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Dengue virus (DENV) is a highly perilous virus that is transmitted to humans through mosquito bites and causes dengue fever. Consequently, extensive efforts are being made to develop effective treatments and vaccines. Mathematical modeling plays a significant role in comprehending the dynamics of DENV within a host in the presence of cytotoxic T lymphocytes (CTL) immune response. This study examines two models for secondary DENV infections that elucidate the dynamics of DENV under the influence of two types of CTL responses, namely non-specific and strain-specific responses. The first model encompasses five compartments, which consist of uninfected monocytes, infected monocytes, free DENV particles, non-specific CTLs, and strain-specific CTLs. In the second model, latently infected cells are introduced into the model. We posit that the CTL responsiveness is determined by a combination of self-regulating CTL response and a predator-prey-like CTL response. The model's solutions are verified to be nonnegativity and bounded and the model possesses two equilibrium states: the uninfected equilibrium EQ 0 and the infected equilibrium EQ ⁎ . Furthermore, we calculate the basic reproduction number R 0 , which determines the existence and stability of the model's equilibria. We examine the global stability by constructing suitable Lyapunov functions. Our analysis reveals that if R 0 ≤ 1 , then EQ 0 is globally asymptotically stable (G.A.S), and if R 0 > 1 , then EQ 0 is unstable while EQ ⁎ is G.A.S. To illustrate our findings analytically, we conduct numerical simulations for each model. Additionally, we perform sensitivity analysis to demonstrate how the parameter values of the proposed model impact R 0 given a set of data. Finally, we discuss the implications of including the CTL immune response and latently infected cells in the secondary DENV infection model. Our study demonstrates that incorporating the CTL immune response and latently infected cells diminishes R 0 and enhances the system's stability around EQ 0 ., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2024 The Author(s).)

This study explores the use of numerical simulations to model the spread of the Omicron variant of the SARS-CoV-2 virus using fractional-order COVID-19 models and Haar wavelet collocation methods. The fractional order COVID-19 model considers various factors that affect the virus's transmission, and the Haar wavelet collocation method offers a precise and efficient solution to the fractional derivatives used in the model. The simulation results yield crucial insights into the Omicron variant's spread, providing valuable information to public health policies and strategies designed to mitigate its impact. This study marks a significant advancement in comprehending the COVID-19 pandemic's dynamics and the emergence of its variants. The COVID-19 epidemic model is reworked utilizing fractional derivatives in the Caputo sense, and the model's existence and uniqueness are established by considering fixed point theory results. Sensitivity analysis is conducted on the model to identify the parameter with the highest sensitivity. For numerical treatment and simulations, we apply the Haar wavelet collocation method. Parameter estimation for the recorded COVID-19 cases in India from 13 July 2021 to 25 August 2021 has been presented.

This paper studies the global stability of viral infection models with CTL immune impairment. We incorporate both productively and latently infected cells. The models integrate two routes of transmission, cell-to-cell and virus-to-cell. In the second model, saturated virus-cell and cell-cell incidence rates are considered. The basic reproduction number is derived and two steady states are calculated. We first establish the nonnegativity and boundedness of the solutions of the system, then we investigate the global stability of the steady states. We utilize the Lyapunov method to prove the global stability of the two steady states. We support our theorems by numerical simulations.