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)
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
Parameter Sensitivity and Elasticity Analysis of a Mathematical Model for Non–Homogenous Population Density of a Weed Species (Published)
In this work, a stage-structured model for non- homogenous population density of an annual weed is analysed for parameter sensitivity and elasticity. The steady state solution of the model is obtained. In order to determine the contribution of identified parameters to the model steady state, the sensitivity and elasticity analyses are performed using matrix calculus approach. The result of the sensitivity analysis shows that the steady state is very responsive to change in established seedling survival rate (e). While, elasticity analysis indicates that, both established and matured weeds steady-state densities are equally affected by small additive changes in maturity rate (m) and establishment rate (e). Besides, seed bank seed density is most sensitive to small additive change in seed production (b) as compared to weed maturity rate (m). Hence, we conclude that increase in the survival and maturity rates possibly may lead to an increase in weed population density.
Keywords: Elasticity, Matrix calculus, Parameter, Partial derivative., Steady-state, sensitivity