Stability Analysis of a Deterministic Epidemic Model in Metapopulation Setting

摘要

We present in this article an epidemic model with saturated in metapopulation setting. We develop the mathematical modelling of HIV transmission among adults in Metapopulation setting. We discussed the positivity of the system. We calculated the reproduction number, If src="Edit_3acb2ccb-2823-454d-899c-b3c54b5f3005.bmp" alt="" /> style="font-size:10pt;font-family:""> style="font-size:10pt;font-family:""> style="font-family:Verdana;font-size:12px;">?for src="Edit_81676077-1b2f-4c8f-96e7-90b211af63da.bmp" alt="" /> style="font-size:10pt;font-family:""> style="font-size:10pt;font-family:""> style="font-family:Verdana;font-size:12px;">, then each infectious individual in Sub-Population style="font-family:Verdana;font-size:12px;"> j style="font-family:Verdana;font-size:12px;">infects on average less than one other person and the disease is likely to die out style="font-family:Verdana;">. style="font-size:10pt;font-family:""> style="font-family:Verdana;font-size:12px;"> Otherwise, if src="Edit_2537f77d-dde2-4b93-826e-1cf0efa2214c.bmp" alt="" /> style="font-size:10pt;font-family:""> style="font-size:10pt;font-family:""> style="font-family:Verdana;font-size:12px;">?for src="Edit_763f8290-5145-4ced-8daf-7760bfb7849d.bmp" alt="" /> style="font-size:10pt;font-family:""> style="font-size:10pt;font-family:""> style="font-family:Verdana;font-size:12px;">, then each infectious individual in Sub-Population style="font-family:Verdana;font-size:12px;"> j style="font-family:Verdana;font-size:12px;">infects on average more than one other person; the infection could therefore establish itself in the population and become endemic. An epidemic model, where the presence or absence of an epidemic wave is characterized by the value of src="Edit_a3131989-3292-44ab-bd08-f9641bb9da9b.bmp" alt="" /> style="font-size:10pt;font-family:""> style="font-family:Verdana;">?both ideas of the inner equilibrium point of stability properties are discussed.