Mathematical assessment of the dynamics of novel coronavirus infection with treatment: A fractional study.

In this paper, a mathematical model is formulated to study the transmission dynamics of the novel coronavirus infection under the effect of treatment. The compartmental model is firstly formulated using a system of nonlinear ordinary differential equations. Then, with the help of Caputo operator, the model is reformulated in order to obtain deeper insights into disease dynamics. The basic mathematical features of the time fractional model are rigorously presented. The nonlinear least square procedure is implemented in order to parameterize the model using COVID-19 cumulative cases in Saudi Arabia for the selected time period. The important threshold parameter called the basic reproduction number is evaluated based on the estimated parameters and is found R 0 ≈ 1.60 . The fractional Lyapunov approach is used to prove the global stability of the model around the disease free equilibrium point. Moreover, the model in Caputo sense is solved numerically via an efficient numerical scheme known as the fractional Adamas-Bashforth-Molten approach. Finally, the model is simulated to present the graphical impact of memory index and various intervention strategies such as social-distancing, disinfection of the virus from environment and treatment rate on the pandemic peaks. This study emphasizes the important role of various scenarios in these intervention strategies in curtailing the burden of COVID-19.

A numerical study of spatio-temporal COVID-19 vaccine model via finite-difference operator-splitting and meshless techniques.

In this paper, a new spatio-temporal model is formulated to study the spread of coronavirus infection (COVID-19) in a spatially heterogeneous environment with the impact of vaccination. Initially, a detailed qualitative analysis of the spatio-temporal model is presented. The existence, uniqueness, positivity, and boundedness of the model solution are investigated. Local asymptotical stability of the diffusive COVID-19 model at steady state is carried out using well-known criteria. Moreover, a suitable nonlinear Lyapunov functional is constructed for the global asymptotical stability of the spatio-temporal model. Further, the model is solved numerically based on uniform and non-uniform initial conditions. Two different numerical schemes named: finite difference operator-splitting and mesh-free operator-splitting based on multi-quadratic radial basis functions are implemented in the numerical study. The impact of diffusion as well as some pharmaceutical and non-pharmaceutical control measures, i.e., reducing an effective contact causing infection transmission, vaccination rate and vaccine waning rate on the disease dynamics is presented in a spatially heterogeneous environment. Furthermore, the impact of the  aforementioned interventions is investigated with and without diffusion on the incidence of disease. The simulation results conclude that the random motion of individuals has a significant impact on the disease dynamics and helps in setting a better control strategy for disease eradication.

Mathematical assessment of monkeypox disease with the impact of vaccination using a fractional epidemiological modeling approach.

This present paper aims to examine various epidemiological aspects of the monkeypox viral infection using a fractional-order mathematical model. Initially, the model is formulated using integer-order nonlinear differential equations. The imperfect vaccination is considered for human population in the model formulation. The proposed model is then reformulated using a fractional order derivative with power law to gain a deeper understanding of disease dynamics. The values of the model parameters are determined from the cumulative reported monkeypox cases in the United States during the period from May 10th to October 10th, 2022. Besides this, some of the demographic parameters are evaluated from the population of the literature. We establish sufficient conditions to ensure the existence and uniqueness of the model's solution in the fractional case. Furthermore, the stability of the endemic equilibrium of the fractional monkeypox model is presented. The Lyapunov function approach is used to demonstrate the global stability of the model equilibria. Moreover, the fractional order model is numerically solved using an efficient numerical technique known as the fractional Adams-Bashforth-Moulton method. The numerical simulations are conducted using estimated parameters, considering various values of the fractional order of the Caputo derivative. The finding of this study reveals the impact of various model parameters and fractional order values on the dynamics and control of monkeypox.

Oscillation result for half-linear delay difference equations of second-order.

In this paper, we obtain the new single-condition criteria for the oscillation of second-order half-linear delay difference equation. Even in the linear case, the sharp result is new and, to our knowledge, improves all previous results. Furthermore, our method has the advantage of being simple to prove, as it relies just on sequentially improved monotonicities of a positive solution. Examples are provided to illustrate our results.

Modified SIR model for COVID-19 transmission dynamics: Simulation with case study of UK, US and India.

Corona virus disease 2019 (COVID-19) is an infectious disease and has spread over more than 200 countries since its outbreak in December 2019. This pandemic has posed the greatest threat to global public health and seems to have changing characteristics with altering variants, hence various epidemiological and statistical models are getting developed to predict the infection spread, mortality rate and calibrating various impacting factors. But the aysmptomatic patient counts and demographical factors needs to be considered in model evaluation. Here we have proposed a new seven compartmental model, Susceptible- Exposed- Infected-Asymptomatic-Quarantined-Fatal-Recovered (SEIAQFR) which is based on classical Susceptible-Infected-Recovered (SIR) model dynamic of infectious disease, and considered factors like asymptomatic transmission and quarantine of patients. We have taken UK, US and India as a case study for model evaluation purpose. In our analysis, it is found that the Reproductive Rate ( R 0 ) of the disease is dynamic over a long period and provides better results in model performance ( > 0 . 98 R-square score) when model is fitted across smaller time period. On an average 40 % - 50 % cases are asymptomatic and have contributed to model accuracy. The model is employed to show accuracy in correspondence with different geographic data in both wave of disease spread. Different disease spreading factors like infection rate, recovery rate and mortality rate are well analyzed with best fit of real world data. Performance evaluation of this model has achieved good R-Square score which is 0 . 95 - 0 . 99 for infection prediction and 0 . 90 - 0 . 99 for death prediction and an average 1 % - 5 % MAPE in different wave of the disease in UK, US and India.