Dengue is a flavivirus,
transmitted to human through the bites of infected Aedesaegypti and A. albopictus mosquitoes. In this
paper, we analyze a new system of ordinary differential equations which
incorporates saturated incidence function, vector biting rate and control
measures at both the aquatic and adult stages of the vector (mosquito). The
stability of the system is analysed for the dengue-free equilibrium via the
threshold parameter (reproduction number) which was obtained using the Next
generation matrix techniques. Routh Hurwitz criterion along together with
Descartes’ rule of signs change established the local asymptotically stability
of the model whenever R0＜1and unstable
otherwise. Furthermore, the sensitivity analysis was carried out and the
numerical simulation reveals that increasing the proportion of human antibody
and putting into place a control strategy that minimize the vector biting rate
are enough to reduce the infection of the disease in the population to its
barest minimum.
Cite this paper
Ojo, M. M. , Gbadamosi, B. , Olukayode, A. and Oluwaseun, O. R. (2018). Sensitivity Analysis of Dengue Model with Saturated Incidence Rate. Open Access Library Journal, 5, e4413. doi: http://dx.doi.org/10.4236/oalib.1104413.
Bowman, C., Gumel, A.B., van den Driessche, P., Wu, J. and Zhu, H. (2005) Mathematical Model for Assessing Control Strategies against West Nile Virus. Bulletin of 682 Mathematical Biology, 67, 1107-1133. https://doi.org/10.1016/j.bulm.2005.01.002
Ranjit, S. and Kissoon, N. (2011) Dengue Hemorrhagic Fever and Shock Syndromes. Pediatric Critical Care Medicine, 12, Article ID: 90100. https://doi.org/10.1097/PCC.0b013e3181e911a7
Iurii, B. (2015) A survey of Mathematical Model of Dengue Fever. Elec-tronic Thesis & Dissertations, 1236. http://digitalcommons.georgiasouthern.edu/etd/1236
Hossain, Md.S., Nayeem, J. and Podder, Dr.C. (2015) Effects of Migratory Population and Control Strategies on the Transmission Dynamics of Dengue Fever. Journal of Applied Mathematics & Bioinformatics, 5, 43-80.
Wilder-Smith, A. and Schwartz, E. (2005) Dengue in Travelers. The New England Journal of Medicine, 353, 924-932. (Effect of Migratory Population and Control Strategies.)
Varatharaj, A. (2010) Encephalitis in the Clinical Spectrum of Dengue Infection. Neurology India, 58, Article ID: 585591. https://doi.org/10.4103/0028-3886.68655
Chowell, G., Diaz-Duenas, P., Miller, J.C., Alcazar-Velazco, A., Hyman, J.M., Fenimore, P.W. and Castillo Chavez C. (2007) Estimation of the Reproduction Number of Dengue Fever from Spatial Epidemic Data. Mathematical Biosciences, 208, 571-589. https://doi.org/10.1016/j.mbs.2006.11.011
Esteva, L. and Vargas, C. (1999) A Model for Dengue Disease with Variable Human Population. Journal of Mathematical Biology, 38, 220-240. https://doi.org/10.1007/s002850050147
Coutinho, F.A.B., Burattini, M.N., Lopez, L.F. and Massad, E. (2006) Threshold Conditions for a Non-Autonomous Epidemic System Describing the Population Dynamics of Dengue. Bulletin of Mathematical Biology, 68, 2263-2282. https://doi.org/10.1007/s11538-006-9108-6
Esteva, L. and Vargas, C. (1998) Analysis of a Dengue Disease Transmission Model. Mathematical Biosciences, 150, 131-151. https://doi.org/10.1016/S0025-5564(98)10003-2
Esteva, L. and Vargas, C. (2000) Influence of Vertical and Mechanical Transmission on the Dynamics of Dengue Disease. Mathematical Biosciences, 167, 51-64.
https://doi.org/10.1016/S0025-5564(00)00024-9
Akinpelu, F.O. and Ojo, M.M. (2016) A Mathematical Model for the Dynamic Spread of Infection Caused by Poverty and Prostitution in Nigeria. International Journal of Mathematics and Physical Sciences Research, 4, 33-47.
Esteva, L., Gumel, A. and Vargas, C. (2009) Qualitative Study of Transmission Dynamics of Drug-Resistant Malaria. Mathematical and Computer Modelling, 50, 611-630. https://doi.org/10.1016/j.mcm.2009.02.012
Akinpelu, F.O. and Ojo, M.M. (2017) Sensitivity Analysis of Ebola Model. Asian Research Journal of Mathematics, 2, 1-10. https://doi.org/10.9734/ARJOM/2017/30642
Iboi, E. and Okuonghae, D. (2016) Population Dynamics of a Mathematical Model for Syphilis. Applied Mathematical Modelling, 40, 3573-3590. https://doi.org/10.1016/j.apm.2015.09.090
Hethcote, H.W. and Thieme, H.R. (1985) Stability of the Endemic Equilibrium in Epidemic Models with Sub Populations. Mathematical Biosciences, 75, 205-227. https://doi.org/10.1016/0025-5564(85)90038-0
Derouich, M. and Boutayeb, A. (2006) Dengue Fever: Mathematical Modelling and Computer Simulation. Applied Mathematics and Computation, 177, 528-544. https://doi.org/10.1016/j.amc.2005.11.031
Olaniyi, S. and Obabiyi, O.S. (2013) Mathematical Model for Malaria Transmission Dynamics in Human and Mosquito Populations with Nonlinear Forces of Infection. International Journal of Pure and Applied Mathematics, 88, 125-156.
Takahashi, L.T., Maidana, N.A., Ferreira Jr, W.C., Pulino, P. and Yang, H.M. (2005) Mathematical Models for the Aedes aegypti Dispersal Dynamics: Travelling Waves by Wing and Wind. Bulletin of Mathematical Biology, 67, 509-528. https://doi.org/10.1016/j.bulm.2004.08.005
Vanden Driessche, P. and Watmough, J. (2002) Repro-duction Numbers and Sub-Threshold Endemic Equilibria for Compartmental Models of Disease Transmission. Mathematical Bio-sciences, 180, 29-48. https://doi.org/10.1016/S0025-5564(02)00108-6
Agusto, F.B. and ELmojtaba, I.M. Optimal Control and Cost-Effective Analysis of Malaria/Visceral Leishmaniasis Co-Infection. PLoS ONE, 12, e0171102. https://doi.org/10.1371/journal.pone.0171102
