Mathematical Modeling of Transmission Dynamics and Optimal Control of Vaccination and Treatment for Hepatitis B Virus

<table>Variation of different reproduction numbers by using of two control variables (vaccination and treatment). Figure <a href="../fig2/">2</a> illustrates the impact of application of two controls (vaccination and treatment) on different basic reproduction numbers. <svg height="15.4" id="M93" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 81.5 15.4" width="81.5" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg>, when there is no vaccination and treatment (<svg height="15" id="M94" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 43.1875 15" width="43.1875" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg>; <svg height="15" id="M95" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 43.1875 15" width="43.1875" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg>). The figure shows that application of vaccination reduces <svg height="15.4" id="M96" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 17.4 15.4" width="17.4" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg> more rapidly than treatment, though mixed intervention strategies always work better to reduce the disease burden.</table>

Computational and Mathematical Methods in Medicine

fig2

Figure 2

Figure 2: Mathematical Modeling of Transmission Dynamics and Optimal Control of Vaccination and Treatment for Hepatitis B Virus 