Dynamical analysis of a mathematical model on the spread of diphtheria disease with vaccination completeness factors

Nailul Izzati; Nanndo Yannuansa; Imamatul Ummah; Dian Anisa Rokhmah Wati; Elly Indahwati; Silviana Maya Purwasih; Nur Kholis

doi:10.30762/f_m.v7i2.3901

Authors

Nailul Izzati University of Hasyim Asy’ari Tebuireng Jombang, East Java, Indonesia
Nanndo Yannuansa University of Hasyim Asy’ari Tebuireng Jombang, East Java, Indonesia
Imamatul Ummah University of Hasyim Asy’ari Tebuireng Jombang, East Java, Indonesia
Dian Anisa Rokhmah Wati University of Hasyim Asy’ari Tebuireng Jombang, East Java, Indonesia
Elly Indahwati University of Hasyim Asy’ari Tebuireng Jombang, East Java, Indonesia
Silviana Maya Purwasih Universitas PGRI Adi Buana Surabaya, East Java, Indonesia
Nur Kholis State University of Surabaya, East Java, Indonesia

DOI:

https://doi.org/10.30762/f_m.v7i2.3901

Keywords:

Diphtheria, Dynamical Analysis, Mathematical Model, Vaccination Completeness

Abstract

The COVID-19 pandemic has impacted many aspects of life, including immunization services. As a result of disruptions in these services, tens of millions of children worldwide are at risk of contracting diphtheria, hundreds of thousands of infants did not receive complete DPT immunization, and more than a million infants missed BCG vaccination at birth. Over the past three years, there has been an increase in mortality rates, reaching 10.6% in 2022. Additionally, the number of diphtheria cases in 2022 was more than twice that of 2021. To address the re-emerging of diphtheria, various studies have been conducted, one of which is through mathematical modeling, which can be useful in predicting the dynamics of disease spread and devising strategies to control it. This study developed a mathematical model to describe the dynamics of diphtheria spread with the influence of vaccination completeness. The dynamical analysis method used is by analyzing the eigenvalues and numerical calculation, while numerical simulations employ Fourth Order Runge-Kutta Method. Results from the dynamical analysis and numerical simulations indicate that the disease-free equilibrium point is stable if basic reproduction number , and the endemic equilibrium point is feasible and stable if . Moreover, increasing the vaccination completeness factor within a given population can aid in efforts to prevent the spread of diphtheria. Based on the simulation of the scenarios developed in this study, diphtheria will not become endemic when the vaccination completeness factor reaches 90% and the treatment rate reaches 30%.

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