Mathematical Model for Lassa Fever Transmission and Control

Anorue Onyinyechi Favour; Okeke Anthony Anya

doi:doi:10.11648/j.mcs.20200506.13

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Mathematical Model for Lassa Fever Transmission and Control

Anorue Onyinyechi Favour, Okeke Anthony Anya

Published in Mathematics and Computer Science (Volume 5, Issue 6)

Received: 15 October 2020 Accepted: 28 October 2020 Published: 16 December 2020

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Abstract

Lassa fever is an acute hemorrhagic zoonotic illness (possible transmission from infected animals to humans), caused by Lassa virus whose reservoir host is the Mastomys natalensis (Rodent). It is a disease with a duration of 2-21 days that strives more in African nations and countries with poor water and environmental sanitation. In this paper, a deterministic model for Lassa fever is formulated buttressing the various stages of infection of the disease. We studied the existence and uniqueness of the solutions. The steady states of the model are determined and the basic reproduction number is analyzed with a threshold parameter R_0 which shows persistence of the disease if and only if R_0>1 using the next generation matrix. The treatment strategies considered amidst others are the use of antiviral drug and to quarantine infected individuals on early diagnosis of the infection on the asymptomatic and symptomatic individuals respectively. Numerically, it was evidential that the quarantine system has a great positive effect on the rate of recovery of the infected individuals and also in curbing the risk of infection in the environment which can help safeguard the population. A relapse on this method will lead to reinfection of the disease thereby bringing the population to a point of danger.

Published in	Mathematics and Computer Science (Volume 5, Issue 6)
DOI	10.11648/j.mcs.20200506.13
Page(s)	110-118
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2020. Published by Science Publishing Group

Keywords

Lassa Fever, Infection Process, Quarantine, Equilibrium, Stability

References

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[3]	Public Health England: lassa Fever: Origins, Reservoirs Transmission and guidelines Archived 2 February 2016 at the wayback machine. First published: 5 September, 2014 Last updated: 1 April 2016.
[4]	Nwasuka C. S., Nwachukwu E. I. and Nwachukwu C. P. Mathematical model of the Transmission Dynamics of Lassa Fever with Separation of Infected individual and treatment as control measures: Journal of Advances in Mathematics and computer 9: Article No. JAMCS. 48982.
[5]	Nigerian Lassa Fever Resurgence: Prevention and control; 2018. Available: http//russelsmithgroup.com/health-and-sofety/Nigerian-lassa-fever-resurgence-prevention-control/. 31^st January, 2018.
[6]	Amorosa V., MacNeil, A., McConnell R. et al. Imported Lassa Fever, Pennsylvania, USA; 2010. Emerging Infectious Diseases. 2010; 16 (10): 1598–600.
[7]	Omalibu, S. A., Badaru, S. O., Okokhere, P., Asogun, D., Drosten, C., Emmerich, P. Lassa Fever, Nigeria 2003 and 2004. Emerging infectious Diseases, 11, 2007; 642–1644.
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[9]	Caminade, C., Turner, T., Metel mann, S., Hesson, J. C., Blagrove, M. S., Solomon, T. Baylis M. Global risk model for vector borne transmission of zika virus reveals the role of elnino 2015. Proceedings of the National Academy of Sciences, 2017, 114 (1); 119–124.
[10]	Kernels, Solen, Koivogui, Lamine, Magassouba, N’faly, Koulemou, Kekoure, Lewis, Rosamund., Aplogan, Aristide, Grais, F. Rebecca., Guerin, J. Philippe, Fichet Calvet, Elisabeth: prevalence and risk factors of Lassa Seropositivity in inhabitants of the forest Region of Guinea: A cross-sectional study.
[11]	Okuonghae, D., Okuonghae, I. A., Mathematical model for Lassa fever, Journal of National Association of Mathematical Physics, 10, 2006, 457–464.
[12]	Ogabi, C. O., Olusa, T. V., Machufor, M. A., Controlling Lassa Fever in Northern part of Edo State, Nigeria using SIR model, New Science Journal, 5 (12), 2012, 115–121.
[13]	Omorah, M. O., Ojo, M. S., Usman, D. J., Ademu, A., Basic reproductive Number for the spread and control of Lassa Fever, International Journal of Mathematics rends and Technology, 30 (1), 2016, 1–7.
[14]	Faniran, S. T., A mathematical modeling of lassa fever dynamics with Non-drug compliance rate. International Journal of Mathematics Trends and Technology (IJMITT) volume 47 Number 5 July 2017.
[15]	Modeling the effect of treatment, vaccination and public health education campaign on the transmission tuberculosis infectious. Inter disciplinary science reviews. 2019; 14 (1); 70–85.
[16]	Peter, O. J., Ibrahim M. O., Akinduko, O. B., Rabiu, M. Mathematical Model for the control of Typhoid Fever. IOSR Journal of Mathematics (IOSR-JM).e-ISSN: 2278-5728, P-ISSN: 2319-765X. Volume 13, Issue 4 ver. 11 (July-August, 2017), pp 60-66. www.Iosrjournals.org.
[17]	Derrick, N. R. and Grossman, S. L. (1976). Differential Equation with application. Addison Wesley Publishing Company. Inc. Philippines.
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[19]	World Health Organization, Lassa fever-Nigeria, World Health Organization, Geneva, Switzerland, 2016.

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APA Style

Anorue Onyinyechi Favour, Okeke Anthony Anya. (2020). Mathematical Model for Lassa Fever Transmission and Control. Mathematics and Computer Science, 5(6), 110-118. https://doi.org/10.11648/j.mcs.20200506.13

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ACS Style

Anorue Onyinyechi Favour; Okeke Anthony Anya. Mathematical Model for Lassa Fever Transmission and Control. Math. Comput. Sci. 2020, 5(6), 110-118. doi: 10.11648/j.mcs.20200506.13

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AMA Style

Anorue Onyinyechi Favour, Okeke Anthony Anya. Mathematical Model for Lassa Fever Transmission and Control. Math Comput Sci. 2020;5(6):110-118. doi: 10.11648/j.mcs.20200506.13

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@article{10.11648/j.mcs.20200506.13,
  author = {Anorue Onyinyechi Favour and Okeke Anthony Anya},
  title = {Mathematical Model for Lassa Fever Transmission and Control},
  journal = {Mathematics and Computer Science},
  volume = {5},
  number = {6},
  pages = {110-118},
  doi = {10.11648/j.mcs.20200506.13},
  url = {https://doi.org/10.11648/j.mcs.20200506.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20200506.13},
  abstract = {Lassa fever is an acute hemorrhagic zoonotic illness (possible transmission from infected animals to humans), caused by Lassa virus whose reservoir host is the Mastomys natalensis (Rodent). It is a disease with a duration of 2-21 days that strives more in African nations and countries with poor water and environmental sanitation. In this paper, a deterministic model for Lassa fever is formulated buttressing the various stages of infection of the disease. We studied the existence and uniqueness of the solutions. The steady states of the model are determined and the basic reproduction number is analyzed with a threshold parameter R_0 which shows persistence of the disease if and only if R_0>1 using the next generation matrix. The treatment strategies considered amidst others are the use of antiviral drug and to quarantine infected individuals on early diagnosis of the infection on the asymptomatic and symptomatic individuals respectively. Numerically, it was evidential that the quarantine system has a great positive effect on the rate of recovery of the infected individuals and also in curbing the risk of infection in the environment which can help safeguard the population. A relapse on this method will lead to reinfection of the disease thereby bringing the population to a point of danger.},
 year = {2020}
}

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TY  - JOUR
T1  - Mathematical Model for Lassa Fever Transmission and Control
AU  - Anorue Onyinyechi Favour
AU  - Okeke Anthony Anya
Y1  - 2020/12/16
PY  - 2020
N1  - https://doi.org/10.11648/j.mcs.20200506.13
DO  - 10.11648/j.mcs.20200506.13
T2  - Mathematics and Computer Science
JF  - Mathematics and Computer Science
JO  - Mathematics and Computer Science
SP  - 110
EP  - 118
PB  - Science Publishing Group
SN  - 2575-6028
UR  - https://doi.org/10.11648/j.mcs.20200506.13
AB  - Lassa fever is an acute hemorrhagic zoonotic illness (possible transmission from infected animals to humans), caused by Lassa virus whose reservoir host is the Mastomys natalensis (Rodent). It is a disease with a duration of 2-21 days that strives more in African nations and countries with poor water and environmental sanitation. In this paper, a deterministic model for Lassa fever is formulated buttressing the various stages of infection of the disease. We studied the existence and uniqueness of the solutions. The steady states of the model are determined and the basic reproduction number is analyzed with a threshold parameter R_0 which shows persistence of the disease if and only if R_0>1 using the next generation matrix. The treatment strategies considered amidst others are the use of antiviral drug and to quarantine infected individuals on early diagnosis of the infection on the asymptomatic and symptomatic individuals respectively. Numerically, it was evidential that the quarantine system has a great positive effect on the rate of recovery of the infected individuals and also in curbing the risk of infection in the environment which can help safeguard the population. A relapse on this method will lead to reinfection of the disease thereby bringing the population to a point of danger.
VL  - 5
IS  - 6
ER  -

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Author Information

Anorue Onyinyechi Favour

Department of Mathematics, Michael Okpara University of Agriculture Umudike Abia-State, Umuahia, Abia–State, Nigeria
Okeke Anthony Anya

Department of Mathematics, Federal University Gashua, Gashua, Yobe-State, Nigeria

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APA Style

Anorue Onyinyechi Favour, Okeke Anthony Anya. (2020). Mathematical Model for Lassa Fever Transmission and Control. Mathematics and Computer Science, 5(6), 110-118. https://doi.org/10.11648/j.mcs.20200506.13

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ACS Style

Anorue Onyinyechi Favour; Okeke Anthony Anya. Mathematical Model for Lassa Fever Transmission and Control. Math. Comput. Sci. 2020, 5(6), 110-118. doi: 10.11648/j.mcs.20200506.13

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AMA Style

Anorue Onyinyechi Favour, Okeke Anthony Anya. Mathematical Model for Lassa Fever Transmission and Control. Math Comput Sci. 2020;5(6):110-118. doi: 10.11648/j.mcs.20200506.13

Copy | Download

@article{10.11648/j.mcs.20200506.13,
  author = {Anorue Onyinyechi Favour and Okeke Anthony Anya},
  title = {Mathematical Model for Lassa Fever Transmission and Control},
  journal = {Mathematics and Computer Science},
  volume = {5},
  number = {6},
  pages = {110-118},
  doi = {10.11648/j.mcs.20200506.13},
  url = {https://doi.org/10.11648/j.mcs.20200506.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20200506.13},
  abstract = {Lassa fever is an acute hemorrhagic zoonotic illness (possible transmission from infected animals to humans), caused by Lassa virus whose reservoir host is the Mastomys natalensis (Rodent). It is a disease with a duration of 2-21 days that strives more in African nations and countries with poor water and environmental sanitation. In this paper, a deterministic model for Lassa fever is formulated buttressing the various stages of infection of the disease. We studied the existence and uniqueness of the solutions. The steady states of the model are determined and the basic reproduction number is analyzed with a threshold parameter R_0 which shows persistence of the disease if and only if R_0>1 using the next generation matrix. The treatment strategies considered amidst others are the use of antiviral drug and to quarantine infected individuals on early diagnosis of the infection on the asymptomatic and symptomatic individuals respectively. Numerically, it was evidential that the quarantine system has a great positive effect on the rate of recovery of the infected individuals and also in curbing the risk of infection in the environment which can help safeguard the population. A relapse on this method will lead to reinfection of the disease thereby bringing the population to a point of danger.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - Mathematical Model for Lassa Fever Transmission and Control
AU  - Anorue Onyinyechi Favour
AU  - Okeke Anthony Anya
Y1  - 2020/12/16
PY  - 2020
N1  - https://doi.org/10.11648/j.mcs.20200506.13
DO  - 10.11648/j.mcs.20200506.13
T2  - Mathematics and Computer Science
JF  - Mathematics and Computer Science
JO  - Mathematics and Computer Science
SP  - 110
EP  - 118
PB  - Science Publishing Group
SN  - 2575-6028
UR  - https://doi.org/10.11648/j.mcs.20200506.13
AB  - Lassa fever is an acute hemorrhagic zoonotic illness (possible transmission from infected animals to humans), caused by Lassa virus whose reservoir host is the Mastomys natalensis (Rodent). It is a disease with a duration of 2-21 days that strives more in African nations and countries with poor water and environmental sanitation. In this paper, a deterministic model for Lassa fever is formulated buttressing the various stages of infection of the disease. We studied the existence and uniqueness of the solutions. The steady states of the model are determined and the basic reproduction number is analyzed with a threshold parameter R_0 which shows persistence of the disease if and only if R_0>1 using the next generation matrix. The treatment strategies considered amidst others are the use of antiviral drug and to quarantine infected individuals on early diagnosis of the infection on the asymptomatic and symptomatic individuals respectively. Numerically, it was evidential that the quarantine system has a great positive effect on the rate of recovery of the infected individuals and also in curbing the risk of infection in the environment which can help safeguard the population. A relapse on this method will lead to reinfection of the disease thereby bringing the population to a point of danger.
VL  - 5
IS  - 6
ER  -

Copy | Download