A three-layered compartmental model of Nipah virus transmission with analysis

Document Type : Research Article

Authors

1 Department of Applied Mathematics, Faculty of Mathematical Science, Ferdowsi University of Mashhad, Mashhad, Iran

2 Department of Science, School of Mathematical Sciences, University of Zabol, Zabol, Iran

Abstract

In this work, we have proposed a three-layered (fruit bat-to-fruit-to-human) compartmental model for the description of the spread of the Nipah virus. We have proved the positivity and boundedness of the model's solutions. The bounded nature of the answers also suggests that the disease spread process eventually reaches a steady state, which helps preventing unrealistic predictions. We have shown that a disease-free equilibrium point has local stability. Besides, the global stability of disease-free equilibrium point has been demonstrated with the help of a fluctuation lemma. We have fitted our model with the reported cases of infection and death in Bangladesh. From sensitivity analysis, we understand which parameters are more sensitive to change. Lastly, we have solved the model equations numerically utilizing the Runge-Kutta method to examine the effect of various parameters on the population of the model classes.

Keywords

Main Subjects

References

[1] R. Amin, S¸ . Y¨uzbas¸, S. Nazir, Efficient Numerical Scheme for the Solution of HIV Infection CD4+
T-Cells Using Haar Wavelet Technique, CMES Comput. Model. Eng. Sci. 131 (2022) 639–653.
[2] Attaullah, R. Jan, S¸ . Y¨uzbas¸, Dynamical behavior of HIV Infection with the influence of variable
source term through Galerkin method, Chaos Solitons Fractals 152 (2021) 111429.
[3] Attaullah, S¸ . Y¨uzbas¸, S. Alyobi, M.F. Yassen, W. Weera, A Higher-Order Galerkin Time Dis-
cretization and Numerical Comparisons for Two Models of HIV Infection, Comput. Math. Methods
Med. 1 (2022) 3599827.
[4] S. Barua, A. Denes, Global dynamics of a compartmental model for the spread of Nipah virus,
Heliyon 9 (2023) e19682.
[5] S. Barua, M. Ibrahim, A. Denes, A compartmental model for the spread of Nipah virus in a periodic
environment, AIMS Math. 8 (2023) 29604-29627.
[6] M.H.A. Biswas, M.M. Haque, G. Duvvuru, A mathematical model for understanding the spread
of Nipah fever epidemic in Bangladesh, International Conference on Industrial Engineering and
Operations Management (IEOM ) (2015) 1–8.
[7] Y. Chen, J. Li, S. Zou, Global dynamics of an epidemics model with relapse and nonlinear inci-
dence, Math. Methods Appl. Sci. 42 (2018)
[8] S. Das, P. Das, P. Das, Control of Nipah virus outbreak in commercial pig-farm with biosecurity
and culling, Math. Model. Nat. Phenom. 15 (2020) 64.
[9] P.V. Driessche, J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for
compartmental models of disease transmission, Math Biosci. 180 (2002) 29–48.
[10] J.H. Epstein, S.J. Anthony, A. Islam, et al., Nipah virus dynamics in bats and implications for
spillover to humans, Proc. Natl. Acad. Sci. 117 (2020) 29190–29201.
[11] N.K. Goswami, F. Hategekimana, Optimal control techniques for the transmission risk of Nipah
virus disease with awareness, Adv. Syst. Sci. Appl. 4 (2022) 176–192.
[12] R. Jan, M.S. Zobaer, S¸ . Y¨uzbas¸, Attaullah, M. Jawad, A. JAN, Fractional derivative analysis of
Asthma with the effect of environmental factors, Sigma. J. Eng. Nat. Sci. 42 (2024) 177–188.
[13] S. Li, S. Ullah, Samreen, I.U. Khan, S.A. Alqahtani, M.B. Riaz, A robust computational study for
assessing the dynamics and control of emerging zoonotic viral infection with a case study: A novel
epidemic modeling approach, AIP Adv. 14 (2024) 015051.
[14] A.C. Loyinmi, S.O. Gbodogbe, Mathematical modeling and control strategies for Nipah virus
transmission incorporating bat-to-pig-to-human pathway, EDUCATUM J. Sci. Math. Tech. 11
(2024) 54–80.
[15] M. Parsamanesh, M. Erfanian Global dynamics of an epidemic model with standard incidence rate
and vaccination strategy, Chaos Solitons Fractals 117 (2018) 192–199.
[16] M. Parsamanesh, M. Erfanian, S. Mehrshad, Stability and bifurcations in a discrete-time epidemic
model with vaccination and vital dynamics, BMC Bioinformatics 21 (2020) 525.
[17] M. Parsamanesh, M. Erfanian, Stability and bifurcations in a discrete-time SIVS model with satu-
rated incidence rate, Chaos Solitons Fractals 150 (2021) 111178.
[18] Samreen, S. Ullah, R. Nawaz, S.A. Alqahtani, S. Li, A. Hassan, A mathematical study unfolding
the transmission and control of deadly Nipah virus infection under optimized preventive measures:
New insights using fractional calculus, Results in Phys. 51 (2023) 106629.
[19] N.H. Shah, N. Trivedi, F. Thakkar, M. Satia, Control strategies for Nipah virus, Int. J. Appl. Eng.
Res. 13 (2018) 21.
[20] H. Smith, An Introduction to Delay Differential Equation with Applications to the Life Sciences,
Springer, New York, 2011.
[21] G. Yildirim, S¸ . Y¨uzbas¸, A Collocation Technique via Pell-Lucas Polynomials to Solve Fractional
Differential Equation Model for HIV/AIDS with Treatment Compartment, Comput. Model. Eng.
Sci. 141 (2024).
[22] G. Yildirim, S¸ . Y¨uzbas¸, Numerical solutions and simulations of the fractional COVID-19 model via
PellLucas collocation algorithm, Math. Methods. Appl. Sci. 47 (2024) 14457–14475.
[23] G. Yildirim, S¸ . Y¨uzbas¸, Numerical solutions of SIRD model of Covid-19 by utilizing Pell- Lucas
collocation methodLucascollocation method, Turk. J. Math. 48 (2024) 1156–1182.
[24] S¸ . Y¨uzbas¸, A numerical approach to solve the model for HIV infection of CD4 + T cells, Appl.
Math. Model. 36 (2012) 5876–5890.
Journal of Mathematical Modeling
Volume 13, Issue 2
May 2025
Pages 445-466

Files

Share

How to cite

Statistics