Global dynamics and optimal control of a nonlinear fractional-order cholera model

In this article, a fractional-order epidemic model for cholera is proposed and analyzed. Two transmission routes for cholera are considered to develop the compartmental epidemic model. The basic biological properties of the solutions of the fractional-order model are investigated. The global asymptotic stability of the equilibrium points have been established using appropriate Lyapunov functional. Moreover, a fractional-order control problem is presented, and its analytical solution is derived using Pontryagin’s maximum principle. Also, some graphical visualizations of the theoretical results are provided. It is found that the factional-order derivative only affect the time to reach the stationary states. Sensitivity analysis reveals that by reducing the rates of new recruitment and both the disease transmission rates, it may be possible to reduce the value of the basic reproduction number

The impact of media awareness on a fractional-order SEIR epidemic model with optimal treatment and vaccination

During any pandemic, to decrease the spreading possibility of infectious diseases to people, boosting public awareness is crucial. Media helps to boost this awareness. This paper aims to check the impact of awareness of media regarding infectious diseases. For this reason, an SEIR-type epidemic model is proposed and examined in this research, along with the memory effect. Here, stability analysis and the existence and uniqueness of the non-negative and bounded solution of our model are explored. The basic reproduction number $$R_0$$ is calculated using the next-generation matrix method. Depending on the value of $$R_0$$, only one endemic equilibrium occurs and is stable for $$R_0>1$$. In addition, it is found that the system encounters a transcritical bifurcation at $$R_0=1$$. Here, the optimal treatment and vaccination are determined using the fractional-order optimal control. The findings are also displayed and corroborated by replicating the model with certain hypothetical parameter values, and it can be concluded that fractional order produces better outcomes when the sickness persists in the population. To determine how sensitive the parameters are to $$R_0$$ and the state variables, we do local and global sensitivity analysis. Sensitivity analysis reveals that by reducing the rates of new recruitment and disease transmission, we might be able to lower the value of $$R_0$$. We might be able to retain more susceptibles in the susceptible class by increasing media literacy as well

An ANFIS model-based approach to investigate the effect of lockdown due to COVID-19 on public health

During the first and second quarters of the year 2020, most of the countries had implemented complete or partial lockdown policies to slow down the transmission of the COVID-19. To cultivate the effect of lockdown due to COVID-19 on public health, we have collected the data of six primary parameters, namely systolic blood pressure, diastolic blood pressure, fasting blood sugar, insomnia, cholesterol, and respiratory distress of 200 randomly chosen people from a municipality region of West Bengal, India before and after lockdown. With the help of these data and Adaptive Neuro-Fuzzy Inference System (ANFIS), we have formulated a model that has established that lockdown due to COVID-19 has negligible impacts on the individuals with better health condition but has significant effects on the health conditions to those populations who have poor health