Fractional Derivative and Optimal Control Analysis of Cholera Epidemic Model

Abstract

In this study, a cholera model with fractional derivative and optimal control analysis is presented. Numerical simulation analysis shows that increasing the order of fractional derivatives contributes to updating the memory of the population to control the effects of cholera infection through available controlling techniques. On the other hand, the optimal analysis gives an indication of applying controlling infection with available treatment and prevention techniques. It provides a better mechanism to prevent the happening of cholera infection. Moreover, cost-effectiveness evaluation of cholera contamination intervention with feasible three or four combos of manipulate measures hygiene, vaccination, remedy of infectives, and chlorination indicates that hygiene, vaccination, and chlorination are the desired higher mixture to govern in addition propagation of cholera contamination. Numerical simulations are performed with the MATLAB platform and numerical solutions and results are discussed.

Optimal Control and Bifurcation Analysis of HIV Model

“…To show the existence of optimal control, we use the approach used in [ 3 ]. We have already proved that the HIV model ( 2 ) is bounded, so this result can be used to prove the existence of optimal control over finite time interval as applied in [ 3 , 52 ]. To ensure the existence of optimal control, we need to check if the following conditions are satisfied: The set of controls and state variables be nonempty The control set U is convex and closed The right hand side of the state system is bounded by a linear function in the state and control variables The integrand of objective functional is convex on U The integrand of objective functional is bounded below by k 2 − k 1 (| u 1 | 2 + | u 2 | 2 ) k /2 .…”

“…To show the existence of optimal control, we use the approach used in [3]. We have already proved that the HIV model ( 2) is bounded, so this result can be used to prove the existence of optimal control over finite time interval as applied in [3,52]. To ensure the existence of optimal control, we need to check if the following conditions are satisfied:…”

“…A mathematical model is a crucial scientific representation of both biological and physical problems in the form of mathematical equations [45][46][47][48][49][50][51][52]. Moreover, different mathematical models have been developed to describe the dynamics of HIV with optimal controls.…”

Mathematical Modelling of Host-Pest Interaction in the Presence of Insecticides and Resistance: A Case of Fall Armyworm

“…To address this gap, this study develops a susceptibleinfected (SI) compartmental model for two interacting populations, FAW-maize population, assessing the efects of insecticide sprays and resistance factors on the interaction patterns and population dynamics. SI models are used to model the rate and transmission dynamics of infectious human or plant diseases [26,27]. Tis study assumes that the FAW larvae depend largely on the maize population for food and survival and considers insecticides which are the most commonly used control methods against FAW.…”