Stability analysis of a mathematical model for awareness initiatives on registration of persons in Kenya
Keywords:Aware-Adopters, Awareness Initiatives, Aware-Non-Adopters, Registration of Persons, Reproduction Number, Stability Analysis, Unaware.
In this paper, we discuss stability analysis of a mathematical model of awareness initiatives in registration of persons in Kenya. Using Ordinary Differential Equations, a mathematical model to compare the efficacy of print media, electronic media and word-of-mouth media in disseminating registration information is developed. Positivity and boundedness of solutions is established to ensure that the model is mathematically meaningful. The Basic Reproduction number R0 is derived using the Next Generation Matrix. We present both awareness free equilibrium and the maximum awareness equilibrium. Stability analysis of the model shows that Awareness free equilibrium is both locally and globally asymptotically stable when R0 < 1 hence no spread of awareness and unstable when R0 > 1 while MAE is locally asymptotically stable when R0 > 1 indicating spread of information in the population.
 G. Olivier. Metadata for identity management of population registers. Future Internet, 3:130â€“143, 2011. doi: FutureInternet2011,3,130-143; https://doi.org/10.3390/fi3020130.
 KNCHR. An Identity Crisis? A Study of Issuance of National Identity Cards in Kenya. Technical report, KNCHR, Nairobi, 2007.
 CAJ. An Investigation Report on the Crisis of Acquiring Identification Documents in Kenya. Technical report, Nairobi, 2015.
 N. O. Onyango. Factors Influencing Timely Registration of Persons in Kisumu City, Kenya. Masterâ€™s thesis, UON, Nairobi, 2014.
 M. Gacheri. Strategy Implementation Practices in the Department of National Registration Bureau in Kenya. Masterâ€™s thesis, UoN, Nairobi, 2012.
 Kenya National Assembly. Report of the Joint Committee on Administration and National Security; and Defence and Foreign Relations, on the Inquiry into the Westgate Mall Terror Attack, and other terrorist Attacks in Mandera in North Eastern and Kilifi in the Coastal Region. Technical report, Nairobi, 2013.
 R. Ullah, G. Zaman, and S. Islam. Stability Analysis of a General SIR Epidemic Model. VFAST Transactions on Mathematics, 1:16â€“20, 2013. doi: http://vfast.org/index.php/ VTM@2013ISSN:2309-0022.
 N. Kaur, M. Ghosh, and S. S. Bhatia. Modeling and Analysis of an SIRS Epidemic Model with Effect of Awareness Programs by Media. Mathematical and Computational Sciences, 8(1):233â€“239, 2014. https://doi.org/10.1155/2014/680743.
 O. G. Agaba, N. Y. Kyrychko, and B. K. Blyuss. Mathematical Model for the Impact of Awareness on Dynamics of Infectious Diseases. Mathematical Bio Sciences, 286: 22â€“30, 2017. https://doi.org/10.1016/j.mbs.2017.01.009.
 P. K. Roy, S. Saha, and F. Al Basir. Effect of Awareness Programs in Controlling the Disease HIV/AIDS: an Optimal Control Theoretic Approach. Advances in Difference Eguation, 2015:217, 2015. https://doi.org/10.1186/s13662-015-0549-9.
 H. Huo and Q. Wang. Modelling the Influence of Awareness Programs by Media on the Drinking Dynamics. Abstract and Applied Analysis, 2014:1â€“8, 2014. https://doi.org/10.1155/2014/938080.
 J. Aminiel, D. Kajunguri, and E. A. Mpolya. Mathematical Modeling on the Spread of Awareness Information to Infant Vaccination. Applied Mathematics, 5(6):101â€“110, 2015.
 M. B. Onyuma. Modelling Cholera Transmission Incorporating Media Coverage. Masterâ€™s thesis, Moi University, Eldoret, 2017.
 O. Diekmann, J. A. P. Heesterbeek, and J. A. J. Metz. On the Definition and the Computation of the Basic Reproduction Ratio R0 in Models for Infectious Diseases in Heterogeneous Populations. Mathematical Biology, 28(4):365â€“382, 1990. https://doi.org/10.1007/BF00178324.
 P. Van Den Driessche and J. Watmough. Reproduction Numbers and Threshhold Endemic Equilibria for Compartmental Models of Disease Transmission. Mathematical Biosciences, 180(1-2):29â€“48, 2002. https://doi.org/10.1016/S0025-5564(02)00108-6.
 C. Castillo-Chavez, Z. Feng, and W. Huang. On the computation of R0 and its role on global stability. Springer-Verlag, 125:229â€“250, 2002. https://doi.org/10.1007/978-1-4757-3667-0_13.
 N. M. Laurencia, S. M. Estomih, and D. M. Oluwole. Temporal Model for Dengue Disease with Treatment. Advances in Infectious Diseases, 5:21â€“36, 2015. https://doi.org/10.4236/aid.2015.51003.
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