Dynamical Analysis of Secondary Dengue Viral Infection with Multiple Target Cells and Diffusion by Mathematical Model

Dengue is an epidemic disease rapidly spreading throughout many parts of the world, which is a serious public health concern. Understanding disease mechanisms through mathematical modeling is one of the most effective tools for this purpose. The aim of this manuscript is to develop and analyze a dynamical system of PDEs that describes the secondary infection caused by DENV, considering (i) the diffusion due to spatial mobility of cells and DENV particles, (ii) the interactions between multiple target cells, DENV, and antibodies of two types (heterologous and homologous). Global existence, positivity, and boundedness are proved for the system with homogeneous Neumann boundary conditions. Three threshold parameters are computed to characterize the existence and stability conditions of the model’s four steady states. Via means of Lyapunov functional, the global stability of all steady states is carried out. Our results show that the uninfected steady state is globally asymptotically stable if the basic reproduction number is less than or equal to unity, which leads to the disappearance of the disease from the body. When the basic reproduction number is greater than unity, the disease persists in the body with an active or inactive immune antibody response. To demonstrate such theoretical results, numerical simulations are presented

Lévy impact on the transmission of worms in wireless sensor network: Stochastic analysis

This manuscript addresses the security challenges wireless sensor networks (WSNs) face due to their operational limitations. The primary challenge stems from the infiltration of worms into the network, where one infected node could uncontrollably propagate the malware to neighboring node(s). First, we proposes a stochastic system based on Lévy noise to explain the spread of worms in WSNs. Then, we establish a unique positive global solution for the proposed model. We also examine the presence and potential extinction of worms within the networks. The results reveal that random environmental perturbations can confine the spread of worms and that the deterministic model tends to overestimate the worms’ spreading capacity. Using different parameter sets, the study obtains approximate solutions to validate these analytical findings and demonstrate the effectiveness of the suggested SEIRS system. The findings of the work reveal that the proposed model surpasses existing models in mitigating worm transmission in WSNs. Our inference suggests that the transmission dynamics of the system are influenced by both white noise and Lévy noise

Global stability of secondary DENV infection models with non-specific and strain-specific CTLs

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 EQ0 and the infected equilibrium EQ⁎. Furthermore, we calculate the basic reproduction number R0, 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 R0≤1, then EQ0 is globally asymptotically stable (G.A.S), and if R0>1, then EQ0 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 R0 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 R0 and enhances the system's stability around EQ0

Numerical Approach for Solving a Fractional-Order Norovirus Epidemic Model with Vaccination and Asymptomatic Carriers

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

Global Properties of Latent Virus Dynamics Models with Immune Impairment and Two Routes of Infection

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

Exploring the effectiveness of control measures and long-term behavior in Hepatitis B: An analysis of an endemic model with horizontal and vertical transmission

This study presents an optimal control and stability analysis of a mathematical model for the spread of Hepatitis B with a harmonic mean type incidence rate, providing insights into the effectiveness of control measures and the long-term behavior of the disease dynamics. The hepatitis B virus causes hepatitis B infection. It is one of the most serious viral infections out there, as well as a global health issue. Various stages, such as chronic and acute carrier stages, serve an essential role in the transition of hepatitis B infection. Chronic disease is characterized by the presence of individuals who do not show any symptoms but are nevertheless able to spread the illness. In this study, we focused on the infectiousness of hepatitis B at different stages of illness and created an endemic model by means of a nonlinear occurrence rate. To accomplish so, we start by dividing the infectious group into two further sub-classes: i.e., acute infected and chronic carriers, both of which can transmit horizontally and vertically. The suggested model’s basic characteristics are provided. The method of the next-generation matrix is utilized to compute the basic reproduction number. The biological significance of the threshold state is thoroughly researched and addressed. We also discover the criteria for investigating all of the model’s potential equilibria in terms of the fundamental reproduction number. Finally, to supplement our analytical work, we do the numerical estimation

Optimal control of a spatiotemporal SIR model with reaction–diffusion involving p-Laplacian operator

The present paper’s primary goal is to make an analysis and study a reaction–diffusion SIR epidemic mathematical model expressed as a parabolic system of partial differential equations using the p-Laplacian operator. Immunity is compelled through vaccination distribution, which is seen as a control variable. Our main goal is to define an optimal control, which reduces the spread of infection and the cost of vaccination over a limited period of time and space. Existence and uniqueness of a positive solution and existence of an optimal control for the proposed model are proved. Then a description and characterization of the optimal control is provided in terms of state and adjoint functions. Optimality system is numerically resolved by a discrete iterative scheme pertained to and the forward–backward algorithm. Furthermore, using various p-values for the p-Laplacian operator, numerical results demonstrate the effectiveness of the suggested control strategy, which yields meaningful outcomes

The Optimal Strategies to Be Adopted in Controlling the Co-Circulation of COVID-19, Dengue and HIV: Insight from a Mathematical Model

The pandemic caused by COVID-19 led to serious disruptions in the preventive efforts against other infectious diseases. In this work, a robust mathematical co-dynamical model of COVID-19, dengue, and HIV is designed. Rigorous analyses for investigating the dynamical properties of the designed model are implemented. Under a special case, the stability of the model’s equilibria is demonstrated using well-known candidates for the Lyapunov function. To reduce the co-circulation of the three diseases, optimal interventions were defined for the model and the control system was analyzed. Simulations of the model showed different control scenarios, which could have a positive or detrimental impact on reducing the co-circulation of the diseases. Highlights of the simulations included: (i) Upon implementation of the first intervention strategy (control against COVID-19 and dengue), it was observed that a significant number of single and dual infection cases were averted. (ii) Under the COVID-19 and HIV prevention strategy, a remarkable number of new single and dual infection cases were also prevented. (iii) Under the COVID-19 and co-infection prevention strategy, a significant number of new infections were averted. (iv) Comparing all the intervention measures considered in this study, it is possible to state that the strategy that combined COVID-19/HIV averted the highest number of new infections. Thus, the COVID-19/HIV strategy would be the ideal and optimal strategy to adopt in controlling the co-spread of COVID-19, dengue, and HIV

Global Dynamics of a Within-Host COVID-19/AIDS Coinfection Model with Distributed Delays

Acquired immunodeficiency syndrome (AIDS) is a spectrum of conditions caused by infection with the human immunodeficiency virus (HIV). Among people with AIDS, cases of COVID-19 have been reported in many countries. COVID-19 (coronavirus disease 2019) is caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). In this manuscript, we are going to present a within-host COVID-19/AIDS coinfection model to study the dynamics and influence of the coinfection between COVID-19 and AIDS. The model is a six-dimensional delay differential equation that describes the interaction between uninfected epithelial cells, infected epithelial cells, free SARS-CoV-2 particles, uninfected CD4+ T cells, infected CD4+ T cells, and free HIV-1 particles. We demonstrated that the proposed model is biologically acceptable by proving the positivity and boundedness of the model solutions. The global stability analysis of the model is carried out in terms of the basic reproduction number. Numerical simulations are carried out to investigate that if COVID-19/AIDS coinfected individuals have a poor immune response or a low number of CD4+ T cells, then the viral load of SARS-CoV-2 and the number of infected epithelial cells will rise. On the contrary, the existence of time delays can rise the number of uninfected CD4+ T cells and uninfected epithelial cells, thus reducing the viral load within the host

Effect of Macrophages and Latent Reservoirs on the Dynamics of HTLV-I and HIV-1 Coinfection

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