ABSTRACT
Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is a novel respiratory virus that causes coronavirus disease 2019 (COVID-19). Symptoms of COVID-19 range from mild to severe illness. It was observed that disease progression in COVID-19 patients depends on their immune response, especially in elderly patients whose immune system suppression may put them at increased risk of infection. Human T-cell lymphotropic virus type-I (HTLV-I) attacks the CD4+ T cells (T cells) of the immune system and leads to immune dysfunction. Co-infection with HTLV-I and SARS-CoV-2 has been reported in recent studies. Modeling HTLV-I and SARS-CoV-2 co-infection can be a helpful tool to understand the in-host co-dynamics of these viruses. The aim of this study was to construct a model that characterizes the in-host dynamics of HTLV-I and SARS-CoV-2 co-infection. By considering the mobility of the viruses and cells, the model is represented by a system of partial differential equations (PDEs). The system contains two independent variables, time t and position x, and seven dependent variables for representing the densities of healthy epithelial cells (ECs), latent SARS-CoV-2-infected ECs, active SARS-CoV-2-infected ECs, SARS-CoV-2, healthy T cells, latent HTLV-I-infected T cells and active HTLV-I-infected T cells. We first studied the fundamental properties of the solutions of the system, then deduced all steady states and proved their global properties. We examined the global stability of the steady states by constructing appropriate Lyapunov functions. The analytical results were illustrated by performing numerical simulations. We discussed the effect of HTLV-I infection on COVID-19 progression. The results suggest that patients with HTLV-I have a weakened immune response;consequently, their risk of COVID-19 infection may be increased.
ABSTRACT
A severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection can lead to morbidity and mortality. SARS-CoV-2 infects the epithelial cells of the respiratory tract and causes coronavirus disease 2019 (COVID-19). The immune system's response plays a significant role in viral progression. This article develops and analyzes a system of partial differential equations (PDEs), which describe the in-host dynamics of SARS-CoV-2 under the effect of cytotoxic T-lymphocyte (CTL) and antibody immune responses. The model characterizes the interplay between six compartments, healthy epithelial cells (ECs), latent infected ECs, active infected ECs, free SARS-CoV-2 particles, CTLs, and antibodies. We consider the logistic growth of healthy ECs. We first investigate the properties of the model's solutions, then, we calculate all steady states and determine the conditions of their existence and global stability. The global asymptotic stability is examined by constructing Lyapunov functions. The analytical findings are supported via numerical simulations.
ABSTRACT
The virus which belongs to the family of the coronavirus was seen first in Wuhan city of China. As it spreads so quickly and fastly, now all over countries in the world are suffering from this. The world health organization has considered and declared it a pandemic. In this presented research, we have picked up the existing mathematical model of corona virus which has six ordinary differential equations involving fractional derivative with non-singular kernel and Mittag-Leffler law. Another new thing is that we study this model in a fuzzy environment. We will discuss why we need a fuzzy environment for this model. First of all, we find out the approximate value of ABC fractional derivative of simple polynomial function ( t - a ) n . By using this approximation we will derive and developed the Legendre operational matrix of fractional differentiation for the Mittag-Leffler kernel fractional derivative on a larger interval [ 0 , b ] , b ⩾ 1 , b ∈ N . For the numerical investigation of the fuzzy mathematical model, we use the collocation method with the addition of this newly developed operational matrix. For the feasibility and validity of our method we pick up a particular case of our model and plot the graph between the exact and numerical solutions. We see that our results have good accuracy and our method is valid for the fuzzy system of fractional ODEs. We depict the dynamics of infected, susceptible, exposed, and asymptotically infected people for the different integer and fractional orders in a fuzzy environment. We show the effect of fractional order on the suspected, exposed, infected, and asymptotic carrier by plotting graphs.