Indexing

Abstract: Escherichia coli is species of bacteria which can be grouped into two types: One that causes illness to human beings and second group is a harmless bacterium. The harmful ones cause disease by producing toxin known as Shiga toxin; they are called Shiga toxin producing Escherichia coli. In this project, a model consisting of three sub populations which named; susceptible population S(t), Infected population I(t) and recovered population R(t). Differential equations were formulated from the model. Disease free equilibrium and Endemic equilibrium were determined from the model equations. The disease-free equilibrium was determined to be asymptotically stable when R₀ < 1 and unstable otherwise. The basic reproductive number (R₀) was computed using Next generation method. Through sensitivity analysis, the most sensitive parameter to the basic reproductive number was determined. Numerical simulation of the model equations was done.

Keywords: Shiga Toxin, Model, Reproductive Number, Numerical Simulation, Equilibrium, Sensitivity, Analysis.

Title: Mathematical Modeling of Shiga Toxin Incorporating the Environment

Author: Serapia Peter Soka, Dr. Mary Wainaina, Dr. Isaac Mwangi

ISSN 2350-1022

International Journal of Recent Research in Mathematics Computer Science and Information Technology

Paper Publications

Abstract: We modeled a four-compartment model that explain the effects of variation of the contact rates between environment, susceptible and infected population in transmission dynamics of infectious bursal disease (IBD). We used Ordinary differential equations in formulating the model equations. Reproductive number has been derived using next generation Matrix. The disease-free equilibrium and endemic equilibrium stability are analyzed. MATLAB was used to carry out the numerical simulation. We found the higher that contact rate between the susceptible flock, infected population and the contaminated environment, the higher rate of transmission of the disease in the system.

Keywords: Modelling, Flock, Bursal, Infectious, environment, Contact rate, Gumboro.

Title: The effects of variation of contact rates between the environment, susceptible and infected population in a mathematical model of the transmission dynamics of Infectious Bursal Disease (IBD)

Author: Emily Atieno Omollo, Dr. George Kimathi, Dr. Isaac Mwangi

ISSN 2350-1022

International Journal of Recent Research in Mathematics Computer Science and Information Technology

Paper Publications

Abstract: The model consists of five compartments; the susceptible humans, vaccinated humans, infectious humans, carriers humans and the recovered humans. We conducted an analysis on the existence of all the equilibrium points; the disease- free equilibrium and endemic equilibrium. The reproduction number was computed by using the next generation matrix approach. Disease -free equilibrium was found to be locally asymptotically stable and globally asymptotically stable if the reproduction number was less than one. The most sensitive parameter to the basic reproduction number was determined by using various sensitivity objectives that the researchers analyzed. Numerical simulations of the system of differential equations of the epidemic model were carried out for interpretations. It is this view that this research highlighted various objectives. The findings showed that the existence of a large number of carriers who are infectious but show no symptoms. Therefore, carriers do not show symptoms; they will not be part of any treatment program, or prevention program in the system.  

Keywords: Modelling, Carrier, Vaccine, Typhoid, Dynamic, Infectious, Analysis.

Title: Modelling the Impact of Carrier and Vaccination in Understanding Typhoid Fever Dynamics

Author: Nzani Borive Esperance, Dr. Isaac Mwangi, Dr. Mary Wainaina

ISSN 2350-1022

International Journal of Recent Research in Mathematics Computer Science and Information Technology

Paper Publications

Abstract: In this paper we developed a SISeTR model, which is a mathematical model of alcoholism as an infectious disease with five compartments i.e. susceptible, infected, sensitized, treated and recovered. The R₀ was developed and the model stability and the existence of equilibrium points determined. The quantitative analysis of the study, established that the local stability existed when R₀<1. The numerical analysis established that, sensitization affects the dynamics of the model. We established that an increase in sensitization leads to a decline in the number of infections. This paper therefore shows that alcoholism can be significantly reduced by sensitizing the population.

Keywords: Alcoholism, Model, Sensitization, Infectious, Local Stability, Equilibrium, Global Stability.

Title: Numerical Solution of Alcoholism as an Infectious Disease

Author: Joseph Ochieng Obuya, George Kimathi, Winnie Kaluki

ISSN 2350-1022

International Journal of Recent Research in Mathematics Computer Science and Information Technology

Paper Publications