Semi-analytical solution and numerical simulations of a coinfection model of Malaria and Zika virus disease

Authors

  • E. C. Duru
    Department of Mathematics, Michael Okpara University of Agriculture, P.M.B. 7267 Umudike, Nigeria
  • M. C. Anyanwu
    Department of Mathematics, Michael Okpara University of Agriculture, P.M.B. 7267 Umudike, Nigeria
  • T. N. Nnamani
    Department of Mathematics, University of Nigeria, P.M.B. 3247 Nsukka, Nigeria
  • C. N. Nwosu
    Department of Mathematics, Michael Okpara University of Agriculture, P.M.B. 7267 Umudike, Nigeria
  • G. C. E. Mbah
    Department of Mathematics, University of Nigeria, P.M.B. 3247 Nsukka, Nigeria

Keywords:

Malaria , Zika virus , Approximate Solution, Homotopy perturbation

Abstract

In this work, a model for the coinfection of malaria and zika virus disease is studied. The model incorporates various control measures against the spread of malaria and zika virus disease such as vaccination, treatment and biological control of mosquitoes using sterile insect technique. The existence and uniqueness of solutions to the model were first shown. Thereafter, the model is shown to be well-posed epidemiologically by showing that all solutions to the system are positive and bounded. Then, the solution of the model is obtained using the homotopy perturbation method which is a semi-analytical method. The solutions obtained are shown to be comparable with those obtained from Runge-Kutta method of order 4. Furthermore, the performance of the controls in comparison to each other when applied separately and when combined were shown. The results showed that combining the three controls performed better than the rest. Hence, efforts should be made to incorporate controls that affect both humans and the vectors for effective control of malaria, zika virus disease and their coinfection. 

Author Biographies

M. C. Anyanwu

Department of Mathematics, Senior Lecturer

T. N. Nnamani

Department of Mathematics 

C. N. Nwosu

Department of Mathematics 

G. C. E. Mbah

Department of Mathematics, Professor of Mathematics.

Dimensions

[1] R. Singh & A. Kumar, “A comparative study of homotopy perturbation method with differential transformation method to solve a reaction diffusion equation”, Indian Journal of Science and Technology 10 (2017) 1. https://doi.org/10.17485/ijst/2017/v10i30/115495.

[2] S. Abuasad, A. Yildirim, I. Hashi, S. A. Abdulkarim & J. F. Gomez- Aguilar, “Fractional multi-step differential transformed method for approximating a fractional stochastic SIS epidemic model with imperfect vaccination”, International Journal of Environmental and Public Health 16 (2019) 973. https://doi.org/10.3390/ijerph16060973.

[3] H. A. Alkresheh & A. I. Ismail, “Multi-step fractional differential transform method for the solution of fractional order stiff systems”, Ain Shams Engineering Journal 12 (2021) 4223. https://doi.org/10.1016/j.asej.2017.03.017.

[4] M. Ghoreishi, A. I. B. Ismail & A. K. Alomari, “Application of the homotopy analysis method for solving a model for HIV infection of CD4+ T-cells”, Mathematical and Computer Modelling 54 (2011) 3007. https://doi.org/10.1016/j.mcm.2011.07.029.

[5] S. O. Akindeinde, “A new multistage technique for approximate analytical solution of nonlinear differential equations”, Heliyon 6 (2020) 1. https://doi.org/10.1016/j.heliyon.2020.e05188.

[6] C. L. Ejikeme, M. O. Oyesanya, D. F. Agbebaku & M. B. Okofu, “Discussing a solution to nonlinear Duffing oscillator with fractional derivatives using homotopy analysis method (HAM)”, Book Chapter, Book Publisher International 6 (2021) 57. https://doi.org/10.9734/bpi/tpmcs/v6/3966D.

[7] H. A. Zedan & E. E. Adrous, “The application of the homotopy perturbation method and the homotopy analysis method to the generalized Zakharov equations”, Hindawi Publishing Corporation Abstract and Applied Analysis 2012 (2012) 1. https://doi.org/10.1155/2012/561252.

[8] E. Babolian, A. R. Vahidi & Z. Azimzadeh, “Comparison between Adomian’s decomposition method and the homotopy perturbation method for solving nonlinear differential equations”, Journal of Applied Sciences 12 (2012) 793. https://doi.org/10.3923/jas.2012.793.797.

[9] H. Aminikhah, “Solutions of the singular IVPs of Lane-Emden type equations by combining Laplace transformation and perturbation technique”, Nonlinear Engineering 7 (2018) 273. https://doi.org/10.1515/nleng-2017-0086.

[10] S. Rekha, P. Balaganesan & J. Renuka, “Homotopy perturbation method for mathematical modelling of dengue fever”, Journal of Physics: Conference Series 1724 (2021) 1. https://doi.org/10.1088/1742-6596/1724/1/012056.

[11] E. C. Duru, G. C. E. Mbah, M. C. Anyanwu & T. N. Nnamani, “Modelling the co-infection of malaria and zika virus disease”, Journal of Nigerian Society for Physical Sciences 6 (2024) 1. https://doi.org/10.46481/jnsps.2024.1938.

[12] M. C. Anyanwu & G. C. E. Mbah, “Stability analysis of a mathematical model for the use of Wolbachia to stop the spread of Zika virus disease”, Biometrical Letters 58 (2021) 41. https://doi.org/10.2478/bile-2021-0003.

[13] S. I. Ouaziz & M. E. Khomssi, “Mathematical approaches to controlling COVID-19: Optimal control and financial benefits”, Mathematical Modelling and Numerical Simulation with Applications 4 (2024) 1. https://doi.org/10.53391/mmnsa.1373093.

[14] B. Bolaji, U. B. Odionyenma, B. I. Omede, P. B. Ojih & A. A. Ibrahim, “Modelling the transmission dynamics of Omicron variant of COVID-19 in densely populated city of Lagos in Nigeria”, Journal of the Nigerian Society of Physical Sciences 5 (2023) 1055. https://doi.org/10.46481/jnsps.2023.1055.

[15] M. C. Anyanwu, G. C. E. Mbah & E. C. Duru, “On mathematical model for Zika virus disease control with Wolbachia-infected mosquitoes”, Abacus Mathematics Science Series 47 (2020) 35. https://www.man-nigeria.org.ng/ABA-SCI-2020-4-1.

[16] G. Adamu, M. Bawa, M. Jiya & U. D. Chado, “A mathematical model for the dynamics of Zika virus disease via homotopy perturbation method”, Journal of Applied Science and Environmental Management 21 (2017) 615. https://doi.org/10.4314/jasem.v21i4.1.

[17] E. Bonyah & K. O. Okosun, “Mathematical modeling of Zika virus”, Asian Pacific Journal of Tropical Disease 6 (2016) 673. https://doi.org/10.1016/S2222-1808(16)61108-8.

[18] S. I. Onah, O. C. Collins, C. Okoye & G. C. E. Mbah, “Dynamics and control measures for malaria using a mathematical epidemiological model”, Electronic Journal of Mathematical Analysis and Applications 7 (2019) 65. https://fcag-egypt.com/Journals/EJMAA/.

[19] F. Fatmawati, F. F. Herdicho, W. Windarto, W. Chukwu & H. Tasman, “An optimal control of malaria transmission model with mosquito seasonal factor”, Results in Physics 25 (2021) 1. https://doi.org/10.1016/j.rinp.2021.104238.

[20] O. C. Collins & K. J. Duffy, “A mathematical model for the dynamics and control of malaria in Nigeria”, Infectious Disease Modelling 7 (2022) 728. https://doi.org/10.1016/j.idm.2022.10.005.

[21] P. Andayani, L. R. Sari, A. Suryanto & I. Darti, “Numerical study for Zika virus transmission with Beddington-Deangelis incidence rate”, Far East Journal of Mathematical Sciences (FJMS) 111 (2019) 145. http://dx.doi.org/10.17654/MS111010145.

[22] J. Lamwong & P. Pongsumpun, “Age structural model of Zika virus”, International Journal of Modelling and Optimization 8 (2018) 17. https://doi.org/10.7763/IJMO.2018.V8.618.

[23] E. Dantas, M. Tosin & A. Cunha, Jr, “Calibration of a SEIR epidemic model to describe Zika virus outbreak in Brazil”, Applied Mathematics and Computation 338 (2018) 249. https://hal.archives-ouvertes.fr/hal-01456776v2.

[24] J. Amaoh-Mensah, I. K. Dontwi & E. Bonyah, “Stability analysis of Zika–malaria co-infection model for malaria endemic region”, Journal of Advances in Mathematics and Computer Science 26 (2018) 1. https://doi.org/10.9734/JAMCS/2018/37229.

[25] A. Nwankwo and D. Okuonghae, “Mathematical assessment of the impact of different microclimate conditions on malaria transmission dynamics”, Mathematical Biosciences and Engineering 16 (2019) 1414. https://doi.org/10.3934/mbe.2019069.

Susceptible humans.

Published

2025-05-01

How to Cite

Semi-analytical solution and numerical simulations of a coinfection model of Malaria and Zika virus disease. (2025). Journal of the Nigerian Society of Physical Sciences, 7(2), 2436. https://doi.org/10.46481/jnsps.2025.2436

Issue

Volume 7, Issue 2, May 2025

Section

Mathematics & Statistics
Copyright & Licensing

Copyright (c) 2025 E. C. Duru, M. C. Anyanwu , T. N. Nnamani , C. N. Nwosu, G. C. E. Mbah

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Semi-analytical solution and numerical simulations of a coinfection model of Malaria and Zika virus disease. (2025). Journal of the Nigerian Society of Physical Sciences, 7(2), 2436. https://doi.org/10.46481/jnsps.2025.2436

Similar Articles

61-70 of 111

You may also start an advanced similarity search for this article.