ON OPTIMAL CONTROL AND COST-EFFECTIVENESS ANALYSIS FOR TYPHOID FEVER MODEL
Abstract
Abstract
Typhoid fever is a disease of a major concern in the developing world because it adversely affects on health and finance of a large chunk of people in this part of the world. This paper is aim to develop an extend and improve the optimal control model of typhoid transmission dynamics that can select the best cost-effective strategy for some interventions. Thus, an optimal control model for typhoid, incorporating control functions representing measures of personal hygiene and sanitation, diagnosis and treatment, and vaccination, was formulated. The corresponding optimality system was characterized via the Pontryagin’s maximum principle. The optimality system was numerically simulated for all possible strategies using Runge-Kutta method of order four. For cost-effectiveness analysis, the method of incremental cost-effectiveness ratio (ICER) was employed. The results show that the model is able to select the most cost-effective strategy for any given set of parameter values and initial conditions.
Key words: Optimal control, Pontryagin’s maximum principle, cost-effectiveness
References
References
Anderson, R.M. and May, R.M. (1991). Infectious diseases of Humans: Dynamics and Control, Oxford University Press.
Amicizia, D., Micale, R.T., Pennati, B.M., Zangrillo, F., Iovine, M., Lecini, E., Marchini, F., Lai, P.L., Panatto, D. (2019;). Burden of typhoid fever and cholera: similarities and differences. Prevention strategies for European travelers to endemic/epidemic areas, J Prev Med Hyg
Athithan, S. and Ghosh, M. (2016). Optimal control of tuberculosis with case detection and treatment, WJMS, 11(2): 111-122
Browne, A J., Hamadani, B. H. K. Kumaran, E. A. P., Rao, P., Longbottom, J., Harriss, E., Moore, C. E., Dunachie, S., Basnyat, B., Baker, S., Lopez, A. D., Day, N. P. J., Hay, S. I. and Dolecek, C. ((2020) ). Drug-resistant enteric fever worldwide, 1990 to 2018: a systematic review and meta-analysis, BMC Medicine 18:1
Buckle, G. C., Walker, C. L. F., Black, R. E. (2012). Typhoid fever and paratyphoid fever: Systematic review to estimate global morbidity and mortality for 2010, Journal of Global Health, vol., 2(1): 2-10
Deksissa, T., and Gebremedhin, E. Z. ((2019). A cross-sectional study of enteric fever among febrile patients at Ambo hospital: prevalence, risk factors, comparison of Widal test and stool culture and antimicrobials susceptibility pattern of isolates, BMC Infectious Diseases, 19:288
Ebenezer, B., Badu, K. and Kwesi, A. S. (, (2016) Optimal Control Application to an Ebola Model, Health Science Journal, 10(2:7): 1-7
Espinoza, L. M. C., McCreedy, E., Holm, M., Im, J., Mogeni, O. D., P., Parajulee, O. D., Panzner, U., Park, S. E., Toy, T., Haselbeck, A., Seo, H. J., Jeon,, H. J., Kim, J., Kwon, S. Y., Kim, J. H., Parry, C. M., and Marks, F. (2019). Occurrence of Typhoid Fever Complications and Their Relation to Duration of Illness Preceding Hospitalization: A Systematic Literature Review and Meta-analysis, Clinical Infectious Diseases; 69(S6):S435–48
Fleming, W.H. and Rishel, R.W. (1975), Deterministic and Stochastic Optimal Control, Wiley, USA
Hattaf, K., M. Rachik, S. Saadi, Y. Tabit and N. Yousfi ((2009) Optimal Control of Tuberculosis with Exogenous Reinfection, Applied Mathematical Sciences, 3(5):231-240
Kahuru, J., Luboobi, L. S., and Yaw N. (, (2017). Optimal Control Techniques on a Mathematical Model for the Dynamics of Tungiasis in a Community, International Journal of Mathematics and Mathematical Sciences, Vol. 2017, 1-20
Khamis, D. El Mouden, C., Kura, K. and Bonsall, M. B. ((2018)). Optimal control of malaria: combining vector interventions and drug therapies, Malar J, 17(174):1-18,
Lakshmikantham, S., Leela, S.,Martynyuk, A. A.,(1989) Stability Analysis of Nonlinear Systems. Marcel Dekker Inc., New York and Busel
Lashari, A. A., Shaban A.,, Hattaf, K., Zaman, G., Jung, H. and Li, X. Z. (2012) Presentation of Malaria Epidemics Using Multiple Optimal Controls, Journal of Applied Mathematics, Article ID 946504,17pagesdoi:10.1155/2012/946504
Mather, R. G., Hopkins, H., Parry, C. M., Dittrich, S. (201). Redefining typhoid diagnosis: what would an improved test need to look like? BMJ Global Health, 4:e001831. doi:10.1136/bmjgh-2019-001831
Mukhopadhyay, B., Sur, D., Gupta , S. S.,and Ganguly, N.K. (2019,). Typhoid fever: Control & challenges in India, Indian J Med Res 150, 437-447
Mwanga, G. G., Haario, H. Nannyonga, B. ((2014). Optimal Control of Malaria Model with Drug Resistance in Presence of Parameter Uncertainty. Applied Mathematical Sciences, 8(55): 2701 – 2730
Ohanu, M. E. Iroezindu, M. O., Maduakor, U., Onodugo, O. D., Gugnani, H. C. (2019).Typhoid fever among febrile Nigerian patients: Prevalence, diagnostic performance of the Widal test and antibiotic multi-drug resistance, Malawi Medical Journal 31 (3): 184-192
Otieno, G , Koske, J. K. and Mutiso, J. M. ((2016). Transmission Dynamics and Optimal Control of Malaria in Kenya, Hindawi Discrete Dynamics in Nature and Society, Volume 2016, 1-27
Radhakrishnan, A., Als, D., E. Mintz, D., Crump, J. A., Stanaway, J., Breiman, R. F., and Bhutta, Z. A., (2018). Introductory Article on Global Burden and Epidemiology of Typhoid Fever. Am. J. Trop. Med. Hyg., 99 (Suppl 3): 4–9
Silva, C. J. and Torres, D.F.M. ((2014)). Optimal Control of Tuberculosis: A Review, Mathematics of the Planet Earth, 1-22
Tchuenche, J. M., Khamis, S. A., Agusto, F. B. and Mpeshe, S. C. (2011). Optimal Control and Sensitivity Analysis of an Influenza Model with Treatment and Vaccination, Acta Biotheor, 59:1–28
Tilahun, G. T., Makinde, O. D. and Malonza, D.( 2017). Modeling and optimal control of typhoid fever disease with cost-effective strategies, Computational and Mathematical Methods in Medicine, 2017, 1-16
WHO (2019).Immunization, Vaccines and Biologicals
Copyright (c) 2020 FUDMA JOURNAL OF SCIENCES
This work is licensed under a Creative Commons Attribution 4.0 International License.
FUDMA Journal of Sciences
