Sensitivity and Stability Analysis of Tuberculosis Disease with Infectious Latent (Published)
Tuberculosis (TB) is a dangerous contagious disease which can even lead to death if no control measure is applied. The disease is caused by mycobacterium which generally affects lungs and other related organs such as lymph gland, intestine, kidneys, uterus, bone and brain. The spread of TB occurs via the bacteria contaminated air which is inhaled into the lungs. Cough, chest pain, shortness of breath, appetite loss, weight loss, fever, cold and fatigue are some of the symptoms of TB. However, we proposed a mathematical model to investigate the transmission dynamics of tuberculosis and it is investigated analytically that the endemic equilibrium point is stable with the help of Routh-Hurwitz criteria. The sensitivity analysis shows that there would be an epidemic if and only if where Finally, using Matlab, it is shown that the disease free equilibrium is unstable which the endemic equilibrium becomes stable beyond 60 days. In addition, the recovered population increased rapidly while the exposed population decreased steeply in the disease-free equilibrium. It is an indication that there will be no outbreak of the tuberculosis infection. Besides, an increased in the effective contact rate increases both the infected population and recovered population. It is equally inferred that the recovered population do not show a trend pattern as increases while the susceptible and infected populations increased and decreased respectively as is increased. The recovered population showed no response pattern for since recovered individuals do not obtain permanent immunity.
Keywords: Disease, Dynamics, Infection, Stability, Transmission, latent, sensitivity, tuberculosis (TB)
High Order Compact Finite Difference Techniques for Stochastic Advection Diffusion Equations (Published)
High order compact finite difference scheme for stochastic advection – diffusion equations (SCDEs) of Ito type is designed. Firstly, Modified Mathematical formulation of the stochastic advection – diffusion was developed, followed by the derivation of stochastic differential advection – diffusion using compact finite difference schemes. Explicit- implicit Euler’s scheme was adopted to established the stability criteria in the resulting linear stochastic system of differential equations. The stability criterion was investigated using Fourier mode. Numerical examples were conducted to test the validity, efficient, accuracy and robustness of the derived schemes.
Keywords: Numerical examples., Stability, Stochastic differential advection– diffusion equation, compact finite difference schemes, explicit- implicit Euler’s method
On the Stability of Solutions of Grand General Third Order Non Linear Ordinary Differential Equation (Published)
This work deals with the stability of solutions of the nonlinear third order autonomous ordinary differential equation. By constructing suitable Liapounov functional, the sufficient conditions for the ordinary stability and asymptotic stability of the trivial solution to the differential equation are established.
Keywords: Liapounov functional; Positive definite; negative definite, Stability, trivial solution
Sensitivity Analysis of Lassa fever Model (Published)
A Mathematical Model was developed for the spread and control of Lassa Lever. Existence and stability were analysed for disease free equilibrium. Key to our analysis is the basic reproductive number which is an important threshold for disease control. Reasonable sets of values for the parameter in the model were compiled, and sensitivity analysis indices of around the baseline parameter value were computed, which shows that the most sensitive parameter to is human birth rate , followed by condom efficacy and compliance. Further, the numerical computation of gave a value of 0.129, finally, numerical simulations were obtained that illustrates the effects of the control parameters on the various compartments of the model.
Keywords: Endemic, Equilibrium, Lassa fever, Stability, sensitivity, spectral radius