Modelling, Analysis, and Simulation of Measles Disease Transmission Dynamics

Abstract

Measles is one of the top communicable diseases, which is still responsible for 2.6 million deaths every year. Due to this reason, the paper focuses on measles transmission dynamics concerning the impact of indirect contact rate (transmitted from the host of the virus to the healthy individual) and improving the SEVIR model into the SVIRP model. From the model, we first estimated the disease-free equilibrium, calculated the effective reproduction number R E f f , and established the stability analysis. The Castillo–Chavez stability criterion is used to demonstrate the global stability of the disease-free equilibrium point, while the linearization method is used to justify its local stability analysis and gives a result R E f f < 1 . The stability analysis of endemic equilibrium point is explained by defining a Lyapunov function, and its global stability exists when R E f f > 1 . To identify the effect of parameters on the transmission dynamics, we performed sensitivity index and numerical simulation. From the result, we obtained that the indirect contact rate has the highest impact in maximizing the transmission dynamics of measles. Also, we found that working on prevention and treatment strategies brings a significant contribution in reducing the disease effect in the community.

Modeling and Simulation of Susceptible - Exposed – Infected – Recovered – Vaccinated - Susceptible Model of Influenza

“…Comparable epidemiological models are under consideration for various infectious diseases, including but not limited to COVID-19 [9], [10], [11], measles [12], [13], [14], and tuberculosis [8].…”

Modeling measles transmission in adults and children: Implications to vaccination for eradication

“…Therefore, mathematical modeling can be a valuable tool for studying measles transmission in children and adult subgroups with different degrees of interactions between intragroup and intergroup populations residing in the same community. Numerous mathematical models have been developed for measles, including SIR, SEIR, SVEIR and SVEIRS, SVEIHR, fractional derivative models, to explore various aspects of measles dynamics ( Edward et al., 2015 ; Farman et al., 2023 ; Haileyesus & Asnakew, 2023 ; Kuddus et al., 2021 ; Peter et al., 2022 , 2023a , 2023b ; Roberts, 2000 ; Song et al., 2019 ; Trottier & Philippe, 2000 ). Specifically in the context of Nepal, previous studies have discussed progress in measles control, case fatality rates, and the genetic type of the Asian measles virus, most incorporating vaccination ( Joshi, 2009 ; Khanal, 2016 ; Poudel, 2019 ; Truong et al., 2001 ).…”

Modelling and Stability Analysis of the Dynamics of Measles with Application to Ethiopian Data

“…Quite recently, studying the dynamics of the measles disease in the context of mathematics is an important issue [4,[18][19][20][21][22][23]. Some authors such as [20,22,23] have studied the dynamics using constant and continuous controls.…”

“…They have studied the global stability analyses of the disease-free and endemic equilibria. Other authors, for instance, [19] investigated the global stability analysis of the disease dynamics but failed to predict the disease dynamics in the context of a particular situation. There are also others such as [21] who proposed a mathematical model of measles and predicted the disease situation in Bangladesh using double vaccination doses.…”