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 ？for , then each infectious individual in Sub-Population j infects on average less than one
other person and the disease is likely to die out. Otherwise, if ？for , then each infectious individual in Sub-Population j 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 ？both ideas of
the inner equilibrium point of stability properties are discussed.
References
[1]
Kermack, W.O. and McKendrick, A.G. (1927) Contributions to the Mathematical Theory of Epidemics. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 115, 700-721.
[2]
Heffernan, J.M., Smith, R.J. and Wahl, L.M. (2005) Perspectives on the Basic Reproductive Ratio. Journal of the Royal Society Interface, 2, 281-291. https://doi.org/10.1098/rsif.2005.0042
[3]
van den Driessche, P. and Watmough, J. (2003) Reproduction Ratio and Endemic Equilibria for Deterministic Models of Disease Transmission. Mathematical Sciences, 181, 25-49.
[4]
Siekmann, O. and Heesterbeek, J.A.P. (2000) Mathematical of Infectious Diseases: Model Structure, Analysis and Interpretation. John Wiley and Sons, New York.
[5]
Cull, P. (1986) Local and Global Stability for Population Models. Biological Cybernetics, 54, 141-149. https://doi.org/10.1007/BF00356852
[6]
Li, J. and Zou, X. (2009) Generalization of the Kermack-McKendrick SIR model to a Patchy Environment for a Disease with Latency. Mathematical Modelling of Natural Phenomena, 4, 92-118. https://doi.org/10.1051/mmnp/20094205
[7]
Ngwenya, O. (2009) The Role of Incidence Functions on the dynamics of SEIR Model. Doctoral Dissertation, University of Manitoba, Canada.
[8]
Tessa, O.M. (2006) Mathematical Model for Control of Measles by Vaccination. Proceedings of Mali Symposium on Applied Sciences, 2006, 31-36.
[9]
van den Driessche, P. and Watmough, J. (2002) Reproduction Numbers and Sub-Threshold Endemic Equilibria for Compartmental Models of Disease Transmission. Mathematical Biosciences, 180, 29-48. https://doi.org/10.1016/S0025-5564(02)00108-6
[10]
Mukherjee, D. (2003) Stability Analysis of a Stochastic Model for Prey-Predator System with Disease in the Prey. Nonlinear Analysis: Modelling and Control, 8, 83-92.
![\"\"](\"Edit_3acb2ccb-2823-454d-899c-b3c54b5f3005.bmp\")
![\"\"](\"Edit_81676077-1b2f-4c8f-96e7-90b211af63da.bmp\")
![\"\"](\"Edit_2537f77d-dde2-4b93-826e-1cf0efa2214c.bmp\")
![\"\"](\"Edit_763f8290-5145-4ced-8daf-7760bfb7849d.bmp\")
![\"\"](\"Edit_a3131989-3292-44ab-bd08-f9641bb9da9b.bmp\")
