Prof.  Md.  Asaduzzaman
Dean, Faculty of Sciences, Islamic university, Kushtia-7003,  Bangladesh

Title: Dynamical behavior analysis and optimal control of a generalized Caputo-type fractional ASIR dengue transmission model in the perspective of Bangladesh

Abstract:

The dengue fever (DF) is a life-threatening virus-related disease for the people of tropical and subtropical countries as like Bangladesh, India, Pakistan, Malaysia, etc. In Bangladesh, DF has been endemic for more than three decades. There is no specific medicine yet to treatment this disease. Although, some preliminary treatments have been running, but every year many people have died by the austerity of this disease and it is clear that this disease will not be removed quickly from our environment. Therefore, we have to work on detecting the dynamical conduct of this disease and a suitable mathematical model of disease transmission (DT) can help us to control this disease effectively. From this context, in this talk we discuss and analyze a six compartmental fractional Aquatic-Susceptible-Infected-Recovered DT model for explaining the DT dynamics. Here, we involve the new generalized Caputo-type fractional order derivative (NGCFOD) to fractionalize the considered DT model. For establishing the existence and uniqueness of model’s solutions, we apply the Banach fixed point theorem. Here, we study a sensitivity analysis for the considered DT model. Furthermore, we formulate and solve an optimal control problem for the considered DT model applying Forward-backward sweep scheme and Pontryagin’s Minimum principle. A numerical simulation has been performed for studying the dynamical behavior of DT applying Modified adaptive predictor-corrector (MAPC) method. The required data has been collected from different health institutions of Bangladesh. Finally, we provide some essential epidemiological remarks and discuss the impact of NGCFOD operator to control the DF in Bangladesh.

Biography:

Professor Dr. Md. Asaduzzaman joined at the Department of Mathematics, Islamic University (IU), Bangladesh in April, 2010. Prior to his current position at IU, he was a Lecturer at Ahsanullah University of Science and Technology, Bangladesh. Furthermore, he has been served as a Visiting Professor at Cankiri Karatekin University, Turkey in 2022. He is graduated from University of Rajshahi holding First-class B.Sc. (Honours), First-class M. Sc. and M.Phil. degree in Mathematics. He completed his Ph.D. from IU with thesis entitle “Determination of the Solvability of Non-linear Differential Equations by Applying Fixed Point Theorems”. In addition, he has been completed various research projects as Principal Investigator. He has 48 published research articles in peer-reviewed journals. His research interests are focused on both theoretical and applied Mathematics. Specifically, his research interest is in Non-linear fractional differential equations, Mathematical and computational modelling of various infectious diseases and therapeutic approaches for Cancer treatment, Optimal control, Fixed-point theory. He was an Invited Speaker in an International Conference at North-Eastern Hill University, Shillong, India. Furthermore, he has been participated in 09 international conferences and guided various thesis of under-graduate, graduate and PhD level’s fellows. Also, he has been worked as a reviewer of 26 international journals.