of SIR Model for Coronavirus Disease - 2019 (COVID-19)

M. Suba; R. Shanmugapriya; S. Balamuralitharan; G. Arul Joseph

European Journal of Molecular & Clinical Medicine, 2020, Volume 7, Issue 5, Pages 41-54

This paper deals with seven mathematical models within the current COVID-19
pandemic situations. We developed a number of mathematical models which are
compartment solutions of nonlinear differential equations. These models are useful for
research scholars, faculty members and academicians in the area of mathematical biology.
Also, we study these models and parameter estimation from real-world problem (data of
COVID-19 in World Health Organization (WHO)). The researchers discussed to analyze
the possible solutions of each model in the general discussion section. The researchers
recommended that at the end of the year 2020, there will be a reduction on the spread and
an increased recovery rate of COVID-19. These situations are fully changed and return to
the normal life very soon. In this paper to the researchers discuss the simple SIR model
compared to real-life data for COVID-19 pandemic in Tamilnadu by district wise. This
model helps to predict the future calculations of Susceptible, Infections, and Removed
people from the total population and reproduction number R0 . The researchers conclude
that the infection rate is increased for the next two months (September and October, 2020),
and death rate percentage is also possible to decrease from the number of total
populations. Also the researchers recommend the continuous lockdown for these two
months and for all people to follow the instruction given by the Tamilnadu Government.