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PROPERTIES OF STABILITY AND HOPF BIFURCATION FOR AN HIV/AIDS EPIDEMIC MODEL WITH SCREENING AND TIME DELAY

Mona Alsolami, Sarah Al-Sheikh, Farida Mosally

Abstract


<p>In this paprer, we consider an HIV/AIDS epidemic model with screening and time delay. We divide the population into four subclasses, one of them is the susceptible population <i>S</i> and the others are HIV infectives (HIV positives that do not know they are infected) <i>I<sub>1</sub></i>, HIV positives that know they are infected (by way of medical screening or other ways) <i>I<sub>2</sub></i> and that of AIDS patients <i>A</i>. Both the disease-free equilibrium and the infected endemic equilibrium are found and their stability is investigated using stability theory of delay differential equations.</p><p>The effect of delay on the stability of the endemically infected equilibrium is investigated. It is shown that the introduction of time delay in the model has a destabilizing effect on the system and periodic solutions can arise by Hopf bifurcation when using the delay as a bifurcation parameter.</p><p>Finally, numerical simulations are presented to illustrate the results.</p>

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