Mathematical Model of In-host Dynamics of Snakebite Envenoming

S. A. Abdullahi; A. G. Habib; N. Hussaini

doi:10.46481/jnsps.2022.548

Authors

S. A. Abdullahi
Department of Mathematics, Modibbo Adama University Yola, Adamawa State, Nigeria; Department of Mathematical Sciences, Bayero University Kano, P.M.B. 3011, Kano, Nigeria
A. G. Habib
Infectious and Tropical Diseases Unit, Department of Medicine, Bayero Univesrity Kano, Nigeria
N. Hussaini
Department of Mathematical Sciences, Bayero University Kano, P.M.B. 3011, Kano, Nigeria

Keywords:

Snakebite, in-host model, venom, antivenom, stability analysis

Abstract

In this paper, we develop an in-host mathematical model of snakebite envenoming that includes tissue, red blood and platelet cells of humans as specific targets of different kinds of toxins in the snake venom. The model is use to study some harmful effects of cytotoxic and hemotoxic snake venom on their target cells under the influence of snake antivenom. The model has two equilibrium points, namely, trivial and venom free. It has been shown that both the equilibrium points are globally asymptotically stable and numerical simulations illustrate the global asymptotic stability of the venom free equilibrium point. Furthermore, simulations reveal the importance of administering antivenom to avert the possible damage from venom toxins on the target cells. It is also shown through simulation that administering the required dose of antivenom can lead to the elimination of venom toxins within one week. Therefore, we recommend the administration of an adequate dose of antivenom therapy as it helps in deactivating venom toxins faster and consequently enhances the recovery time.

Dimensions

REFERENCES

J. M. Gutierrez, R. D. G. Theakston & D. A. Warrell, “Confronting the neglected problem of snake bite envenoming: the need for a global partnership”, PLoS Med 3 (2006) 6.

J. M. Gutierrez, D. Williams, H. W. Fan & D. A. Warrell, “Snakebite envenoming from a global perspective: the need of an integrated approach”, Toxicon 56 (2010).

A. Kasturiratne, A. R. Wickremasinghe, N. de Silva, N. K. Gunawardena, A. Pathmeswaran, R. Premaratna, L. Savioli, D. G. Lallo & H. J. de Silva, “The global burden of snakebite: a literature analysis and modelling based on regional estimates of envenoming and deaths”, PLoS Med 5 (2008) 11.

J.P. Chippaux, “Snake-bites: appraisal of the global situation”, Bull World Health Organ 76 (1998) 5.

S. S. Williams, C. A. Wijesinghe, S. F. Jayamanne, N. A. Buckley, A. H. Dawson, D.G.Lalloo&H.J.deSilva, “Delayedpsychological morbidity associated with snakebite envenoming”, PLoS Negl Trop Dis 5 (2011) 8, doi:10.1371/journal.pntd.0001255.

J. P. Chippaux,“Estimate of the burden of snakebites in sub-Saharan Africa: a meta-analytic approach”, Toxicon 57 (2011).

R.A.Harrison, A.Hargreaves, S.C.Wagstaff, B.Faragher&D.G.Lalloo, “Snake envenoming: a disease of poverty”, PLoS Negl. Trop. Dis. 3 (2009).

B. Mohapatra, D. A. Warrell, W. Suraweera, P. Bhatia, N. Dhingra, R. M. Jotkar, P. S. Rodriguez, K. Mishra, R. Whitaker, P. Jha & J. O. Gyapong, “Snakebite Mortality in India: A Nationally Representative Mortality Survey”, PLoS Neglected Tropical Diseases 5 (2011) 4, doi:10.1371/journal.pntd.0001018.

Animal bites: Fact sheet N?373, World Health Organization. https://www.who.int/mediacentre/factsheets/fs373/en/. Accessed: February, 2021.

J. P. Chippaux, “Snakebite envenomation turns again into a neglected tropical disease”, J Venom Anim Toxins Incl Trop Dis. (2017).

J. M.Gutierrez, J. J. Calvete, A. G. Habib, R. A. Harrison, D. G. Williams &D.A.Warrell, “Snakebite envenoming”, Nat Rev Dis Primers 3 (2017) 17063.

World Health Organization, Prevalence of snakebite envenoming, https://www.who.int/snakebites/epidemiology/en/. Accessed: February, 2021.

World Health Organization, Animal bites, https:www.who.int/en/newsroom/fact-sheets/detail/animal-bites. Accessed March, 2021.

World Health Organization, Regional Office for Africa. Guidelines for the prevention and clinical management of snakebite in Africa, (2010), http://apps.who.int/medicinedocs/ documents/s17810en/s17810en.pdf. Accessed: March, 2021.

B. S. Naik,“Dry bite in venomous snakes: A review” Toxicon, 133 (2017) 63, doi:10.1016/j.toxicon.2017.04.015.

B. A. Young & K. Zahn, “Venom flow in rattlesnakes: mechanics and metering”, Journal of Experimental Biology, 204 (2001) 24, doi:10.1242/jeb.204.24.4345.

D. A. Warrell, C. Bon & M. Goyffon, “Envenomings and Their Treatments. In: Clinical features of envenoming from snake bites”, Fondation Marcel M´erieux: Lyon, (1996).

L. A. Ribeiro, G. Puorto & M. T. Jorge, “Bites by the colubrid snake Philodryas olfersii. a clinical and epidemiological study of 43 cases”, Toxicon 37 (1999).

B. Alina, Live Science. Snake Facts and Types of Snakes. https://www.livescience.com/27845-snakes.html. Accessed 2021. March,

R. E. Hill & S. P. Mackessy, “Characterization of venom (Duvernoy’s secretion) from twelve species of colubrid snakes and partial sequence of four venom proteins”, Toxicon 38 (2000).

M. E.Peichoto, P. Teibler, R. Ru´?z, L. Leiva & O. Acosta, “Systemic pathological alterations caused by Philodryas patagoniensis colubrid snake venom in rats”. Toxicon 48 (2006).

S. Weinstein & D. Keyler, “Local envenoming by the Western hognose snake (Heterodon nasicus): A case report and review of medically significant Heterodon bites”, Toxicon 54 (2009).

D. A. Warrell, N. M. D.Davidson & B. M. Greenwood, “Poisoning by bites of the saw-scaled or carpet viper (Echis carinatus) in Nigeria”, Q J Med. 46 (1977).

R. Bailey, How Does Snake Venom https://www.thoughtco.com/how-snake-venom-works-4161270. cessed: February, 2021. Work? Ac

G. Leon, L. S´anchez, A. Hern´andez, M. Villalta, M. Herrera, A. Segura, R. Estrada & J. M.Guti´errez, “Immune Response towards Snake Venoms. Inflammation and Allergy -Drug Targets”, Journal of Inflammation and Allergy Drug Target 10 (2011) 5.

B. S. Gold, C. D. Richard & A. B. Robert, “Bites of venomous snakes”, The New England Journal of Medicine, 5 (2002), doi:10.1056/NEJMra013477.

B. J. Daley & J. Torres, “Venomous snakebites”, A Journal of Emergency Medical Services 39 (2014) 6.

United State National Institute for Occupational Safety and Health, Venomous Snakes, Accessed: February, 2021, https://www.cdc.gov/niosh/topics/snakes/.

M. Peden & World Health Organization, “World report on child injury prevention”, World Health Organization, (2008), https://apps.who.int/iris/handle/10665/43851, Accessed May, 2021.

World Health Organization, Snakebite envenoming: a strategy for prevention and control, Geneva, (2019).

F. Chappuis, S. K. Sharma, N. Jha, L. Loutan & P. A. Bovier, “Protection against snake bites by sleeping under a bed net in southeastern Nepal”, Am. J. Trop. Med. Hyg. 77 (2007).

H.A.deSilva, A. Pathmeswaran, C. D. Ranasinha, S. Jayamanne, A. Hittharage, R. Kalupahana, G. A. Ratnatilaka, W. Uluwatthage, J. K. Aronson, J. M. Armitage, D. G. Lalloo & H. J. de Silva, “Low-dose adrenaline, promethazine, and hydrocortisone in the prevention of acute adverse reactions to antivenom following snakebite: a randomised, double-blind, placebo-controlled trial”, PLoS Med, 8 (2011) 5, doi: 10.1371/journal.

J. M. Gutierrez, L. Bruno, L. Guillermo, R. Alexandra, C. Fernando & A. Yamileth, “Trends in Snakebite Envenomation Therapy: Scientific, Technological and Public Health Considerations. Current Pharmaceutical Design”, 13 (2007) 28, doi:10.2174/138161207782023784.

A. G. Habib, U. I. Gebi & G. C. Onyemelukwe, “Snake bite in Nigeria”, Afr J Med Med Sci. 30 (2001) 3.

A. G. Habib, “Public health aspects of snakebite care in West Africa: perspectives from Nigeria”, J Venom Anim Toxins Incl Trop Dis, 19 (2013) 27.

A. G. Habib,“Effect of pre-medication on early adverse reactions following antivenom use in snakebite: a systematic review and meta-analysis”, Drug Saf. 34 (2011)10, doi: 10.2165/11592050-000000000-00000.

K. Maduwage, “Snakebite coagulopathy: controversies in understanding and management”, Sri Lanka Journal of Medicine 26 (2017) 2.

P. Malasit, D. A. Warrell, P. Chanthavanich, C. Viravan, J. Mongkolsapaya, B. Singhthong & C. Supich, “Prediction, prevention, and mechanism of early (anaphylactic) antivenom reactions in victims of snake bites”, British Medical Journal, 292 (1986), DOI:10.1136/bmj.292.6512.17

V. M. Morais & H. Massaldi,“Snake antivenoms: adverse reactions and production technology”,J Venom Anim Toxins incl Trop Dis. 15 (2009) 1.

Neglected tropical diseases: Snakebite. World Health Organization, https://www.who.int/health-topics/snakebite. Accessed: March, 2021.

United State National Institute for Occupational Safety and Health, “Venomous Snakes”, https://www.cdc.gov/niosh/index.htm, Accessed: April, 2021.

A. G. Habib, A. Kuznik, M. Hamza, M. I. Abdullahi, B. A. Chedi, J-P. Chippaux, & D. A. Warrell, “Snakebite is under appreciated:appraisal of burden from West Africa”, PLoS Negl.Trop. Dis. 9 (2015).

H. A. Reid & R. D. G. Theakston, “The Management of Snake bite”, Bulletin of the World Health Organization 61 (1983) 6.

M.A.Syed, A. A.Mohib, M.Jyotsna, C. Adarash & P. Jyotishka, “Emergency treatment of a snake bite: Pearls from literature”, J Emerg Trauma Shock 1 (2008) 2.

S. R.Vijeth, T. K. Dutta, J. Shahapurkar & A. Sahai, “Dose and frequency of anti-snake venom injection in treatment of Echis carinatus (saw-scaled viper) bite”, J Assoc Physicians India 48 (2000) 2.

D. A. Warrell, Clinical toxicology of snakebite in Africa and the Middle East/Arabian peninsula, Asia In Meier J,White J eds. Handbook of Clinical Toxicology of Animal Venoms and Poisons. Florida, CRC Press, (1995).

D. Williams, J. M. Gutierrez, R. Harrison, D. A. Warrell, J. White, K. D. Winkel & P. Gopalakrishnakone, “The Global Snake Bite Initiative: an antidote for snake bite”, Lancet (London, England) 375 (2010) 9708, doi.org/10.1016/s0140-6736(09)61159-4

D. A. Warrell, “Snakebite”, Erratum in: Lancet 375 (2010) 9708, doi: 10.1016/S0140-6736(09)61754-2

Z. U. Abdullahi, S. S. Musa, D. He & U. M. Bello, “Antiprotozoal Effect of Snake Venoms and their Fractions: A Systematic Review”, Pathogens 10 (2021) 1632, doi.org/10.3390/pathogens10121632

T. A. Reeks, B. G. Fry & P. F. Alewood, “Privileged frameworks from snake venom. Review”, Cell. Mol. Life Sci. (2015). DOI 10.1007/s00018015-1844-z

S. A. Zainal Abidin, Y. Q. Lee, Y. O. Lekhsan & N. Rakesh, “ Malaysian Cobra Venom: A Potential Source of Anti-Cancer Therapeutic Agents”, Toxins, 11 (2019) c2.

A. T. Mohamed, S. A. Garcia & J. D. Stockand, “Snake Venoms in Drug Discovery: Valuable Therapeutic Tools for Life Saving”, Toxins 11 (2019) 10, doi.org/10.3390/toxins11100564

B. Lomonte, J. Fern´andez, L. Sanz, Y. Angulo, M. Sasa, J. M. Guti´errez & J. J. Calvete, “Venomous snakes of Costa Rica: biological and medical implications of their venom proteomic profiles analyzed through the strategy of snake venomics”, J Proteomics 13 (2014) 105, doi: 10.1016/j.jprot.2014.02.020.

T. T. Yusuf, A. Abidemi, A. S. Afolabi & E. J. Dansu, “Optimal Control of the Coronavirus Pandemic with Impacts of Implemented Control Measures”, Journal of the Nigerian Society of Physical Sciences 4 (2022) 1, doi: 10.46481/jnsps.2022.414.

A. S. Hassan & N. Hussaini, “Analysis of an HIV -HCV simultaneous infection model with time delay”, Journal of the Nigerian Society of Physical Sciences 3 (2021) 1, doi.org/10.46481/jnsps.2021.109

S. A. Ayuba, I. Akeyede, & A. Olagunju, “Stability and Sensitivity Analysis of Dengue-Malaria Co-Infection Model in Endemic Stage”, Journal of the Nigerian Society of Physical Sciences 3 (2021) 2, doi.org/10.46481/jnsps.2021.196

I. Babaji Muhammad & S. Usaini, “Dynamics of Toxoplasmosis Disease in Cats population with vaccination”, Journal of the Nigerian Society of Physical Sciences 3 (2021) 1.

S. A. Abdullahi, A. G. Habib, & N. Hussaini, “Control of snakebite envenoming: A mathematical modeling study”, PLOS Neglected Tropical Diseases 15 (2021) 8, doi.org/10.1371/journal.pntd.0009711(2021).

F. Y. Eguda, A. James & S. Babuba. “The Solution of a Mathematical Model for Dengue Fever Transmission Using Differential Transformation Method”, Journal of the Nigerian Society of Physical Sciences 1 (2019) 3, doi:10.46481/jnsps.2019.18.

L. Adamu & N. Hussaini, “An Epidemic Model of Zoonotic Visceral Leishmaniasis with Time Delay”, Journal of the Nigerian Society of Physical Sciences 1 (2019) 1, doi: 10.46481/jnsps.2019.5.

A. Goyal, L. E. Laura & A. S. Perelson, “Within-host mathematical models of hepatitis B virus infection: Past, present, and future. Current Opinion in Systems Biology”, (2019), doi.org/10.1016/j.coisb.2019.10.003.

H. Dahari, J. E. Layden-Almer, E. Kallwitz, R.M. Ribeiro, S. J. Cotler, T. J. Layden & A. S. Perelson, “ A mathematical model of hepatitis C virus dynamics in patients with high baseline viral loads or advanced liver disease”, Gastroenterology, 136 (2009) 4, doi.org/10.1053/j.gastro.2008.12.060

O. Sharomi & A. B. Gumel, “Mathematical study of in-host dynamics of Chlamydia trachomatis”, IMA Journl of Applied Mathemtics 77 (2012) 2, doi:10.1093/imamat/hxq057

L. M. de Freitas, T. U. Maioli, H. A. L. de Ribeiro, P. Tieri & F. Castiglione,“A mathematical model of Chagas disease infection predicts inhibition of the immune system”, [IEEE 2018 IEEE International Conference on Bioinformatics and Biomedicine (BIBM) -Madrid, Spain (2018.12.3-2018.12.6)] 2018 IEEE International Conference on Bioinformatics and Biomedicine (BIBM), (2018), doi:10.1109/BIBM.2018.8621389.

A. Ishaiku & N. Hussaini, “Modelling Effects of HCV Plus-Strand RNA Influx into a Cell during HCV replication”, J.Indones. math. Soc. 26 (2020) 01.

P. Ngina, R. W. Mbogo & L. S. Luboobi, “The In-Vivo Dynamics of HIV Infection with the Influence of Cytotoxic T Lymphocyte Cells”, International Scholarly Research Notices (2017), doi:10.1155/2017/2124789

R. M. Kini & H . J. Evans, “A model to explain the pharmacological effects of snake venom phospholipases A2”, Toxicon (1989) 27. [68] S. Stagg, Pharmacokinetics of Snake Bites, http://www.umich.edu/ elements/fogler&gurmen/html/web?mod/cobra/avenom.htm. Accessed: January, 2019.

S. Stagg, Pharmacokinetics of Snake Bites, http://www.umich.edu/ elements/fogler&gurmen/html/web?mod/cobra/avenom.htm. Accessed: January, 2019.

P. P. Tanos, G. K.Isbister, D. G. Lalloo, C. M. Kirkpatrick & S. B. Duffull, “A model for venom-induced consumptive coagulopathy in snake bite”, Toxicon 52 (2008).

TheLancet, “TheSnakebiteenvenoming:apriority neglected tropical disease”, Lancet, 1 (2017) 2, doi: 10.1016/S0140-6736(17)31751-8. PMID: 28677550.

J. Horky, J. Vacha & V. Znojil, “Comparison of life span of erythrocytes in some inbred strains of mouse using 14C-labelled glycine”, Physiol. Bohemoslovaca 27 (1977).

J. W. Goodman &L.H.Smith, “Erythrocyte life span in normal mice and in radiation bone marrow chimeras”. Am. J. Physiol. 200 (1961).

V. Lakshmikanthan, S. Leela & A. A. Martyniuk, A Stability Analysis of Nonlinear Systems, CRC Press, (1989).

K. Okuneye & A. B. Gumel, “Analysis of a temperature and rainfalldependent model for malaria transmission dynamics”, Mathematical Biosciences 000 (2016).

Y. Dumont & F.Chiroleu, “Vector control for the Chikungunya disease”, Mathematical Biosciences and Engineering 7 (2010).

S. M. Sabiu & N. Hussaini, “Modeling the Dynamics of Dengue Virus in Human and Mosquito Populations”, Journal of Nigerian Association of Mathematical Physics 43 (2017).

J. P. LaSalle, The Stability of Dynamical Systems, Regional Conference Series in Applied Mathematics, SIAM Philadephia, (1976).

M. Lebois & E. C. Josefsson, “Regulation of Platelet lifespan by apoptosis. Platelets”, Journal of Platelets Sep (2016) 6, doi:10.3109/09537104.2016.1161739.

H. S. Bawaskar, “Snake venoms and antivenoms: Critical supply issues”, J Assoc Phys India 52 (2004).

A. G. Habib, M. Lamorde, M. M. Dalhat, Z. G. Habib & A. Kuznik, “Cost-effectiveness of Antivenoms for Snakebite Envenoming in Nigeria”, PLoS Negl Trop Dis 9 (2015) 1, doi.org/10.1371/journal.pntd.0003381