Modelling transmission dynamics of measles: the effect of treatment failure in complicated cases

• Published in: Modeling earth systems and environment 2024-10, Vol.10 (5), p.5871-5889
• Main Authors: Peter, Olumuyiwa James, Cattani, Carlo, Omame, Andrew
• Format: Article
• Language: English
• Subjects: Chemistry and Earth Sciences; Computer Science; Control stability; Disease control; Earth and Environmental Science; Earth Sciences; Earth System Sciences; Ecosystems; Environment; Epidemics; Failure; Hypercubes; Immunization; Impact analysis; Latin hypercube sampling; Math. Appl. in Environmental Science; Mathematical Applications in the Physical Sciences; Measles; Original Article; Physics; Robust control; Sensitivity analysis; Stability analysis; Statistics for Engineering; Steady state models; Vaccination
• ISSN: 2363-6203; 2363-6211
• DOI: 10.1007/s40808-024-02120-1

Measles has emerged as one of the leading causes of child mortality globally, leading to an estimated 142,300 fatalities annually, despite the existence of a reliable and safe vaccine. Moreover, a surge in global measles cases has occurred in recent years, predominantly among children below 5 years old and immunocompromised adults. The escalating incidence of measles can be attributed to the continual decline in vaccination coverage. This phenomenon has attracted considerable attention from both the public and scientific communities. In this work, we develop and analyze a fractional-order model for measles epidemic by incorporating vaccination as control strategy and investigating the effect of treatment failure in complicated cases. The model is analyzed qualitatively and quantitatively to gain robust understanding into control measures required to curb this menace. Stability analysis around the neighbourhood of measles-free steady state is carried out to determine properties of the important threshold called reproduction number, which is necessary to quantitatively analyze the formulated model. Sensitivity analyses of this threshold and the state solutions using the Latin hypercube sampling (LHS) and contour/surface plots reveal the dominance of effective contact rate, progression and transition rates in influencing the general dynamics of measles epidemic. Furthermore, the fractional non-standard discretization scheme using a well defined denominator function is used to numerically solve the designed model. Scenario analyses to assess the impact of vaccination and treatment failure show that an effective and safe vaccination programme could significantly reduce the spread of measles while uncontrolled treatment failure could adversely increase the burden of measles within a population.