Abstracts
Despite the availability of measles vaccine since 1963, the infectious disease is still endemic in many parts of the world including developed nations. Elimination of measles requires maintaining the effective reproduction number less than unity, Re <1 as well as achieving low levels of susceptibility. Infectious diseases are great field for mathematical modeling, and for connecting mathematical models to primary or secondary data. In this project, we concentrated on the mathematical model for control and elimination of transmission dynamics of measles. We have obtained disease free equilibrium (DFE) point, effective reproduction number and basic reproduction number for the model. Simulations of different variables of the model have been performed and sensitivity analysis of different embedded parameters has been done. MATLAB has been used in simulations of the ordinary differential equations (ODEs) as well as the reproduction numbers.
CHAPTER ONE
INTRODUCTION
In this section we discussed general description of measles, statement of the problem, objectives of the project, project questions and significance of the project.
1.1. General Description of Measles
In this section we discussed background of measles, symptoms of measles, transmission of measles, treatment of measles, immunization of measles and the current situation of measles.
1.1.1. Background of Measles
Measles (also called rubeola) is a highly contagious viral infection that can be found around the world through person-to-person transmission mode, with over 90% attack rate among susceptible persons. It is the first worth eruptive fever occurring during childhood. The measles virus is a paramyxovirus, genus morbillivirus. Even though an effective vaccine is available and widely used, measles continues to occur even in developed countries. Children under five years are most at risk. Measles infects about 30 to 40 million children each year and causing mortality of over one million often from complication related to pneumonia, diarrhea and malnutrition [2]. One of the earliest written descriptions of measles as a disease was provided by an Arab physician in the 9th century who described differences between measles and smallpox in his medical notes. A Scottish physician, Francis Home, demonstrated in 1757 that measles was caused by an infectious agent present in the blood of patients. In 1954 the virus that causes measles was isolated in Boston, Massachusetts, by John F. Enders and Thomas C. Peebles. Before measles vaccine, nearly all children got measles by the time they were 15 years of age [3].
1.1.2. Symptoms of Measles
The main symptoms of measles are fever, runny nose, cough and a rash all over the body, it also produces characteristics-red rash and can lead to serious and fatal complications including pneumonia, diarrhea and encephalitis. Many infected children subsequently suffer blindness, deafness or impaired vision. Measles confer lifelong immunity from further attacks [1].
1.1.3. Transmission of Measles
Measles is a highly contagious virus that lives in the nose and throat mucus of an infected person. It can spread to others through coughing and sneezing. Also, measles virus can live for up to two hours in an airspace where the infected person coughed or sneezed. If other people breathe the contaminated air or touch the infected surface, then touch their eyes, noses, or mouths, they can become infected. Measles is so contagious that if one person has it, 90% of the people close to that person who are not immune will also become infected. Infected people can spread measles to others from four days before through four days after the rash appears. Measles is a disease of humans; measles virus is not spread by any other animal species.
1.1.4. Treatment of Measles
There is no specific treatment for measles. People with measles need bed rest, fluids, and control of fever. Patients with complications may need treatment specific to their problem.
1.1.5. Immunization of Measles
There are two doses for measles vaccine, the first dose of Measles Mumps-Rubella (MMR) should be given on or after the child’s first birthday; the recommended age range is from 12–15 months. A dose given before 12 months of age will not be counted, so the child’s medical appointment should be scheduled with this in mind. The second dose is usually given when the child is 4–6 years old, or before he or she enters kindergarten or first grade. However, the second dose can be given earlier as long as there has been an interval of at least 28 days since the first dose. The first dose of MMR produces immunity to measles in 90% to 95% of recipients. The second dose of MMR is intended to produce immunity in those who did not respond to the first dose, but a very small percentage of people may not be protected even after a second dose. Anyone who had a severe allergic reaction (e.g., generalized hives, swelling of the lips, tongue, or throat, difficulty breathing) following the first dose of MMR should not receive a second dose. Anyone knowing they are allergic to an MMR component (e.g., gelatin, neomycin) should not receive this vaccine. As with all live virus vaccines, women known to be pregnant should not receive the MMR vaccine, and pregnancy should be avoided for four weeks following vaccination with MMR. Children and other household contacts of pregnant women should be vaccinated according to the recommended schedule. Women who are breastfeeding can be vaccinated. Severely immuno- compromised people should not be given MMR vaccine. This includes people with conditions such as congenital immunodeficiency, AIDS, leukemia, lymphoma, generalized malignancy, and those receiving treatment for cancer with drugs, radiation, or large doses of corticosteroids. Household contacts of immunocompromised people should be vaccinated according to the recommended schedule. Although people with AIDS or HIV infection with signs of serious immunosuppression should not be given MMR, people with HIV infection that do not have laboratory evidence of severe immunosuppression can and should be vaccinated against measles.
1.1.6. Current Situation of the Disease
Each year in the United States about 450-500 people died because of measles, 48,000 were hospitalized, 7,000 had seizures, and about 1,000 suffered permanent brain damage or deafness. Today there are only about 60 cases a year reported in the United States, and most of these originate outside the country. For 65 countries with adequate vital registration data (≥85% of estimated deaths of children younger than 5 years registered and coded), they used the reported number of measles deaths. These deaths accounted for less than 0.01% of global measles mortality, according to vital registration data and estimated mortality [3]. For 128 remaining countries with inadequate vital Registration data, WHO estimated country-specific measles deaths through a three-step process. WHO estimated annual measles incidence on the basis of reported measles cases for each country, then WHO distributed estimated incidence across age groups, and finally WHO calculated the number of deaths in each age class by applying age-specific and country-specific measles Case-Fatality Ratios (CFRs). Measles cases and vaccination coverage are reported annually to WHO by all member states through the WHO/ UNICEF Joint Reporting Form [4]. WHO derived coverage estimates for the first routine dose of Measles-Containing Vaccine (MCV1) from reported coverage data and survey results by use of computational logic [5]. Measles cases reported through surveillance systems typically represent a fraction of the true number of cases because many children do not present for medical attention and when medical care is sought, cases can be misdiagnosed or not reported to central authorities [6].
1.2. Statement of the Problem
Despite the availability of the measles vaccine since 1963, the infectious disease is still endemic in many parts of the world including developed nations. The disease has continued causing both economic and health problems to large population worldwide mostly affecting children. Due to these impacts, this study aims to develop a mathematical model for control and elimination of the transmission dynamics of measles.
1.3. Objectives of the Project
1.3.1. Main Objective of the Project
The main objective of this project is to develop a mathematical model for control and elimination of the transmission dynamics of measles.
1.3.2. Specific Objectives of the Project
This project intends to achieve the following specific objectives:
i. Formulate a mathematical model for control and elimination of the transmission dynamics of measles.
ii. To obtain the disease free equilibrium (DFE) point.
iii. To obtain and analyze the effective reproduction number and basic reproduction number.
iv. To perform sensitivity analysis of each parameter involved in the model.
v. To perform simulation of the mathematical model.
1.4. Project Questions
Important questions about control and elimination of the transmission dynamics of measles to be answered by this project are:
i. Can a mathematical model for control and elimination of the transmission dynamics of measles be formulated?
ii. Does the disease free equilibrium (DFE) point for the model exist?
iii. Do the effective reproduction number and basic reproduction number for the model exist?
iv. How sensitive is each embedded parameter?
v. Can measles be eliminated from a population?
1.5. Significance of the Project
The significances of this project are as follows:
i. The analysis of dynamics of measles transmission can be used to predict measles outbreak before it occurs.
ii. The government and health organizations can use findings of this project to plan vaccination programmes and hence prevent future measles outbreak.
iii. The public will participate in vaccination programmes because they will be aware of how it is best way to protect future measles outbreaks.
iv. This project will contribute to improve future studies of measles mathematical modeling.
v. Detailed explanation of transmission of measles between different groups in a population and sensitivity analysis of each parameter can help to control measles outbreak when it occurs.
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