`a`
Mathematical Biosciences and Engineering (MBE)
 

Optimal control analysis of malaria–schistosomiasis co-infection dynamics
Pages: 377 - 405, Issue 2, April 2017

doi:10.3934/mbe.2017024      Abstract        References        Full text (962.8K)           Related Articles

Kazeem Oare Okosun - Department of Mathematics, Vaal University of Technology, Andries Potgieter Boulevard, Vanderbijlpark, 1911, South Africa (email)
Robert Smith? - Department of Mathematics and Faculty of Medicine, The University of Ottawa, 585 King Edward Ave Ottawa, ON K1N 6N5, Canada (email)

1 B. M. Adams, H. T. Banks, H. Kwon and H. T. Tran, Dynamic multidrug therapies for HIV: Optimal and STI control approaches, Mathematical Biosciences and Engineering, 1 (2004), 223-241.       
2 F. B. Agusto, Optimal chemoprophylaxis and treatment control strategies of a tuberculosis transmission model, World Journal of Modelling and Simulation, 5 (2009), 163-173.
3 F. B. Agusto and K. O. Okosun, Optimal seasonal biocontrol for Eichhornia crassipes, International Journal of Biomathematics, 3 (2010), 383-397.       
4 R. M. Anderson and R. M. May, Infectious Diseases of Humans: Dynamics and Control, Oxford University Press, 1991, Oxford.
5 K. W. Blayneh, Y. Cao and H. D. Kwon, Optimal control of vector-borne diseases: Treatment and Prevention, Discrete and Continuous Dynamical Systems Series B, 11 (2009), 587-611.       
6 J. G. Breman, M. S. Alilio and A. Mills, Conquering the intolerable burden of malaria: What's new, what's needed: A summary, Am. J. Trop. Med. Hyg., 71 (2004), 1-15.
7 C. Castillo-Chavez and B. Song, Dynamical model of tuberculosis and their applications, Math. Biosci. Eng., 1 (2004), 361-404.       
8 Z. Chen, L. Zou, D. Shen, W. Zhang and S. Ruan, Mathematical modelling and control of Schistosomiasis in Hubei Province, China, Acta Tropica, 115 (2010), 119-125.
9 E. T. Chiyaka, G. Magombedze and L. Mutimbu, Modelling within host parasite dynamics of schistosomiasis, Comp. Math. Meth. Med., 11 (2010), 255-280.       
10 J. A. Clennon, C. G. King, E. M. Muchiri and U. Kitron, Hydrological modelling of snail dispersal patterns in Msambweni, Kenya and potential resurgence of Schistosoma haematobium transmission, Parasitology, 134 (2007), 683-693.
11 S. Doumbo, T. M. Tran, J. Sangala, S. Li and D. Doumtabe et al, Co-infection of long-term carriers of Plasmodium falciparum with Schistosoma haematobium enhances protection from febrile malaria: A prospective cohort study in Mali, PLoS Negl. Trop. Dis., 8 (2014), e3154.
12 M. Finkel, Malaria: Stopping a Global Killer, National Geographic, July 2007.
13 Z. Feng, A. Eppert, F. A. Milner and D. J. Minchella, Estimation of parameters governing the transmission dynamics of schistosomes, Appl. Math. Lett., 17 (2004), 1105-1112.       
14 W. H. Fleming and R. W. Rishel, Deterministic and Stochastic Optimal Control, Springer Verlag, New York, 1975.       
15 J. H. Ge, S. Q. Zhang, T. P. Wang, G. Zhang, C. Tao, D. Lu, Q. Wang and W. Wu, Effects of flood on the prevalence of schistosomiasis in Anhui province in 1998, Journal of Tropical Diseases and Parasitology, 2 (2004), 131-134.
16 P. J. Hotez, D. H. Molyneux, A. Fenwick, E. Ottesen, Ehrlich and S. Sachs et al., Incorporating a rapid-impact package for neglected tropical diseases with programs for HIV/AIDS, tuberculosis, and malaria, PLoS Med., 3 (2006), e102.
17 M. Y. Hyun, Comparison between schistosomiasis transmission modelings considering acquired immunity and age-structured contact pattern with infested water, Mathematical Biosciences, 184 (2003), 1-26.       
18 H. R. Joshi, Optimal control of an HIV immunology model, Optimal Control Applications in Mathematics, 23 (2002), 199-213.       
19 A. Kealey and R. J. Smith?, Neglected Tropical Diseases: Infection, modelling and control, J. Health Care for the Poor and Underserved, 21 (2010), 53-69.
20 J. Keiser, J. Utzinger, M. Caldas de Castro, T. A. Smith, M. Tanner and B. Singer, Urbanization in sub-Saharan Africa and implication for malaria control, Am. J. Trop. Med. Hyg., 71 (2004), 118-127.
21 D. Kirschner, S. Lenhart and S. Serbin, Optimal Control of the Chemotherapy of HIV, J. Math. Biol., 35 (1997), 775-792.       
22 J. C. Koella and R. Anita, Epidemiological models for the spread of anti-malaria resistance, Malaria Journal, 2 (2003), p3.
23 C. M. Kribs-Zaleta and J. X. Velasco-Hernandez, A simple vaccination model with multiple endemic states, Math. Biosci., 164 (2000), 183-201.
24 V. Lakshmikantham, S. Leela and A. A. Martynyuk, Stability Analysis of Nonlinear Systems, Marcel Dekker, New York and Basel, 1989.       
25 S. Lenhart and J. T. Workman, Control Applied to Biological Models, Chapman and Hall, London, 2007.       
26 J. Li, D. Blakeley and R. J. Smith?, The failure of $R_0$, Comp. Math. Meth. Med., 2011 (2011), Article ID 527610, 17pp.       
27 G. Li and Z. Jin, Global stability of a SEIR epidemic model with infectious force in latent, infected and immune period, Chaos, Solutions and Fractals, 25 (2005), 1177-1184.       
28 Q. Longxing, J. Cui, T. Huang, F. Ye and L. Jiang, Mathematical model of schistosomiasis under flood in Anhui province, Abstract and Applied Analysis, 2014 (2014), Article ID 972189, 7pp.       
29 A. D. Lopez, C. D. Mathers, M. Ezzati, D. T. Jamison and C. J. Murray, Global and regional burden of disease and risk factors, 2001: Systematic analysis of population health data, Lancet, 367 (2006), 1747-1757.
30 E. Mtisi, H. Rwezaura and J. M. Tchuenche, A mathematical analysis of malaria and Tuberculosis co-dynamics, Discrete and Continuous Dynamical Systems Series B, 12 (2009), 827-864.       
31 Z. Mukandavire, A. B. Gumel, W. Garira and J. M. Tchuenche, Mathematical analysis of a model for HIV-Malaria co-infection, Mathematical Biosciences and Engineering, 6 (2009), 333-362.       
32 S. Mushayabasa and C. P. Bhunu, Modeling Schistosomiasis and HIV/AIDS co-dynamics, Computational and Mathematical Methods in Medicine, 2011 (2011), Article ID 846174, 15pp.       
33 S. Mushayabasa and C. P. Bhunu, Is HIV infection associated with an increased risk for cholera? Insights from mathematical model, Biosystems, 109 (2012), 203-213.
34 I. S. Nikolaos, K. Dietz and D. Schenzle, Analysis of a model for the Pathogenesis of AIDS, Mathematical Biosciences, 145 (1997), 27-46.       
35 K. O. Okosun, R. Ouifki and N. Marcus, Optimal control analysis of a malaria disease transmission model that includes treatment and vaccination with waning immunity, BioSystems, 106 (2011), 136-145.
36 K. O. Okosun and O. D. Makinde, Optimal control analysis of malaria in the presence of non-linear incidence rate, Appl. Comput. Math., 12 (2013), 20-32.       
37 K. O. Okosun and O. D. Makinde, A co-infection model of malaria and cholera diseases with optimal control, Mathematical Biosciences, 258 (2014), 19-32.       
38 L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze and E. F. Mishchenko, The Mathematical Theory of Optimal Processes, Wiley, New York, 1962.       
39 R. Ross, The Prevention of Malaria, Murray, London, 1911.
40 P. Salgame, G. S. Yap and W. C. Gause, Effect of helminth-induced immunity on infections with microbial pathogens, Nature Immunology, 14 (2013), 1118-1126.
41 A. A. Semenya, J. S. Sullivan, J. W. Barnwell and W. E. Secor, Schistosoma mansoni Infection Impairs Antimalaria Treatment and Immune Responses of Rhesus Macaques Infected with Mosquito-Borne Plasmodium coatneyi, Infection and Immunity, 80 (2012), 3821-3827.
42 K. D. Silué, G. Raso, A. Yapi, P. Vounatsou, M. Tanner, E. Ńgoran and J. Utzinger, Spatially-explicit risk profiling of Plasmodium falciparum infections at a small scale: A geostatistical modelling approach, Malaria J., 7 (2008), p111.
43 R. J. Smith? and S. D. Hove-Musekwa, Determining effective spraying periods to control malaria via indoor residual spraying in sub-saharan Africa, Journal of Applied Mathematics and Decision Sciences, 2008 (2008), Article ID 745463, 19pp.       
44 R. W. Snow, C. A. Guerra, A. M. Noor, H. Y. Myint and S. I. Hay, The global distribution of clinical episodes of Plasmodium falciparum malaria, Nature, 434 (2005), 214-217.
45 R. C. Spear, A. Hubbard, S. Liang and E. Seto, Disease transmission models for public health decision making: Toward an approach for designing intervention strategies for Schistosomiasis japonica, Environ. Health Perspect., 10 (2002), 907-915.
46 P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48.       
47 R. B. Yapi, E. Hürlimann, C. A. Houngbedji, P. B. Ndri and K. D. Silué et al., Infection and Co-infection with Helminths and Plasmodium among School Children in Côte d'Ivoire: Results from a National Cross-Sectional Survey, PLoS Negl. Trop. Dis., 8 (2014), e2913.
48 X. N. Zhou, J. G. Guo and X. H. Wu et al., Epidemiology of schistosomiasis in the people's republic of China, 2004, Emerging Infectious Diseases, 13 (2007), 1470-1476.

Go to top