Backward bifurcation analysis in SIRS-SI of the dynamics of malaria transmission model with treatment

[1] M.B. Abdullahi, Y.A. Hasan, F.A. Abdullah, A mathematical model of malaria and the effectiveness of drugs, Appl. Math. Sci. 7 (2013), no. 62, 3079–3095.
[2] F.B. Agusto, N. Marcus and K.O. Okosun, Application of optimal control to the epidemiology of malaria, Electronic J. Differ. Equ. 2012 (2012), no. 81, 1–22.
[3] R.M. Anderson and R.M. May, Infectious diseases of humans: dynamics and control, Oxford University Press, London, 1991.
[4] H. Arabi, E.H. Labriji, M. Rachik and A. Kaddar, Optimal control of an epidemic model with a saturated incidence rate, Model. Control 17 (2012), no. 4, 448–459.
[5] J.L. Aron and R.M. May, The population dynamics of malaria, In Population Dynamics of Infectious Disease, Chapman and Hall, 1982.
[6] J.L. Aron, Mathematical modeling of immunity to malaria, Math Bios., 90 (1988), 385–396.
[7] N.T.J. Bailey, The Biomathematics of malaria, Charles Grin and Co Ltd, London, 1982.
[8] G. Birkho and G.C. Rota, Ordinary differential equations, Needham Heights, Ginny, 1982.
[9] C. Castillo-Chavez and B. Song, Dynamical models of tuberculosis and their applications, Math. Biosci. Engin. 1 (2004), 361404.
[10] K. Dietz, L. Molineaux and A. Thomas, A malaria model tested in the African savannah, Bul. World Health Organ. 50 (1974), 347–357.
[11] A.A. Gebremeskel and H.E. Krogstad, Mathematical modeling of endemic malaria transmission, Amer. J. Appl. Math. 3 (2015), no. 2, 36–46.
[12] J. Li, R.M. Welch, U.S. Nair, T.L. Sever, D.E. Irwin, C. Cordon-Rosales and N. Padilla, Dynamic Malaria Models with Environmental Changes, Proc. Thirty- Fourth Southeastern Symp. Syst. Theory Huntsville, AL, 2002, pp. 396–400.
[13] G. Macdonald, The Epidemiology and Control of Malaria, Oxford university press, 1957.
[14] G. Macdonald, Epidemiological basis of malaria control, Bul. World Health Organ. 15 (1956), 613–626.
[15] S. Mandal, R.R. Sarkar and S. Sinha, Mathematical models of malaria review, Malaria J. 10 (2011), no. 1, 1–19.
[16] H. Namawejje, Modeling the Effect of Stress on the Dynamics and Treatment of Tuberculosis M.Sc. (Mathematical Modeling) Dissertation, University of Dares Salaam, Tanzania, 2011.
[17] G.A. Ngwa and W.S. Shu, A mathematical model for endemic malaria with variable human and mosquito populations, Math. Comput. Model. J. 32 (2000), 747–763.
[18] E. Pampana, A Text book of Malaria Eradication, London, Oxford University Press, 1969.
[19] J. Ratovonjato, M. Randrianarivelojosia, M.E. Rakotondrainibe, V. Raharimanga, L. Andrianaivolambo, G. Le Goff, C. Rogier, F. Ariey, S. Boyer and V. Robert, Entomological and parasitological impacts of indoor residual spraying with DDT, alphacypermethrin and deltamethrin in the western foothill area of Madagascar, Malaria J. 13 (2014), no. 1, 1–18.
[20] R. Ross, The prevention of malaria, John Murray, London, 1911.
[21] L. Schwartz, G.V. Brown, B. Genton and V.S. Moorthy, A review malaria vaccine clinical projects based on the rainbow table, Malaria J. 11 (2012).
[22] J. Tumwiine, J. Mugisha and L. Luboobi, A mathematical model for the dynamics of malaria in a human host and mosquito vector with temporary immunity, J. Appl. Math. Comput. 189 (2005), 1953–1965.
[23] World Health Organization, Investing in health research for development, Technical Report, Geneva, 1996.
[24] H.M. Yang, Malaria transmission model for different levels of acquired immunity and temperature-dependent parameters (vector), Rev. SaudePublica 34 (2000), 223–231.

[25] H.M. Yang and M.U. Ferreira, Assessing the effects of global warming and local social and economic conditions on the malaria transmission, Rev. SaudePublica 34 (2000), 214–222.
[26] H. Yang , H. Wei H. and X. Li, Global stability of an epidemic model for vector born disease, J. Syst. Sci. Complexity 23 (2010), no. 2, 279–292
[27] M. Zhien, Z. Yicang and W. Jianhong, (2009). Modeling and Dynamics of Infectious disease, World Scientific Publishing Co Pte Ltd., Singapore, 2009.