Applied and Computational Mathematics
Volume 4, Issue 3, June 2015, Pages: 181-191
Received: May 12, 2015;
Accepted: May 22, 2015;
Published: Jun. 3, 2015
Views 4724 Downloads 290
Laurencia Ndelamo Massawe, Faculty of Science, Technology and Environmental Studies, The Open University of Tanzania, Dar es Salaam, Tanzania
Estomih S. Massawe, Mathematics Department, University of Dar es salaam, Dar es Salaam, Tanzania
Oluwole Daniel Makinde, Faculty of Military Science, Stellenbosch University, Saldanha, South Africa
A mathematical model is presented to examine the interaction between human and vector populations. The model consists of five control strategies i.e. campaign aimed in educating careless individuals as a mean of minimizing or eliminating mosquito-human contact, control effort aimed at reducing mosquito-human contact, the control effort for removing vector breeding places, insecticide application and the control effort aimed at reducing the maturation rate from larvae to adult in order to reduce the number of infected individual. Optimal Control (OC) approach is used in order to find the best strategy to fight the disease and minimize the cost.
Laurencia Ndelamo Massawe,
Estomih S. Massawe,
Oluwole Daniel Makinde,
Modelling Infectiology and Optimal Control of Dengue Epidemic, Applied and Computational Mathematics.
Vol. 4, No. 3,
2015, pp. 181-191.
Rodrigues, H.S., Monteiro, M.T.T. and Torres, D.F.M. Dynamics of Dengue epidemics using optimal control. Mathematical and Computer Modelling, 2010, 1-10.
Lenhart, S. and Workman, J.T. Optimal Control Applied to Biological Models, Mathematical and Computational Biology Series, Chapman and Hall/CRC, London, UK, 2007.
WHO. Dengue and Dengue Haemorrhagic Fever. Fact Sheet No. 117. Geneva: World Health Organization, 2002
Gibbons, R.V. and Vaughn, D.W. Dengue, an escalating problem. BMJ: British Medical Journal, 2002, 324: 1563.
Seidu, B. and Makinde, O.D. Optimal Control of HIV/AIDS in the workplace in the Presence of Careless Individuals, Computational and Mathematical Methods in Medicine:2014:1-19.
Ozair, M., Lashari, A.A., Jung, Il.H. and Okosun K.O. Stability Analysis and Optimal Control of a Vector-Borne Disease with Nonlinear Incidence. Discrete Dynamics in Nature and Society, 2012: 1-21.
Thome, R.C.A., Yang, H.M. and Esteva, L. Optimal control of Aedes aegypti mosquitoes by the sterile insect technique and insecticide. Math. Biosci .2010, 223 :12-23.
Rodrigues, H.S., Monteiro, M.T.T and Torres, D.F.M. Modeling and Optimal Control Applied to a Vector Borne Disease. International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE, 2012, 1063-1070.
Rodrigues, H.S., Monteiro, M.T.T. and Torres, D.F.M.(2010). Insecticide control in a dengue epidemics model. In Numerical Analysis and Applied Mathematics, T. Simos, ed., AIP Conf. Proc.,2010, 1281(1) :979–982.
Rodrigues, H.S., Monteiro, M.T.T. and Torres, D.F.M. Dengue disease, basic reproduction number and control. International Journal of Computer Mathema tics ,2011, 1–13.
Laarabi, H., Labriji, E.H., Rachik, M. and Kaddar, A. Optimal control of an epidemic model with a saturated incidence rate. Nonlinear Analysis: Modelling and Control, 2012, 17(4) 448–459
El hia, M., Balatif, O., Rachik, M. and Bouyaghroumni, J. Application of optimal control theory to an SEIR model with immigration of infectives. International Journal of Computer Science Issues , 2013, 10 (2): 1694-0784
Mwamtobe, P.M., Abelman ,S., Tchuenche,J.M. and Kasambara. Optimal (Control of) Intervention Strategies for Malaria Epidemic in Karonga District, Malawi. Abstract and Applied Analysis 2014: 1-20
Massawe, L.N., Massawe, E.S. and Makinde, O.D. Temporal model for dengue disease with treatment. Advances in Infectious Diseases, 2015, 5(1):1-16.
Rodrigues HS, Monteiro MTT and Torres DFM. Sensitivity Analysis in a Dengue Epidemiological Model. Conference Papers in Mathematics Volume, 2013.
Makinde, O.D. and Okosun, K.O. “Impact of chemo-therapy on optimal control of malaria disease with infected immigrants,” BioSystems, 2011, 104 (1): 32–41.
Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V. and Mishchenko, E.F. The Mathematical Theory of Optimal Processes. Wiley, New York,1962.
W.H. Fleming and R.W. Rishel, Deterministic and Stochastic Optimal Control, vol.1, Springer, New York, NY, USA, 1975.
Dumont Y, Chiroleu F and Domerg C. “On a temporal model for the Chikungunya disease: modelling, theory and numerics,” Mathematical Biosciences, 2008, 213(1): 80–91.
Okosun K.O. O.D. Makinde, I. Takaidza. Impact of optimal control on the treatment of HIV/AIDS and screening of unaware infectives, Applied Mathematical Modelling , 2013, 37: 3802–3820.