A Metapopulation Model for Cholera with Variable Media Efficacy and Imperfect Vaccine

Year 2024, Volume: 7 Issue: 1, 20 - 32, 08.05.2024

Phoebe Amadi , George Lawı Job Bonyo

https://doi.org/10.33187/jmsm.1289684

Abstract

In this paper, a metapopulation model has been developed and analysed to describe the transmission dynamics of cholera between two communities linked by migration, in the presence of an imperfect vaccine and a varying media awareness impact. Stability analysis shows that the disease-free equilibrium is both locally and globally asymptotically stable when the vaccine reproduction number is less than unity. The endemic equilibria have also been shown to be locally asymptotically stable when the vaccine reproduction number is greater than unity. The simulation results show that with an imperfect vaccine and efficient media awareness, cholera transmission is reduced. The transmission rates have also been shown to be nonidentical in the two communities. It is therefore advisable, that health practitioners embrace the use of both vaccination and media awareness when designing and implementing community-specific cholera intervention strategies.

Keywords

Cholera, Imperfet vaccine, Media awareness, Metapopulation, Migration

References

• [1] WHO, Cholera Vaccines: WHO position paper - August 2017, Weekly Epidemological Record, 92(34) (2017), 477-500.
• [2] B. Dumitru, A. Fahimeh, J. Juan, J. Amin, On a new and generalized fractional model for a real cholera outbreak, Alex. Eng. J., 61(11) (2022), 9175 - 9186.
• [3] C. Eric, N. Eric, L. Suzanne, Y. Abdul - Aziz, Mathematical modeling of the influence of cultural practices on cholera infection in Cameroon, Math. Biosci. Eng., 18(6) (2021), 8374-8391.
• [4] Cholera Vaccines, WHO position paper, Weekly Epidemiological Record, 85(13) (2010),117.
• [5] D. Sur et. al., Efficacy and safety of a modified killed-whole-cell oral cholera vaccine in India: an interim analysis of a cluster-randomised, double-blind, placebo-controlled trial, Lancet, 374(9702) (2009), 1694-1702.
• [6] E. Marcelino et. al., Effectiveness of mass cholera vaccination in Beira, Mozambique, N. Engl. J. Med., 352(8) (2005), 757-767.
• [7] Cholera, V. Cholerae Infection in Africa, Available at www.cdc.gov
• [8] N. Hellen, O. Emmanuel, L. Livingstone, Modeling optimal control of cholera disease under the interventions of vaccination, treatment and education awareness, J. Math. Res., 10(5) (2018), 137-152.
• [9] B. Musundi, G. Lawi, F. Nyamwala, Mathematical analysis of a cholera transmission model incorporating media coverage, Int. J. Pure Appl. Math., 111(2) (2016), 219 - 231.
• [10] J. Njagarah, F. Nyabadza, Modelling optimal control of cholera in communities linked by migration, Comput. Math. Methods Med., (2015), Article ID 898264.
• [11] L. Rachael, N. Miller, S. Elsa, G. Holly, K. Renee and L. Suzanne, Modeling optimal intervention strategies for cholera, Bull. Math. Biol., 72 (2010), 2004–2018.
• [12] R. Michael, H. Joseph, C. Marisa and L. Suzanne, The impact of spatial arrangements on epidemic disease dynamics and intervention strategies, J. Biol. Dyn., 10(1) (2016), 222–249.
• [13] P. Amadi, A Metapopulation Model for Cholera with Variable Media Efficacy and Imperfect Vaccine, MSc Thesis, Maseno University (2021).
• [14] Z. Xueyong, S. Xiangyun, W. Ming, Stochastic modeling with optimal control: Dynamical behavior and optimal control of a stochastic mathematical model for cholera, Chaos, Solutions and Fractals, 156 (2022), 111854.
• [15] M. Mehmet, B. Zafer, K. Tulay and K. Tahir, Transmission of cholera disease with Laplacian and triangular parameters, IJMSI, 17(2) (2022), 289-305.
• [16] P. Prabir, K. Shyamal and C. Joydev, Dynamical study in fuzzy threshold dynamics of a cholera epidemic model, Fuzzy Inf. Eng., 9(3) (2017), 381-401.
• [17] J. Harris, Cholera: immunity and prospects in vaccine development, J. Infect. Dis., 218(3) (2018), 141-146 .
• [18] C. Codeco, Endemic and epidemic dynamics of cholera: the role of the aquatic reservoir, BMC Infect. Dis., 1(1) (2001). DOI:10.1186/1471-2334-1-1.
• [19] P. Driessche and W. James, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48.
• [20] C. Leopard, K. Damian, A. Emmanuel, Modeling and stability analysis for measles metapopulation model with vaccination, Appl. Comput. Math., 4(6) (2015), 431-444.
• [21] C. Castillo-Chavez, Z. Feng, W. Huang, On the computation of R0 and its role on global stability, Mathematical Approaches for Emerging and Reemerging Infectious Diseases, 125 (2002), 229-250.
• [22] J. Njagarah, F. Nyabudza, A metapopulation model for cholera transmission dynamics between communities linked by migration, Appl. Math. Comput., 241 (2014), 317 - 331.
• [23] C. Jing’an, W. Zhanmin, Z. Xueyong, Mathematical analysis of a cholera model with vaccination, J. Appl. Math, 2014, Article ID 324767, 16 pages.
• [24] M. Jennifer, N. Farai, M. Josiah, Modelling cholera transmission dynamics in the presence of limited resources, BMC Res. Notes, 12(475) (2019).
• [25] H. Nyaberi, D. Malonza, Mathematical model of cholera transmission with education campaign and treatment through quarantine, J. Adv. Math. Comput., 32(3) (2019), 1-12.
• [26] J. Wang, M. Charairat, Modeling cholera dynamics with controls, Can. Appl. Math. Q., 19(3) (2011).
• [27] M. Al-Arydah, A. Mwasa, J. Tchuenche, Modelling cholera disease with education and chlorination, J. Biol. Syst., 21(4) (2013), Article number 1340007.
• [28] M. Yanli, L. Jia-Bao, L. Haixia, Global dynamics of an SIQR model with vaccination and elimination hybrid strategies, Mathematics, 6(12), (2018), 328.
• [29] P. Ana, J. Cristiana, F. Delfim, A cholera mathematical model with vaccination and the biggest outbreak of world’s history, AIMS Mathematics, 3(4)(2018), 448 - 463.