Mathematical Analysis Of Effect Of Area On The Dynamical Spread Of Measles

This paper presents a robust compartmental mathematical model of (SVEIR) which incorporated area only. Where this area is the size of the environment where the study is being investigated. It shows that model has a disease free equilibrium which is globally asymptotically stable (GAS). There exists a unique endemic equilibrium point which is locally stable whenever the association threshold quantity (R0) exceeds unity i.e. R0 > 1. We solved the model numerically using Runge-kutta of order four (4). It is shown that as the area is increasing the total number of infected individual is decreasing. This implies that to reduce the spread of measles, measles patients are to be kept separately for treatment so as to reduce the effective contract rate. The results were presented graphically. Measles is caused by the measles virus. The measles virus is a paramyxovirus of the genus Morbillivirus. It is transmitted by close contact via airborne propagules and spread through droplet transmission from the nose, throat, and mouth of someone who is infected with the virus. These droplets are sprayed out when the infected person coughs or sneezes. Among unimmunized people exposed to the virus, over 90% will contact the disease. Infection leads to the development of a typical rash. The infected person is highly contagious with the rash appearing four days after the person has been infected. The measles virus can remain in the air (and still be able to cause disease) for up to two hours after an infected person has left a room. Individuals infected with measles virus are believed to be immune for life. Also, individual who have received two doses of vaccine after their first birthday has a 98% likelihood of being immune, that is, the probability of having measles even when in contact with those infected with measles is above 0.02, which is very low. Though infants receive some immunity from their mother, this immunity is not complete and they are at increased risk for infection until they receive the vaccinations at 12 to 15 months of age (3, 14). The infectious period is in the order of a week, after which the hosts recover and develop lifelong immunity. Hosts therefore, are normally infected only once in their lifetime and if the dose of the infectious agent is sufficiently large, this happens at a young age, hence measles is a childhood disease. Although in unvaccinated populations measles is a common disease, infection is not without danger (3, 14). Individuals at high risk for measles include but not limited to children less than 1 year of age who, though have some immunity passed from their mother, is not 100% effective; Individual who have not received the proper vaccination series; individual who received immunoglobulin at the time of measles vaccination and individual immunized from 1963 until 1967 with an older ineffective killed measles vaccine. Mortality rates from measles are often high in tropical Africa because of malnutrition, concurrent infection and inadequate case management. Mortality rates of 5% and 10% are common and rates of 20% have been reported (3, 14). In Nigeria, measles is an important cause of childhood morbidity and mortality. Failure to deliver at least one dose of measles vaccine to all infants remains the main reason for high measles morbidity and mortality as 95% coverage is required to interrupt measles transmission. The National Program on Immunization aim of reducing measles case fatality to near zero has depended on the adoption and implementation of the WHO four prong strategy; improving routine immunization with at least one dose of measles vaccine at 9 months, providing a second opportunity for measles immunization through supplemental immunization activities, establishing case based surveillance with laboratory confirmation and improving case management (World Health Organization, 2001). Many physicians and scientists have studied the nature, characteristics, effect and spread of measles in many communities across the globe; these studies are either experimental or theoretical. Similarly, some mathematical modeling studies have been carried out to gain insight into the transmission dynamics and control of measles spread in human population. In this paper, we design a compartmental mathematical model which we sue to investigate the effect of habitat area in the control of the spread of measles in the society. The model designed is