JKK Asamoah uses ordinary differential equations, partial differential equations, optimal control theory, and fractional derivatives to gain insights into the qualitative behaviour of nonlinear dynamical systems arising from the mathematical modelling of phenomena in the natural sciences, with an emphasis on the transmission dynamics and control of emerging and re-emerging human and animal diseases of public health and socio-economic interest.
JKK Asamoah's math models usually consist of deterministic systems of nonlinear differential equations. The goal is to find the range of parameters within which a particular disease can be managed effectively. JKK Asamoah employs or develops theories and approaches for analyzing dynamical systems to better understand the qualitative dynamics of such models. Exciting aspects of the models include the existence and asymptotic stability of steady-state solutions and the types of bifurcation linked to them. JKK Asamoah fits models to data using optimization techniques to estimate unknown parameters or uses literature values and parameter assumptions to conduct global uncertainty and sensitivity analysis for the models' basic reproduction numbers. JKK Asamoah uses cost-effectiveness theories to find the most cost-effective strategy for mitigating infectious diseases.
JKK Asamoah has published research articles in Science Journals, such as Chaos, Solitons & Fractals; Fractals; Journal of Mathematical Biology; Journal of Mathematics; Alexandria Engineering Journal; Results in Physics; Journal of Nanomaterials; Physica A: Statistical Mechanics and its Applications; The European Physical Journal Plus; Computational Intelligence and Neuroscience; Computational and Mathematical Methods in Medicine; Mathematics; Journal of Applied Mathematics; Computational and Mathematical Biophysics, Healthcare Analytics, Partial Differential Equations in Applied Mathematics; AIMS Mathematics; Fractal and Fractional; Decision Analytics Journal, Applied Mathematical Modelling; International Journal of Computing Science and Mathematics; American Institute of Physics AIP-Advances
JKK Asamoah has peer-reviewed over 100 academic research papers; see Web of Science for more details.
PHYSICS AND ASTRONOMY: 16
COMPUTER SCIENCE : 5
MEDICINE : 2
DECISION SCIENCES: 2, ENGINEERING: 1
Mathematical Models and Optimisation Strategies for Infectious Diseases and Biological Processes
Goal: This project seeks to develop and analyse compartmental models for diseases and biological processes in humans and animals. We will also predict control measures to reduce the spread of diseases in the selected population while assessing the socio-economic evaluations of the implemented control interventions.
Keywords: Mathematical biology; Mathematical models; Diseases; Stability analysis; Seasonal dynamics; Sensitivity analysis; Optimal control theory; Cost-effectiveness analysis; Riemann--Liouville--Caputo derivative; Atangana-Baleanu-Caputo (ABC) derivative; Caputo-Fabrizio (CF) derivatives; Fractal-fractional derivatives.
Methods: Differential Equations, Fractional Calculus, Optimal Control Theory
- Mathematical Epidemiology
- Applied Fractional Calculus
RESEARCH PROFILE LINKS
MATH 554: DYNAMICAL SYSTEMS AND BIFURCATION THEORY
BACG 561: PRINCIPLES OF SYSTEMS AND COMPUTATIONAL BIOLOGY
MATH 252: CALCULUS OF SEVERAL VARIABLES
MATH 158: CALCULUS
BRIEF DESCRIPTION OF RESEARCH INTEREST
Mathematical Modelling of Infectious Disease:
Infectious disease epidemics can be predicted using mathematical models to guide public health and plant health measures. Calculations based on the parameters of various contagious diseases, such as mass vaccination campaigns, can be made using models that use fundamental assumptions or collected statistics and mathematics. For example, it may be able to anticipate future growth trends or help determine which interventions to avoid and which to test.
To describe the hereditary characteristics of various behaviours, we need proper tools. Fractional derivatives are beautiful means for achieving such an objective. Another advantage of fractional derivatives is that they perform a vital function in representing dynamics between a couple of various points in several stages. Multiple definitions of such derivatives have been developed. These derivatives are based on concepts such as differentiation with a power law, the exponential law and the Mittag-Leffler operator by memory as the nonlocal and nonsingular kernel. Several real-world applications of these innovative fractional operators are available in the literature. We require numerical techniques to acquire the approximate answers to these issues because obtaining analytical solutions to equations of a different order is difficult. Some numerical methods are Lagrange interpolation, Newton polynomial, and Chebyshev collocation techniques.