Aeshah A. Raezah

This paper presents two viral infection models that describe dynamics of the virus under the effect of two distinct types of antibodies. The first model considers the population of five compartments, target cells, infected cells, free virus particles, antibodies type-1 and antibodies type-2. The presence of two types of antibodies can be a result of secondary viral infection. In the second model, we incorporate the latently infected cells. We assume that the antibody responsiveness is given by a combination of the self-regulating antibody response and the predator–prey-like antibody response. For both models, we verify the nonnegativity and boundedness of their solutions, then we outline all possible equilibria and prove the global stability by constructing proper Lyapunov functions. The stability of the uninfected equilibrium EQ0 and infected equilibrium EQ* is determined by the basic reproduction number R0. The theoretical findings are verified through numerical simulations. According to the outcomes, the trajectories of the solutions approach EQ0 and EQ* when R0≤1 and R0>1, respectively. We study the sensitivity analysis to show how the values of all the parameters of the suggested model affect R0 under the given data. The impact of including the self-regulating antibody response and latently infected cells in the viral infection model is discussed. We showed that the presence of the self-regulating antibody response reduces R0 and makes the system more stabilizable around EQ0. Moreover, we established that neglecting the latently infected cells in the viral infection modeling leads to the design of an overflow of antiviral drug therapy.

The modeling of biological processes has increasingly been based on fractional calculus. In this paper, a novel fractional-order model is used to investigate the epidemiological impact of vaccination measures on the co-dynamics of viral hepatitis B and COVID-19. To investigate the existence and stability of the new model, we use some fixed point theory results. The COVID-19 and viral hepatitis B thresholds are estimated using the model fitting. The vaccine parameters are plotted against transmission coefficients. The effect of non-integer derivatives on the solution paths for each epidemiological state and the trajectory diagram for infected classes are also examined numerically. An infection-free steady state and an infection-present equilibrium are achieved when R0<1 and R0>1, respectively. Similarly, phase portraits confirm the behaviour of the infected components, showing that, regardless of the order of the fractional derivative, the trajectories of the disease classes always converge toward infection-free steady states over time, no matter what initial conditions are assumed for the diseases. The model has been verified using real observations.

This paper explored the impact of population symmetry on the spread and control of a norovirus epidemic. The study proposed a mathematical model for the norovirus epidemic that takes into account asymptomatic infected individuals and vaccination effects using a non-singular fractional operator of Atanganaa–Baleanu Caputo (ABC). Fixed point theory, specifically Schauder and Banach’s fixed point theory, was used to investigate the existence and uniqueness of solutions for the proposed model. The study employed MATLAB software to generate simulation results and demonstrate the effectiveness of the fractional order q. A general numerical algorithm based on Adams–Bashforth and Newton’s Polynomial method was developed to approximate the solution. Furthermore, the stability of the proposed model was analyzed using Ulam–Hyers stability techniques. The basic reproductive number was calculated with the help of next-generation matrix techniques. The sensitivity analysis of the model parameters was performed to test which parameter is the most sensitive for the epidemic. The values of the parameters were estimated with the help of least square curve fitting tools. The results of the study provide valuable insights into the behavior of the proposed model and demonstrate the potential applications of fractional calculus in solving complex problems related to disease transmission.

Human immunodeficiency virus type 1 (HIV-1) and human T-lymphotropic virus type I (HTLV-I) are two retroviruses that have a similar fashion of transmission via sharp objects contaminated by viruses, transplant surgery, transfusion, and sexual relations. Simultaneous infections with HTLV-I and HIV-1 usually occur in areas where both viruses have become endemic. CD4+T cells are the main targets of HTLV-I, while HIV-1 can infect CD4+T cells and macrophages. It is the aim of this study to develop a model of HTLV-I and HIV-1 coinfection that describes the interactions of nine compartments: susceptible cells of both CD4+T cells and macrophages, HIV-1-infected cells that are latent/active in both CD4+T cells and macrophages, HTLV-I-infected CD4+T cells that are latent/active, and free HIV-1 particles. The well-posedness, existence of equilibria, and global stability analysis of our model are investigated. The Lyapunov function and LaSalle’s invariance principle were used to study the global asymptotic stability of all equilibria. The theoretically predicted outcomes were verified by utilizing numerical simulations. The effect of including the macrophages and latent reservoirs in the HTLV-I and HIV-1 coinfection model is discussed. We show that the presence of macrophages makes a coinfection model more realistic when the case of the coexistence of HIV-1 and HTLV-I is established. Moreover, we have shown that neglecting the latent reservoirs in HTLV-I and HIV-1 coinfection modeling will lead to the design of an overflow of anti-HIV-1 drugs.