Transport Phenomena of Hepatitis B with Special Reference to Jacobian Matrix in the Null Space

Authors

  • Jagjeevan Ram Associate Professor, Department of Physics, Ramjas College (University of Delhi), India
  • Charu Kapoor Associate Professor, Department of Physics, Ramjas College (University of Delhi), India
  • Tuhin Datta Assistant Professor, Department of Physics, Ramjas College (University of Delhi), India
  • Shravan Kumar Meena Associate Professor, Department of Physics, Motilal Nehru College (University of Delhi), India
  • Sanjeev Kumar Associate Professor, Department of Physics, Motilal Nehru College (University of Delhi), India

Keywords:

Normalized sensitivity index, Mathematical Model, Basic Reproductive Number, Disease, Free Equilibrium, Jacobian matrix.

Abstract

A mathematical model representing the transmission dynamics of Hepatitis B virus was presented with system of non-linear differential equations which explain the interaction of Acute, Chronic, Recovered, Treatment, Vaccinated classes of the infection with another epidemiological parameter. The aim of this work is to carry out detailed sensitivity analysis of the model parameters. The disease-free equilibrium points and basic reproduction number of the cases were analyzed. Sensitivity analysis of R0 with respect to the model parameters was carried out using normalized forward sensitivity index with graphical illustrations for clarity on the effects of this sensitive parameters. Sensitivity analysis of R0 shows transmission rate b is the most sensitive parameter. It was deduced that sensitivity analysis of model parameters gives an insight into how best the spread of Hepatitis B Virus could be curtailed.

References

Abdulrahman S, Akinwande NI, Awojoyogbe OB, Abubakar UY. Mathematical solutions for Hepatitis B virus infection in Nigeria. Journal of Indian. 2013 Jun; 11 (1).

Akinwande, N.I., 2005. A mathematical model of the chaotic dynamics of the AIDS disease pandemic. J. Nig. Math. Soc, 24, pp. 8–16.

Anjum, A.U.R., Chaudhry, Q.A. and Almatroud, A.O., 2020. Sensitivity analysis of mathematical model to study the effect of T cells infusion in treatment of CLL. Mathematics, 8 (4), p. 564.

Bailey, N.T., 1975. The mathematical theory of infectious diseases and its applications. In The mathematical theory of infectious diseases and its applications (pp. 413–413).

Van den Driessche, P. and Watmough, J., 2002. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical biosciences, 180 (1–2), pp. 29–48.

Rodrigues, H.S., Monteiro, M.T.T. and Torres, D.F., 2013. Sensitivity analysis in a dengue epidemiological model. In Conference Papers in Science (Vol. 2013). Hindawi.

Adu, I.K., Aidoo, A.Y., Darko, I.O. and Osei-Frimpong, E., 2014. Mathematical model of hepatitis B in the Bosomtwe district of Ashanti region, Ghana. Applied Mathematical Sciences, 8 (67), pp. 3343–3358.

Abubakar, I.I., Tillmann, T. and Banerjee, A., 2015. Global, regional, and national age-sex specific all-cause and cause-specific mortality for 240 causes of death, 1990–2013: a systematic analysis for the Global Burden of Disease Study 2013. Lancet, 385 (9963), pp. 117–171.

Schweitzer, A., Horn, J., Mikolajczyk, R.T., Krause, G. and Ott, J.J., 2015. Estimations of worldwide prevalence of chronic hepatitis B virus infection: a systematic review of data published between 1965 and 2013. The Lancet, 386 (10003), pp. 1546–1555.

Gower, E., Estes, C., Blach, S., Razavi-Shearer, K. and Razavi, H., 2014. Global epidemiology and genotype distribution of the hepatitis C virus infection. Journal of hepatology, 61 (1), pp. S45–S57.

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Published

2022-04-30

Issue

Vol. 11 No. 1 (2022)

Section

Research Article

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