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Multiplayer games and HIV transmission via casual encounters
Optimal control analysis of malaria-schistosomiasis co-infection dynamics
1. | Department of Mathematics, Vaal University of Technology, Andries Potgieter Boulevard, Vanderbijlpark, 1911, South Africa |
2. | Department of Mathematics, The University of Ottawa, 585 King Edward Ave, Ottawa ON K1N6N5, Canada |
This paper presents a mathematical model for malaria-schistosom-iasis co-infection in order to investigate their synergistic relationship in the presence of treatment. We first analyse the single infection steady states, then investigate the existence and stability of equilibria and then calculate the basic reproduction numbers. Both the single-infection models and the co-infection model exhibit backward bifurcations. We carrying out a sensitivity analysis of the co-infection model and show that schistosomiasis infection may not be associated with an increased risk of malaria. Conversely, malaria infection may be associated with an increased risk of schistosomiasis. Furthermore, we found that effective treatment and prevention of schistosomiasis infection would also assist in the effective control and eradication of malaria. Finally, we apply Pontryagin's Maximum Principle to the model in order to determine optimal strategies for control of both diseases.
References:
[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.
doi: 10.3934/mbe.2004.1.223. |
[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.
doi: 10.1142/S1793524510001021. |
[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.
doi: 10.3934/dcdsb.2009.11.587. |
[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.
doi: 10.3934/mbe.2004.1.361. |
[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.
doi: 10.1080/17486701003614336. |
[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,
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.
doi: 10.1016/j.aml.2004.02.002. |
[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 and 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.
doi: 10.1016/S0025-5564(03)00045-2. |
[18] |
H. R. Joshi,
Optimal control of an HIV immunology model, Optimal Control Applications in Mathematics, 23 (2002), 199-213.
doi: 10.1002/oca.710. |
[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.
doi: 10.1007/s002850050076. |
[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.
doi: 10.1016/j.chaos.2004.11.062. |
[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.
doi: 10.1155/2014/972189. |
[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.
doi: 10.3934/dcdsb.2009.12.827. |
[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.
doi: 10.3934/mbe.2009.6.333. |
[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.
doi: 10.1016/S0025-5564(97)00018-7. |
[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.
doi: 10.1016/j.mbs.2014.09.008. |
[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] | |
[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.
doi: 10.1155/2008/745463. |
[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.
doi: 10.1016/S0025-5564(02)00108-6. |
[47] |
R. B. Yapi, E. Hürlimann, C. A. Houngbedji, P. B. Ndri and K. D. Silué,
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,
Epidemiology of schistosomiasis in the people's republic of China, 2004, Emerging Infectious Diseases, 13 (2007), 1470-1476.
|
show all references
References:
[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.
doi: 10.3934/mbe.2004.1.223. |
[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.
doi: 10.1142/S1793524510001021. |
[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.
doi: 10.3934/dcdsb.2009.11.587. |
[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.
doi: 10.3934/mbe.2004.1.361. |
[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.
doi: 10.1080/17486701003614336. |
[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,
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.
doi: 10.1016/j.aml.2004.02.002. |
[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 and 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.
doi: 10.1016/S0025-5564(03)00045-2. |
[18] |
H. R. Joshi,
Optimal control of an HIV immunology model, Optimal Control Applications in Mathematics, 23 (2002), 199-213.
doi: 10.1002/oca.710. |
[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.
doi: 10.1007/s002850050076. |
[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.
doi: 10.1016/j.chaos.2004.11.062. |
[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.
doi: 10.1155/2014/972189. |
[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.
doi: 10.3934/dcdsb.2009.12.827. |
[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.
doi: 10.3934/mbe.2009.6.333. |
[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.
doi: 10.1016/S0025-5564(97)00018-7. |
[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.
doi: 10.1016/j.mbs.2014.09.008. |
[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] | |
[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.
doi: 10.1155/2008/745463. |
[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.
doi: 10.1016/S0025-5564(02)00108-6. |
[47] |
R. B. Yapi, E. Hürlimann, C. A. Houngbedji, P. B. Ndri and K. D. Silué,
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,
Epidemiology of schistosomiasis in the people's republic of China, 2004, Emerging Infectious Diseases, 13 (2007), 1470-1476.
|










Parameter | Description | Sensitivity index | Sensitivity index |
if | if | ||
snail mortality | |||
mosquito mortality | 0.56 | 0.07 | |
prob. of snail getting infected with schisto | 0.5 | 0.5 | |
snail birth rate | 0.5 | 0.5 | |
prob. of human getting infected with malaria | |||
| prob. of mosquito getting infected | ||
mosquito birth rate | |||
| human birth rate | ||
malaria-induced death | 0.12 | ||
recovery from schisto | 0.26 | ||
schisto-induced death | 0.05 | ||
recovery from malaria | 0.003 |
Parameter | Description | Sensitivity index | Sensitivity index |
if | if | ||
snail mortality | |||
mosquito mortality | 0.56 | 0.07 | |
prob. of snail getting infected with schisto | 0.5 | 0.5 | |
snail birth rate | 0.5 | 0.5 | |
prob. of human getting infected with malaria | |||
| prob. of mosquito getting infected | ||
mosquito birth rate | |||
| human birth rate | ||
malaria-induced death | 0.12 | ||
recovery from schisto | 0.26 | ||
schisto-induced death | 0.05 | ||
recovery from malaria | 0.003 |
Parameter | Description | Sensitivity index | Sensitivity index |
if | if | ||
prob. of mosquito getting infected | 0.5 | 0.5 | |
| mosquito birth rate | 0.5 | 0.5 |
prob. of human getting infected with schisto | |||
prob. of snail getting infected with schisto | |||
snail birth rate | |||
malaria-induced death | |||
recovery from schisto | 0.41 | 0.41 | |
schisto-induced death | 0.09 | 0.09 | |
recovery from malaria | |||
snail mortality | 0.0000002 | 0.000007 | |
human birth rate | 0.0000001 | 0.000004 |
Parameter | Description | Sensitivity index | Sensitivity index |
if | if | ||
prob. of mosquito getting infected | 0.5 | 0.5 | |
| mosquito birth rate | 0.5 | 0.5 |
prob. of human getting infected with schisto | |||
prob. of snail getting infected with schisto | |||
snail birth rate | |||
malaria-induced death | |||
recovery from schisto | 0.41 | 0.41 | |
schisto-induced death | 0.09 | 0.09 | |
recovery from malaria | |||
snail mortality | 0.0000002 | 0.000007 | |
human birth rate | 0.0000001 | 0.000004 |
Parameter | Description | value | Reference |
malaria-induced death | 0.05-0.1 day | [43] | |
| malaria transmissibility to humans | 0.034 day | assumed |
malaria transmissibility to mosquitoes | 0.09 day | [5] | |
schistosomiasis transmissibility to humans | 0.406 day | [45] | |
schistosomiasis transmissibility to snails | 0.615 day | [9] | |
Natural death rate in humans | 0.00004 day | [5] | |
Natural death rate in mosquitoes | 1/15-0.143 day | [5] | |
Natural death rate in snails | 0.000569 day | [9,45] | |
malaria immunity waning rate | 1/(60 | [5] | |
schistosomiasis immunity waning rate | 0.013 day | assumed | |
human birth rate | 800 people/day | [9] | |
| mosquitoes birth rate | 1000 mosquitoes/day | [5] |
snail birth rate | 100 snails/day | [13] | |
recovery rate of co-infected individual | 0.35 day | assumed | |
recovery rate of schistosomiasis-infected individual | 0.0181 day | assumed | |
recovery rate of malaria-infected individual | 1/(2 | [5] | |
co-infected proportion who recover from malaria only | 0.1 | assumed | |
schistosomiasis-induced death | 0.0039 day | [9] |
Parameter | Description | value | Reference |
malaria-induced death | 0.05-0.1 day | [43] | |
| malaria transmissibility to humans | 0.034 day | assumed |
malaria transmissibility to mosquitoes | 0.09 day | [5] | |
schistosomiasis transmissibility to humans | 0.406 day | [45] | |
schistosomiasis transmissibility to snails | 0.615 day | [9] | |
Natural death rate in humans | 0.00004 day | [5] | |
Natural death rate in mosquitoes | 1/15-0.143 day | [5] | |
Natural death rate in snails | 0.000569 day | [9,45] | |
malaria immunity waning rate | 1/(60 | [5] | |
schistosomiasis immunity waning rate | 0.013 day | assumed | |
human birth rate | 800 people/day | [9] | |
| mosquitoes birth rate | 1000 mosquitoes/day | [5] |
snail birth rate | 100 snails/day | [13] | |
recovery rate of co-infected individual | 0.35 day | assumed | |
recovery rate of schistosomiasis-infected individual | 0.0181 day | assumed | |
recovery rate of malaria-infected individual | 1/(2 | [5] | |
co-infected proportion who recover from malaria only | 0.1 | assumed | |
schistosomiasis-induced death | 0.0039 day | [9] |
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