Open AccessModeling the Transmission Dynamics of Measles in the Presence of Treatment as Control Strategy
Author(s) -
Rose Veronica Paul,
William Atokolo,
Salawu Ademu Saka,
Achonu Omale Joseph
Publication year - 2021
Publication title -
asian research journal of mathematics
Language(s) - English
Resource type - Journals
ISSN - 2456-477X
DOI - 10.9734/arjom/2021/v17i830324
Subject(s) - basic reproduction number , equilibrium point , population , stability (learning theory) , transmission (telecommunications) , measles , extinction (optical mineralogy) , value (mathematics) , mathematics , control theory (sociology) , computer science , control (management) , mathematical economics , statistics , medicine , physics , virology , mathematical analysis , differential equation , telecommunications , environmental health , machine learning , artificial intelligence , vaccination , optics
We present in this research work, mathematical modeling of the transmission dynamics of measles using treatment as a control measure. We determined the Disease Free Equilibrium (DFE) point of the model after which we obtained the Basic Reproduction Number ( R0 ) of the model using the next generation approach. The model Endemic Equilibrium (EE) point was also determined after which we performed Local Stability Analysis(LAS) of the Disease Free Equilibrium point and result shows that the Disease Free Equilibrium point of the model would be stable if ( R0 <1). Global Stability Analysis (GAS) result shows that, ( R0 ≤ 1) remains the necessary and sufficient condition for the infection to go into extinction from a population. We carried out Sensitivity Analysis of the model using the Basic Reproduction Number and we discovered that ( δ , μ, ν , θ ) are sensitive parameters that should be targeted towards control intervention strategy as an increase in these values can reduce the value of ( R0 ) to a value less than unity and such can reduce the spread of measles in a population. Model simulation was carried out using mat lab software to support our analytical results.