A mathematical analysis of the impact of maternally derived immunity and double-dose vaccination on the spread and control of measles

Abstract

Measles is a highly communicable viral infection that mostly affects children aged 5 years and below. Maternal antibodies in neonates help protect them from infectious diseases, including measles. However, maternal antibodies disappear a few months after birth, necessitating vaccination against measles. A mathematical model of measles, incorporating maternal antibodies and a double-dose vaccination, was proposed. Whenever ℛ0<1{{\mathcal{ {\mathcal R} }}}_{0}\lt 1, the model is shown to be locally asymptotically stable. This means that the measles disease can be eliminated under such conditions in a finite time. It was established that ℛ0{{\mathcal{ {\mathcal R} }}}_{0} is highly sensitive to β\beta (the transmission rate). A numerical simulation of the model using the Runge-Kutta fourth-order scheme was carried out, showing that varying the parameters to reduce ℛ0{{\mathcal{ {\mathcal R} }}}_{0} will help control the measles disease and ultimately lead to eradication. The measles-mumps-rubella (MMR) vaccine dosage should be adjusted for babies from recovered mothers, as maternal antibodies are usually high in such babies and can interfere with the effectiveness of the MMR vaccine.

Keywords

• basic reproduction number
• runge-kutta fourth-order method
• stability
• bifurcation
• sensitivity
• 92d30
• 37n25
• 34d20
• 92b05
• 92d25