Mathematical Model of HIV-1 Circulating Recombinants Forms in Mali
Affiliation(s)
1 Département de Mathématiques et d’Informatique, Faculté des Sciences et Techniques, Bamako, Mali. 2 Institut National des Sciences Appliquées de Lyon, Lyon, France.
1 Département de Mathématiques et d’Informatique, Faculté des Sciences et Techniques, Bamako, Mali. 2 Institut National des Sciences Appliquées de Lyon, Lyon, France.
ABSTRACT
In this paper, we propose a determinist mathematical model for the co-circulating into two circulating recombinants forms (CRFs) Of HIV-disease in Mali. We divide the sexually active population within three compartments (susceptible, CRF-1 infected and CRF-2 or CRF-12 infected) and study the dynamical behavior of this model. Then, we define a basic reproduction number of the CRF-2 or CRF-12 infected individuals R0 and shown that the CRF-2 or CRF-12 infected-free equilibrium is locally-asymptotically stable if R0 < 1 (thus the CRF-2 or CRF-12 infected becomes extinct in population) and unstable if R0 > 1 (thus the CRF-2 or CRF-12 infected invade in the population). Fur-thermore, we prove that under certain conditions on the parameters of the model the controllability of CRF-2 or CRF-12 infected with regard to the CRF-1 infected. Numerical simulations are given to illustrate the results.
In this paper, we propose a determinist mathematical model for the co-circulating into two circulating recombinants forms (CRFs) Of HIV-disease in Mali. We divide the sexually active population within three compartments (susceptible, CRF-1 infected and CRF-2 or CRF-12 infected) and study the dynamical behavior of this model. Then, we define a basic reproduction number of the CRF-2 or CRF-12 infected individuals R0 and shown that the CRF-2 or CRF-12 infected-free equilibrium is locally-asymptotically stable if R0 < 1 (thus the CRF-2 or CRF-12 infected becomes extinct in population) and unstable if R0 > 1 (thus the CRF-2 or CRF-12 infected invade in the population). Fur-thermore, we prove that under certain conditions on the parameters of the model the controllability of CRF-2 or CRF-12 infected with regard to the CRF-1 infected. Numerical simulations are given to illustrate the results.
KEYWORDS
Asymptotic Stability, Basic Reproduction Number of the CRF-2 or CRF-12 Infected, Controllability
Asymptotic Stability, Basic Reproduction Number of the CRF-2 or CRF-12 Infected, Controllability
Cite this paper
Alassane, M. , Mahamane, A. , Diallo, O. and Pousin, J. (2015) Mathematical Model of HIV-1 Circulating Recombinants Forms in Mali. Open Journal of Modelling and Simulation, 3, 137-145. doi: 10.4236/ojmsi.2015.34015.
Alassane, M. , Mahamane, A. , Diallo, O. and Pousin, J. (2015) Mathematical Model of HIV-1 Circulating Recombinants Forms in Mali. Open Journal of Modelling and Simulation, 3, 137-145. doi: 10.4236/ojmsi.2015.34015.
References
[1] Mahamadou, S. Hanki, Y., Maazou, A.R.A., Aoula, B. and Diallo, S. (2011) Genetic Diversity and Drug Resistance Mutation in HIV-1 from Untreated Patients in Niamey, Niger. International Scholary Research Network ISRN Microbiology, Article ID: 797463. [2] Ballesteros, S., Camacho, A. and Cazelles, B. (2009) Introducing Gradual Antigenic Drift in Co-Circulating Cross- Reactive Antigenic Clusters Models. Proceedings of the International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE. [3] Imamichi, H., Koita, O., Dabitao, D., Dao, S., Ibrahim, M., Sogoba, D., Dewar, R.L., Berg, S.C., Jiang, M.-K., Parta, M., Washington, J.A., Polis, M.A., Clifford Lane, H. and Tounkara, A. (2009) Identifaction and Characterization of CRF02_AG,CRF06_cpx, and CRF09_cpx Recombinant Subtypes in Mali, West Africa. Aids Research and Humain Retroviruses, Mary Ann Liebert, Inc., 25. [4] Diallo, O., Koné, Y. and Pousin, J. (2010) Dynamics and Thresholds of a Simple Epidemiological Model: Example of HIV-AIDS in Mali. International Journal of Mathematics and Mathematical Science, Article ID: 638021. [5] Picq, M. (2007) Résolution de l’équation du transport sous contraintes. Thèse de doctorat, Institut National des Sciences Appliquées (INSA) de lyon. http://docinsa.insa-lyon.fr/these/point.php?&id=picq
[1] Mahamadou, S. Hanki, Y., Maazou, A.R.A., Aoula, B. and Diallo, S. (2011) Genetic Diversity and Drug Resistance Mutation in HIV-1 from Untreated Patients in Niamey, Niger. International Scholary Research Network ISRN Microbiology, Article ID: 797463. [2] Ballesteros, S., Camacho, A. and Cazelles, B. (2009) Introducing Gradual Antigenic Drift in Co-Circulating Cross- Reactive Antigenic Clusters Models. Proceedings of the International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE. [3] Imamichi, H., Koita, O., Dabitao, D., Dao, S., Ibrahim, M., Sogoba, D., Dewar, R.L., Berg, S.C., Jiang, M.-K., Parta, M., Washington, J.A., Polis, M.A., Clifford Lane, H. and Tounkara, A. (2009) Identifaction and Characterization of CRF02_AG,CRF06_cpx, and CRF09_cpx Recombinant Subtypes in Mali, West Africa. Aids Research and Humain Retroviruses, Mary Ann Liebert, Inc., 25. [4] Diallo, O., Koné, Y. and Pousin, J. (2010) Dynamics and Thresholds of a Simple Epidemiological Model: Example of HIV-AIDS in Mali. International Journal of Mathematics and Mathematical Science, Article ID: 638021. [5] Picq, M. (2007) Résolution de l’équation du transport sous contraintes. Thèse de doctorat, Institut National des Sciences Appliquées (INSA) de lyon. http://docinsa.insa-lyon.fr/these/point.php?&id=picq