Theoretical Study of the Impact of Availability and
Efficacy of Controls on the Transmission Dynamics of
Schistosomiasis

Owin Olowu; Ann Nwankwo

doi:https://doi.org/10.14445/22315373/IJMTT-V69I8P502

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 69 | Issue 8 | Year 2023 | Article Id. IJMTT-V69I8P502 | DOI : https://doi.org/10.14445/22315373/IJMTT-V69I8P502

Theoretical Study of the Impact of Availability and Efficacy of Controls on the Transmission Dynamics of Schistosomiasis

Owin Olowu, Ann Nwankwo

Received	Revised	Accepted	Published
08 Jun 2023	24 Jul 2023	05 Aug 2023	18 Aug 2023

Citation :

Owin Olowu, Ann Nwankwo, "Theoretical Study of the Impact of Availability and Efficacy of Controls on the Transmission Dynamics of Schistosomiasis," International Journal of Mathematics Trends and Technology (IJMTT), vol. 69, no. 8, pp. 10-24, 2023. Crossref, https://doi.org/10.14445/22315373/IJMTT-V69I8P502

Abstract

In this paper we present a deterministic nonlinear model which provides mathematical and epidemiological insights to the influence of availability and efficacy of control on the transmission dynamics of Schistosomiasis. Schistosomiasis is second only to Malaria in terms of impact as the most brutal parasitic disease. There is also presently no vaccine in commercial quantity against the parasite, Schistosoma spp. Thus, the need to explore other control measures. The disease free equilibrium of the model was shown to be locally asymptotically stable if ℛ𝑐 < 1, and unstable and if ℛ𝑐 > 1. Again, the endemic equilibrium as also shown to be globally asymtotically stable for the special case when there is permanent immunity upon recovery.

Keywords

- Schistosomiasis, Reproduction Number, Availability, Efficacy, Control.

References

[1] Abiola Fatimah Adenowo et al., “Impact of Human Schistosomiasis in Sub-Saharan Africa,” The Brazilian Journal of Infectious Diseases, vol. 19, no. 2, pp. 196-205, 2015.
[CrossRef] [Publisher Link]
[2] E. J. Allen, and H. D. Victory, “Modelling and Simulation of a Schistosomiasis Infection with Biological Control,” Acta Tropica, vol. 87, no. 2, pp. 251-267, 2003.
[CrossRef] [Google Scholar] [Publisher Link]
[3] Center for Disease Control and Prevention Website, 2012. [Online]. Available: https://www.cdc.gov/parasites/Schistosomiasis/
[4] L. Chitsulo et al., “The Global Status of Schistosomiasis and its Control,” Acta Tropica, vol. 77, no. 1, pp. 41-51, 2000.
[CrossRef] [Google Scholar] [Publisher Link]
[5] Edward T. Chiyaka, Gesham Magombedze, and Lawrence Mutimbu, “Modelling within Host Parasite Dynamics of Schistosomiasis,” Computational and Mathematical Methods in Medicine, vol. 11, no. 3, pp. 255-280, 2010.
[Google Scholar] [Publisher Link]
[6] Edward T. Chiyaka, and Winston Garira, “Mathematical Analysis of the Transmission Dynamics of Schistosomiasis in the Human-Snail Hosts,” Journal of Biological Systems, vol. 17, no. 3, pp. 397-423, 2009.
[CrossRef] [Google Scholar] [Publisher Link]
[7] Nick Feasey et al., “Neglected Tropical Diseases,” British Medical Bulletin, vol. 93, no. 1, pp. 179-200, 2010.
[CrossRef] [Google Scholar] [Publisher Link]
[8] Zhilan Feng, Cheng-Che Li, and Fabio A. Milner, “Schistosomiasis Models with Density Dependence and Age of Infection in Snail Dynamics,” Mathematical Biosciences, vol. 177-178, pp. 271-286, 2002.
[CrossRef] [Google Scholar] [Publisher Link]
[9] Peter J. Hotez, and Aruna Kamath, “Neglected Tropical Diseases in Subsaharan Africa: Review of Their Prevalence, Distribution, and Disease Burden,” PLoS Neglected Tropical Diseases, vol. 3, no. 8, 2009.
[CrossRef] [Google Scholar] [Publisher Link]
[10] Peter J. Hotez, and John P. Ehrenberg, “Escalating the Global Fight against Neglected Tropical Diseases through Interventions in the Asia Pacific Region,” Advances in Parasitology, vol. 72, pp. 31-53, 2010.
[CrossRef] [Google Scholar] [Publisher Link]
[11] Peter J. Hotez, Oluwatoyin A. Asojo, and Adekunle M. Adesina, “Nigeria: “Ground Zero” for the High Prevalence Neglected Tropical Diseases,” PLoS Neglected Tropical Disease, vol. 6, no. 7, 2012.
[CrossRef] [Google Scholar] [Publisher Link]
[12] Marianette T Inobaya et al., “Prevention and Control of Schistosomiasis: A Current Perspective,” Research and Reports in Tropical Medicine, vol. 5, pp. 65-75, 2014.
[Google Scholar] [Publisher Link]
[13] Longxing Qi et al., “Mathematical Model of Schistosomiasis under Flood in Anhui Province,” Abstract and Applied Analysis, 2014.
[CrossRef] [Google Scholar] [Publisher Link]
[14] Tara D. Mangal, Steve Paterson, and Andrew Fenton, “Predicting the Impact of Long-Term Temperature Changes on the Epidemiology and Control of Schistosomiasis: A Mechanistic Model,” PLoS ONE, vol. 3, no. 1, 2008.
[CrossRef] [Google Scholar] [Publisher Link]
[15] S. Mushayabasa, and C. P. Bhunu, “Modeling Schistosomiasis and HIV/AIDS Codynamics,” Computational and Mathematical Methods in Medicine, 2011.
[CrossRef] [Google Scholar] [Publisher Link]
[16] E.T. Ngarakana-Gwasira et al., “Transmission Dynamics of Schistosomiasis in Zimbabwe: A Mathematical and GIS Approach,” Communications in Nonlinear Science and Numerical Simulation, vol. 35, pp. 137-147, 2016.
[CrossRef] [Google Scholar] [Publisher Link]
[17] The UNAIDS-WHO Website, 2004. [Online]. Available: http://www.unaids.org/
[18] P. van den Driessche, and James Watmough, “Reproduction Numbers and Sub-Threshold Endemic Equilibria for Compartmental Models of Disease Transmission,” Mathematical Biosciences, vol. 180, no. 1-2, pp. 29-48, 2002.
[CrossRef] [Google Scholar] [Publisher Link]
[19] The World Health Organization (WHO) Website, 1993. [Online]. Available: www.who.org/schistosomiasis/factchecks/
[20] The World Health Organization (WHO) Website, 2017. [Online]. Available: www.who.org/schistosomiasis/factchecks/
[21] Hyun Mo Yang, “Comparison between Schistosomiasis Transmission Modeling Considering Acquired Immunity and Age-Structured Contact Pattern with Infested Water,” Mathematical Biosciences, vol. 184, no. 1, pp. 1-26, 2003.
[CrossRef] [Google Scholar] [Publisher Link]
[22] Lan Zou, and Shigui Ruan, “Schistosomiasis Transmission and Control in China,” Acta Tropica, vol. 143, pp. 51-57, 2015.
[CrossRef] [Google Scholar] [Publisher Link]
[23] O. I. Bada et al., “Mathematical Analysis of Schistosomiasis with Case Detection,” Journal of the Nigerian Association of Mathematical Physics, vol. 59, pp. 75-88, 2021.
[24] Ignatius Imariabe Ako, Rosemary Uwaila Akhaze, and Owin Oghenewaire Olowu, “The Impact of Reduced Re-Infection of Schistosomiasis Transmission Dynamics at Population Level: A Theoretical Study,” Journal of the Nigerian Association of Mathematical Physics, vol. 59, pp. 61-74, 2021.
[25] O. O. Olowu, I. I. Ako, and R. U. Akhaze, “On the Analysis of a two Patch Schistosomiasis Model,” Transactions of the Nigerian Association of Mathematical Physics, vol. 14, pp. 69-78, 2021.
[26] O. O. Olowu, I. I. Ako, and R. U. Akhaze, “Theoretical Study of a two Patch Metapopulation Schistosomiasis Model,” Transactions of the Nigerian Association of Mathematical Physics, vol. 14, pp. 53-68, 2021.