Abstract
In this paper, a five compartmental model has been considered and investigated the transmission dynamics of measles disease in the human populations. The only one infected compartment in the standard model has been split into two: Infected catarrh, and infected eruption. Measles is a deadly disease that is very common and contagious in the world. However, if enough care is taken one can survive easily against Measles disease. The Measles disease has no specific treatment but vaccination is available. It has been shown that the model has a positive solution and is bounded. The basic reproduction number is derived using the next generation matrix method. The disease free equilibrium point is found and endemic equilibrium state is identified. It is shown that the disease free equilibrium point is locally and globally asymptotically stable if the reproduction number takes a value less than one unit and unstable if it is more than one unit. Numerical simulation study is conducted using ode 45 of MATLAB. The results and interpretations are elaborated and included in the text. Description of the model, Mathematical analysis, stability analysis, and simulation studies are conducted and the results are included. The standard model and the proposed models have been compared and the observations are presented in a tabular form.
Highlights
Measles is one of the communicable diseases still causing preventable mortality and morbidity in the country
The mathematical modeling of infectious diseases is used to study the means by which diseases spread, to forecast the future course of an outbreak and to evaluate strategies to control an epidemic
(2) If L < 1 disease free equilibrium point is locally asymptotically stable i.e. no measles epidemic can develop in the population and (3) if L > 1 the disease free equilibrium point L is unstable i.e. measles epidemic can develop in the population
Summary
Measles is one of the communicable diseases still causing preventable mortality and morbidity in the country. Measles is an infectious diseases highly contagious through person-to-person transmission mode, with more than 90% secondary attack rates among susceptible persons. It resides in the mucus in the nose and throat of an infected person, so transmission typically occurs through coughing and sneezing [1 – 3]. Symptoms and signs of Measles: Prodromal or catarrh, and general symptoms of measles infection presents with a two to four day prodromal of fever, malaise, cough, and runny nose or coryza prior to rash onset. The mathematical modeling of infectious diseases is used to study the means by which diseases spread, to forecast the future course of an outbreak and to evaluate strategies to control an epidemic. The modified model is named as and is used in the present work for further analysis and interpretations [13 – 14]
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