Abstract
In this paper, a five (5) compartmental model is presented to study the transmission dynamics of Measles in a population at any point in time. The model is rigorously analyzed to gain insight into the dynamical features of Measles and also, optimal control theory is applied to give an optimality system which we used to minimize the number of infected individuals and propose the most suitable control strategy for the spread of measles. It is shown that the model has a diseases free equilibrium which is globally asymptotically stable (GAS). Also, there exists a unique endemic equilibrium point which is locally stable whenever the associated threshold quantity exceeds (one) unity. We also show that there exists a solution for the optimality system. From the result, it was observed that vaccine control strategy is more efficient in reducing the number of infected individuals as compared to other control strategies.
Highlights
Measles is a communicable and deadly viral disease caused by the measles virus, of the genus Morbillivirus which belongs to the family paramyxoviridae
When an infected individual sneezes or coughs, measles is spread through droplet transmission from the nose, throat, and mouth of someone who is infected with Measles virus
We presented and analyzed five (5) compartmental models which incorporated isolated infected individual during treatment so as to gain insight into the measles infection transmission dynamics
Summary
Measles is a communicable and deadly viral disease caused by the measles virus, of the genus Morbillivirus which belongs to the family paramyxoviridae. The leading vaccine-preventable killer of children worldwide, is estimated to have caused 614 000 global deaths annually in 2002, with 50% of all global measles deaths occurring in sub-Saharan Africa. Measles infection is still prevalent in many developing countries especially in parts of Africa and Asia where more than 20 million measles cases are reported annually [30]. The more children in a community that are vaccinated, the less likely it is that any children, even those who have not been immunized, will get sick because there are fewer hosts for the infectious agents This is referred to as “herd” immunity and it is vital with extremely contagious diseases such as measles, where immunization of 90 to 95 per cent of infants is needed to protect a community from measles epidemics.
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