The Effect of Chemoprophylaxis for Exposed Individuals on Lymphatic Filariasis Model
Applied and Computational Mathematics
Volume 5, Issue 1, February 2016, Pages: 30-39
Received: Dec. 29, 2015;
Accepted: Jan. 14, 2016;
Published: Feb. 19, 2016
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Aziza Juma Iddi, Mathematics Department, University of Dar Es Salaam, Dar Es Salaam, Tanzania
Estomih Massawe, Mathematics Department, University of Dar Es Salaam, Dar Es Salaam, Tanzania
Gamba Nkwengulila, Zoology and Wildlife Conservation Department, University of Dar Es Salaam, Dar Es Salaam, Tanzania
Moatlhodi Kgosimore, Mathematics Department, Botswana College of Agriculture, Gaborone, Botswana
In this paper, a deterministic Lymphatic Filariasis (LF) model is formulated and analyzed with the aim of assessing the effect of chemoprophylaxis for the exposed individuals and treatment of symptomatic LF infections. Qualitative and quantitative analysis are implemented to determine the basic reproduction number Re necessary for the control of the diseases in the communities. The disease-free equilibrium (DFE) exists and is locally and globally asymptotically stable if Re<1, whereas if Re>1 the endemic equilibrium exists and it is locally asymptotically stable. Numerical simulations are carried to complement the analytical results.
Aziza Juma Iddi,
The Effect of Chemoprophylaxis for Exposed Individuals on Lymphatic Filariasis Model, Applied and Computational Mathematics.
Vol. 5, No. 1,
2016, pp. 30-39.
C. Bhunu and S. Mushayabasa, “Transmission Dynamics of Lymphatic Filariasis, Mathematical Approach,” International Scholarly Research Network ISRN Biomathematics, vol 2012, Article ID 930130, 9 pages.
K. Blayneh, Y. Cao, and H. Kwon, “Optimal Control of Vector borne Diseases: Treatment and Prevention,” Discrete and Continuous Dynamical Systems Series B. 11(3) 2009. pp 1-xx.
S. Bowong, J. J Tewa and J. C. Kamgang, “Transmission Dynamics of Tuberculosis Model,” World Journal of Modelling and Simulation vol. 7, 2011, pp. 83-100.
M. S. Chan, A. Srividya, R. A. Norman, S. P. Pani, K. D. Ramaiah, P. Vanamail, E. Michael, P. K. Das, and D. A. P. Bundy. “EPIFIL: A Dynamic Model of Infection and Disease in Lymphatic Filariasis,” The American Society of Tropical Medicine and Hygiene 59(4), 1998, pp. 606–614.
C. Chavez-Castillo and B. Song, “Dynamical Models of Tuberculosis and their Applications,” Mathematical Biosciences and Engineering vol. 2, 2004 pp. 361-404.
N. Chitnis, J. M. Hyman and J. M. Cushing, “Determining Important Parameters in the Spread of Malaria Through the Sensitivity Analysis of a Mathematical Model,” Bulletin of Mathematical Biology vol. 70, 2008, pp. 1272-1296.
H. A Ishikawa, A. Ishi, N. Nagai, H. Ohmae, H. Masakazu, S. Suguri and J. Leafa- sia. “A mathematical model for the transmission of Plasmodium vivax malaria,” Parasitology International, vol. 52, 2003, pp. 81-93.
P. Jambulingam, S. Subramanian, S. J de Vlas, C. Vinubala, W. A Stolk, “Mathematical modelling of lymphatic filariasis elimination programs in India: required duration of mass drug administration and post treatment level of infection indicators”, Parasites and Vectors. November, 2015.
R. J. Kastner, C. M. Stone, P. Steinmann, M. Tanner, and F. Tediosi, “What Is Needed to Eradicate Lymphatic Filariasis? A Model-Based Assessment on the Impact of Scaling Up Mass Drug Administration Programs” PLoS Negl. Trop Dis vol. 9 (10). 2015.
A. Korobeinikov, “Global properties of basic virus dynamicals models,” Bull. Math. Biol. 2004, pp 879-883.
Korobeinikov, Lyapunov functions and global proper ties for SEIR and SEIS epidemic models, Math. Med. Biol. vol 21 2004, pp. 75-83.
A. Korobeinikov, Global properties of infectious dis ease models with nonlinear incidence, Bull. Math. Biol. Vol. 69, 2007, pp. 1871-1886.
V. Lakshmikantham, S. Leela and A. A Martynyuk. “Stability analysis of nonlinear systems Pure and Ap plied Mathematics” Marcel Dekker, New York A Series of Monographs and Textbooks, Vol. 125. 2009. ISBN 0-8247-8067-1.
C. C. McCluskey, “Lyapunov functions for tuberculo sis models with fast and slow Progression,” Math Biosci Eng. 3, 2006, pp. 603–614.
I. Miranda. Teboh-Ewungkem, N. Chandra, Podder, and B. A. Gumel. “Mathematical Study of the Role of Gametocytes and an Imperfect Vaccine on Malaria Transmission Dynamic,” Bulletin of Mathematical Biology vol. 1007(11) 2009, pp. 538-009-9437-3.
A. M, Niger and A. B. Gumel, “Mathematical Analy sis of the Role of Repeated Exposure on Malaria Transmission Dynamics,” Differential Equations and Dynamical Systems, vol. 16 (3), 2008, pp 251-287.
W. A Stolk, S. J de Vlas, and J. D. F Habbema, “Advances and Challenges in Predicting the Impact of Lymphatic Filariasis Elimination Programmes,” Fi larial Journal vol 5: 5, 2006.
W. A. Stolk, Subramanian Swaminathan, Gerrit J. van Oortmarssen, P. K. Das, and J. Dik F. Habbe ma. “Prospects for Elimination of Bancroftian Filariasis by Mass Drug Treatment in Pondicherry, India” JID, 2003, 188.
S. Swaminathan, Pani P Subash, Ravi Rengachari, Krishnamoorthy, Kaliannagounder and Das K Pradeep “Mathematical models for lymphatic filariasis transmission and control: Challenges and prospects,” Parasites & Vectors, 2008.
TACAIDS-Tanzania, Joint Bi-annual HIV/AIDS Sector Review: Report of Technical Review: Dar-es-Salaam, Tanzania, 2008.
J. Z. G. Tan, ‘‘The Elimination of Lymphatic Filariasis: A Strategy for Poverty Alleviation and Sustainable Development Perspectives from the Philippines’’, Filaria Journal, vol. 2. 2003.
J. Tumwiine, J. Y. T. Mugisha and L. S. Luboobi. “On oscillatory pattern of malari dynamics in a population with temporary immunity,” Computational and Mathematical Methods in Medicine vol. 8(3), 2007, pp. 191–203.