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Articles 1 - 3 of 3
Full-Text Articles in Vital and Health Statistics
A Mathematical Model For Malaria With Age-Heterogeneous Biting Rate, Sho Kawakami
A Mathematical Model For Malaria With Age-Heterogeneous Biting Rate, Sho Kawakami
All Graduate Theses, Dissertations, and Other Capstone Projects
We propose a mathematical model for malaria with age-heterogeneous biting rate from mosquitos. The existence of the model, the local behavior of the disease free equilibrium are explored. Furthermore the model is extended to an optimal control problem and the corresponding adjoint equations and optimality conditions are derived. Age dependent parameter values are estimated and numerical simulations are carried out for the model. The new model better accounts for difference in biting rates of mosquitos to different age groups, and improvements in stability to the explicit algorithm. The optimal control is also shown to depend on the age distribution of …
Mathematical Modeling Of Tick-Borne Encephalitis In Humans, Amanda Kriesel, Michael Meyer, Geoffrey Peterson
Mathematical Modeling Of Tick-Borne Encephalitis In Humans, Amanda Kriesel, Michael Meyer, Geoffrey Peterson
Journal of Undergraduate Research at Minnesota State University, Mankato
Tick-Borne Encephalitis is a virus that affects ones nervous system and is transmitted from tick to human through tick bite. In recent years, the number of cases of tick-borne encephalitis in Europe has been increasing. This mathematical biological model of Tick-Borne Encephalitis was created in order to further our understanding of such phenomenon, as well as study the relationship between vectors and their hosts. Specifically, we will investigate the population model of ticks in certain regions and its correlation to tick-borne encephalitis infections in the region.
Herd Immunity And The Necessity Of Vaccinations: Modeling The Effects Of Mmr Vaccinations, Caitlyn Cardetti, Katie Groskreutz, Melissa Zins
Herd Immunity And The Necessity Of Vaccinations: Modeling The Effects Of Mmr Vaccinations, Caitlyn Cardetti, Katie Groskreutz, Melissa Zins
Journal of Undergraduate Research at Minnesota State University, Mankato
The MMR vaccination is a two dose vaccine given to children between the ages of 12 – 15 months and the second dose between the ages of 4 – 6 years to prevent measles, mumps, and rubella. The objective was to mathematically model the effects of the MMR vaccinations in a hypothetical school through multiple compartment and spatial models. These models were based on each disease individually with their respective vaccine effectiveness and disease infection rates. These models demonstrated the limits of herd immunity. Herd immunity occurs when a high enough percentage of the population is immune or vaccinated to …