Mathematical Modelling and Analysis Of water Scarcity Resources Related Dynamics

Abstract

The main objective of our work, Mathematical Modelling of Water Scarcity Water newlinescarcity is one of the major problems faced by all those living around the world. So, newlinethere should be a multiple-way approach to be adopted to conquer the effects of water newlinescarcity in the future. Keeping this in mind, we developed a mathematical model and newlinedemonstrated the effect of water scarcity through deterministic and stochastic formats. newlineThe equilibrium point of the model is found, and its stability is analysed analytically. newlineA numerical simulation of both the deterministic and stochastic models is exhibited to newlinevalidate our analytical findings. Using the basic reproduction number, the stability of newlinethe equilibrium point is analyzed. The next-generation matrix was used to get a basic newlinereproduction number. Local and global stability of equilibria were determined by the newlineRouth-Hurwitz criterion and a suitable Lyapunov function. The numerical simulation newlineshows that the important parameter may transform the dynamics of the system from a newlinelimit to a stable focus when its value increases. newlineFurther, a nonlinear mathematical delay model is analysed in cholera with newlinesusceptible populations affected by carrier population density in the environment. In the newlineepidemic model, disease-free equilibrium always occurs. The instability of the diseasefree newlinestate suggests the presence of an endemic equilibrium state. If the time delay newlineparameter is lower than its critical value, the endemic equilibrium stays asymptotically newlinestable; otherwise, it might become unstable newline