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

Jagjeevan Ram, Charu Kapoor, Tuhin Datta, Shravan Kumar Meena, Sanjeev Kumar

#### 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.

#### Keywords

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

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#### References

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