Dynamics of Caputo Fractional Order SEIRV Epidemic Model with Optimal Control and Stability Analysis

Analysis of optimal control strategies on the fungal Tinea capitis infection fractional order model with cost-effective analysis

In this study, we have formulated and analyzed the Tinea capitis infection Caputo fractional order model by implementing three time-dependent control measures. In the qualitative analysis part, we investigated the following: by using the well-known Picard-Lindelöf criteria we have proved the model solutions' existence and uniqueness, using the next generation matrix approach we calculated the model basic reproduction number, we computed the model equilibrium points and investigated their stabilities, using the three time-dependent control variables (prevention measure, non-inflammatory infection treatment measure, and inflammatory infection treatment measure) and from the formulated fractional order model we re-formulated the fractional order optimal control problem. The necessary optimality conditions for the Tinea capitis fractional order optimal control problem and the existence of optimal control strategies are derived and presented by using Pontryagin's Maximum Principle. Also, the study carried out the sensitivity and numerical analysis to investigate the most sensitive parameters and to verify the qualitative analysis results. Finally, we performed the cost-effective analysis to investigate the most cost-effective measures from the possible proposed control measures, and from the findings we can suggest that implementing prevention measures only is the most cost-effective control measure that stakeholders should consider.

Analysis of fractional order model on higher institution students' anxiety towards mathematics with optimal control theory

Anxiety towards mathematics is the most common problem throughout nations in the world. In this study, we have mainly formulated and analyzed a Caputo fractional order mathematical model with optimal control strategies on higher institution students' anxiety towards mathematics. The non-negativity and boundedness of the fractional order dynamical system solutions have been analysed. Both the anxiety-free and anxiety endemic equilibrium points of the Caputo fractional order model are found, and the local stability analysis of the anxiety-free and anxiety endemic equilibrium points are examined. Conditions for Caputo fractional order model backward bifurcation are analyzed whenever the anxiety effective reproduction number is less than one. We have shown the global asymptotic stability of the endemic equilibrium point. Moreover, we have carried out the optimal control strategy analysis of the fractional order model. Eventually, we have established the analytical results through numerical simulations to investigate the memory effect of the fractional order derivative approach, the behavior of the model solutions and the effects of parameters on the students anxiety towards mathematics in the community. Protection and treatment of anxiety infectious students have fundamental roles to minimize and possibly to eradicate mathematics anxiety from the higher institutions.

Clinical effects of 2-DG drug restraining SARS-CoV-2 infection: A fractional order optimal control study

Fractional calculus is very convenient tool in modeling of an emergent infectious disease system comprising previous disease states, memory of disease patterns, profile of genetic variation etc. Significant complex behaviors of a disease system could be calibrated in a proficient manner through fractional order derivatives making the disease system more realistic than integer order model. In this study, a fractional order differential equation model is developed in micro level to gain perceptions regarding the effects of host immunological memory in dynamics of SARS-CoV-2 infection. Additionally, the possible optimal control of the infection with the help of an antiviral drug, viz. 2-DG, has been exemplified here. The fractional order optimal control would enable to employ the proper administration of the drug minimizing its systematic cost which will assist the health policy makers in generating better therapeutic measures against SARS-CoV-2 infection. Numerical simulations have advantages to visualize the dynamical effects of the immunological memory and optimal control inputs in the epidemic system.

Study of a Nonlinear System of Fractional Differential Equations with Deviated Arguments Via Adomian Decomposition Method

This paper studies a system of nonlinear fractional differential equations (FDEs) with deviated arguments. Many linear and nonlinear problems are faced in the real-life. Generally, linear problems are solved quickly, but some difficulties appear while solving nonlinear problems. Our purpose is to approximate those solutions numerically via the Adomian decomposition method (ADM). Here, our main goal is to apply the ADM to solve higher-order nonlinear system of FDEs with deviated arguments. We prove the existence and uniqueness of the solution using Banach contraction principle. Moreover, we plot the figures of ADM solutions using MATLAB.