Sensitivity analysis of Typhoid Fever model with Saturated Incidence rate.

Document Type : Original Article

Authors

1 Department of Statistics, Osun State University, Osogbo, Nigeria

2 Department of Mathematical Sc. Osun State University, Osogbo

3 Department of Statistics, Osun State University, Nigeria

4 Department of Mathematical Sc. Osun State University, Nigeria

5 Department of Statistics, Osun State University, Osogbo, Nigeria.

Abstract

In this study, a dynamic model for typhoid fever incorporating protection against infection in the presence of saturated incidence rate is proposed. The existence and uniqueness solution is proved in order to ascertain the existence of the model. Stability analysis of endemic and disease free equilibrium was carried out to investigate the dynamic behavior of the transmission of the disease in a given population. Sensitivity analysis was also carried out to detect the impact of the parameters of the reproductive number and which parameters should focus as a control intervention. Numerical simulation of the model was carried out and the result is presented graphically, the result shows that an increase in the probability of the sources of protection and sociology factor dictate low disease prevalence in a population.

Keywords

Main Subjects


[1] H. Abdolabadi, M. Ardestani, Hasanlou, Evaluation of water quality parameters using multivariate statistical analysis
(Case study: Atrak River), Journal of Water and Wastewater, Ab va Fazilab, 25(3) 2014, 110-117.
[2] O. Adebimpe, K.A. Bashiru, T.A. Ojurongbe, Stability of an SIR Epidemic Model with Non-Linear incidence rate and
treatment, Open Journal of Modeling and simulation, 3 2015, 104 -110.
[3] I.A. Adetunde, A Mathematical models for the dynamics of typhoid fever in Kass- ena-Nankana district of upper east
region of Ghana, J. Mod. Math. Stat, 2(2) 2008, 45-49.
[4] K.A. Bashiru, A.O. Fasoranbaku, O. Adebimpe, T.A. Ojurongbe, Stability analysis of Mother-to-Child transmission of HIV/AIDS dynamic model with treatment, Annals, Computer Science Series, 15(2) 2017.
[5] C.P. Bhunu, E.T. Ngarahana-Gwasira, Mathematical analysis on a typhoid model with carriers, direct and indirect disease transmission. International Journal of Mathematical Sciences and Engineering applications 7(1) 2013, 79-90.
[6] H.W. Conall, E.W. John, A review of typhoid fever transmission dynamics models and economic evaluations of vaccination, Centre for the mathematical modeling of infectious diseases, London School of Hygiene and Tropical Medicine, 2015.
[7] M. Daraie, S.H. Jahani Zadeh, M. Chegeny, Chemical and physical indicators in drinking water and water sources of Boroujerd using principal components analysis, Medical Laboratory Journal, 8 2014, 76-82.
[8] N.R. Derrick, S.L. Grossman, Differential Equation with application, Addision Wesley Publishing Company, Inc. Philippines 1976.
[9] O. Diekmann, J.A.P. Heesterbeck, Mathematical epidemiology of infectious disease, Mathematical and computational biology, 2000.
[10] M. Ezzati, J. Utzinger, S. Cairncross, A.J. Cohen, B.H. Singer, Environmental risks in the developing world: exposure indicators for evaluating, inventions, programmes and policies. Journal of Epidermial community Health, 59(1) 2005, 15-22.
[11] S. Faryadi, K. Shahedi, M. Nabatpoor, Investigation of water quality parameters in Tadjan River using Multivariate Statistical Techniques. Watershed Management Research Journal, 3 2012, 75-92.
[12] A.A, Fatiregun, E.E. Isere, A.I. Ayede, S.A. Olowookere, Epidemiology of an outbreak of cholera in a south-west state of Nigeria: brief report, Southern African Journal of Epidemiology and Infection, 27(4), 201-204.
[13] J.O. Jeje, K.T. Oladepo, Assessment of Heavy Metals of Boreholes and Hand Dug Wells in Ife North Local Government Area of Osun State, Nigeria. International Journal of Science and Technology, 3(4) 2014.
[14] M.L. Kaljee, A. Pach, D. Garrett, D. Bajracharya, K. Karki, I. Khan, Social and Economic Burden Associated with Typhoid Fever in Kathmandu and Surrounding Areas: A Qualitative study, Nepal, the Journal of infectious diseases, 4 2018, S243-S249.
[15] E.J. Klemn, S. Shakoor, A.J. Page, et al., Emergence of an extensively drug-resistant salmonella enterica serovar Typhi clone harboring a promiscuous plasmid encoding resistance to fluoroquinolones and third-generation cephalosporins, Mbio, 9(1) 2018, 10-1128.
[16] M. Kgosimore, R. Gosalamang, Mathematical Analysis of Typhoid Infection with treatment, Journal of Mathematical Sciences; Advances and Applications, 40 2016, 75-91.
[17] D. Kaladzievska, M.Y. Li, Modelling the effects of carriers on transmission dynamics of infectious diseases. Math. Biosci. Eng, 8(3) 2011, 711-722.
[18] M.A. Khan, M. Parvez, S. Islam, I. Khan, S. Shafie, T. Gul, Mathematical Analysis of Typhoid Model with Saturated Incidence Rate. Advanced Studies in Biology, 7(2) 2015, 65-78.
[19] M.A. Khan, Parvez, M. Islam., I. Khan, S. Shafie, T. Gul, Mathematical Analysis with Saturated Incidence Rate, Advanced Studies in Biology, 7(2) 2015, 65-78.
[20] D.T. Lauria, B. Maskery, C. Poulos, D. Whittington, An optimization model for reducing typhoid cases in developing countries without increasing public spending, Vaccine, 27(10) 2009, 1609-1621.
[21] C.P. Mushayabasa, Bhunu, E.T. Ngarakana-Gwasira, Assessing the Impact of Drug Resistance on the Transmission Dynamics of Typhoid Fever, Article ID 303645, 2013.
[22] S. Mushayabasa, C.P. Bhunu, E.T. Ngarakana-Gwasira, Mathematical analysis of a typhoid model with carriers, direct and indirect disease transmission, International Journal of Mathematical Sciences and Engineering Applications, 7(I) 2013, 79-90.
[23] S. Mushayabasa, A Simple Epidemiological Model for Typhoid with Saturated Incidence Rate and Treatment Effect, International Journal of Sciences: Based and Applied Research (IJSBAR), 32(1) 2017, 151-168.
[24] S. Mushayabasa, S. Mushayabasa, C.P. Bhunu, E.T, Ngarahana-Gwasira, Mathematical analysis on a typhoid model with carriers, direct and indirect disease transmission. International Journal of Mathematical Sciences and Engineering applications 7(1) 2013, 79-90.
[25] J.K. Nthiri, G.O. Lawi, C.O. Akinyi, D.O. Oganga, W.C. Muriuki, M.J. Musyoka, L. Koech, Mathematical Modeling of Typhoid Fever Disease incorporating Protection against the Disease, British Journal of Mathematics and Computer Science, 14(1) 2016, 1-10.
[26] J.K. Nthiiri, Global Stability of the equilibrium points of typhoid fever model with protection. British journal of mathematics and computer, 21(5) 2017, 1-6.
[27] O.J. Peter, M.O. Ibrahim, H.O. Edogbanya, Direct and indirect transmission of typhoid fever model with optimal control, Results Phys, 27 2021, 104463.
[28] V.E. Prizer, C. Cayley, Predicting the impact of vaccination on the transmission dynamics of typhoid in South Asia: A mathematical modeling study, PLoS Neglected Tropical Diseases, 8(1) 2014, e264.
[29] V.E. Pitzer, Bowles, C.C. Baker, S. Kang, G. Balaji, V. Farrar, j. Predicting the impact of vaccination on the transmission dynamics of typhoid in South Asia, A Mathematical Modeling Study, 8(1) 2014 , 1-12.
[30] V.E. Pitzer, N.A. Feasey, C.Msefula, J. Mallewa, N. Kennedy, Dube, Q. Dube, B. Denis, M. A. Gordon, R. S. Heyderman, Mathematical modeling to access the Drivers of the Recent Emergence of Typhoid Fever in Blantyre, Malawi, Clinical Infectious Diseases, 4 2015, S251-S258.
[31] O.J. Peter, M.O. Ibrahim, O.B. Akinduko, M. Rabiu, Mathematical Model for the Control of Typhoid Fever, IOSR Journal of Mathematics, 13(4) 2017, 60-66.
[32] M.G. Samson, Swaminathan, N. Venkat Kumar, Assessing Groundwater Quality for Portability, Computer Modelling and New Technologies, 14(2) 2010, 58-68.
[33] World Health Organization, Guidelines for drinking-water quality. World Health Organization, 2002.