ABSTRACT:In this paper, a deterministic mathematical model is formulated to analyse the degree of sensitivity of some factors that aid cholera transmission and management. We obtain the disease-free equilibrium point and conduct the local stability of the disease-free and endemic equilibria of the model. Reproduction number with interventions is stated and the method of normalised forward sensitivity index is employed to determine the numerical value of the key model parameters with respect to the effective reproduction number in order to determine their relative importance to cholera transmission and management. The results obtained show that the most important parameter to cholera transmission is the contact rate between susceptible and infectious individuals while the most crucial parameter to cholera management is the rate of cholera awareness.
The situation has aggravated poverty and brought about untold hardship particularly for the unemployed. Currently, there is intense debate regarding the adjustment in the statutory age of retirement in Nigeria. To that end, a deterministic compartmental mathematical model is designed to study the implication of the proposed increase in the national statutory age of retirement on the national output and the trend of unemployment in Nigeria. The mathematical interpretation of the compartments of the model leads to the corresponding first-order ordinary differential equations. The resulting equations are proved to satisfy the basic features of a good mathematical model. The unemployment-free equilibrium is derived and the stability analysis is performed via stability theory of nonlinear differential equations. Numerical simulation is conducted to validate the analytical results. Results from the simulation show that increasing the national statutory age of retirement will limit the rate at which individuals are moving from the unemployed state to the employed state but widen the rate at which individuals are joining and remaining in the unemployed state.
The rising number of out-of-school children (OOSC) constitutes a major obstacle to growth and development in Nigeria. Despite various institutional frameworks and policy initiatives, Nigeria accounts for the highest number of OOSC worldwide with one out of every five OOSC globally residing in Nigeria. In an attempt to characterize dynamics of OOSC and how it could be tackled to fount sustainable development in Nigeria, a new mathematical model was formulated. The validity of the model was examined using some mathematical theorems and the model equilibria were derived. The inclusive schooling ratio, an analytic parameter that quantified the extent to which the rising OOSC was being tackled to fount development, was computed. The stability properties of the model were studied via stability theory of differential equations based on the derived inclusive schooling ratio. Sensitivity analysis was conducted for some major parameters following the normalized forward sensitivity index approach to examine the relative importance of the model parameters to OOSC expansion and contraction. Numerical simulation was later conducted to justify the theoretical results and the results of the simulation showed that efforts to fount development through minimization of OOSC were fruitful if the inclusive schooling ratio was greater than one otherwise the menace of OOSC persisted. The policy implication of the result is that tackling the menace of OOSC to fount sustainable development in Nigeria is a long-term process and any policies designed to pursue the course must be sustained.
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