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The coronavirus disease 2019 (COVID-19) is a respiratory disease that appeared in 2019 caused by a virus called severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). COVID-19 is still spreading and causing deaths around the world. There is a real concern of SARS-CoV-2 coinfection with other infectious diseases. Tuberculosis (TB) is a bacterial disease caused by Mycobacterium tuberculosis (Mtb). SARS-CoV-2 coinfection with TB has been recorded in many countries. It has been suggested that the coinfection is associated with severe disease and death. Mathematical modeling is an effective tool that can help understand the dynamics of coinfection between new diseases and well-known diseases. In this paper, we develop an in-host TB and SARS-CoV-2 coinfection model with cytotoxic T lymphocytes (CTLs). The model investigates the interactions between healthy epithelial cells (ECs), latent Mtb-infected ECs, active Mtb-infected ECs, SARS-CoV-2-infected ECs, free Mtb, free SARS-CoV-2, and CTLs. The model’s solutions are proved to be nonnegative and bounded. All equilibria with their existence conditions are calculated. Proper Lyapunov functions are selected to examine the global stability of equilibria. Numerical simulations are implemented to verify the theoretical results. It is found that the model has six equilibrium points. These points reflect two states: the mono-infection state where SARS-CoV-2 or TB occurs as a single infection, and the coinfection state where the two infections occur simultaneously. The parameters that control the movement between these states should be tested in order to develop better treatments for TB and COVID-19 coinfected patients. Lymphopenia increases the concentration of SARS-CoV-2 particles and thus can worsen the health status of the coinfected patient.

The world has been suffering from the coronavirus disease 2019 (COVID-19) since late 2019. COVID-19 is caused by a virus called the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). The human immunodeficiency virus (HIV) coinfection with SARS-CoV-2 has been reported in many patients around the world. This has raised the alarm for the importance of understanding the dynamics of coinfection and its impact on the lives of patients. As in other pandemics, mathematical modeling is one of the important tools that can help medical and experimental studies of COVID-19. In this paper, we develop a within-host SARS-CoV-2/HIV coinfection model. The model consists of six ordinary differential equations. It depicts the interactions between uninfected epithelial cells, infected epithelial cells, free SARS-CoV-2 particles, uninfected CD4

Coronavirus disease 2019 (COVID-19) is a new respiratory disease caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). It started in China and spread quickly to all continents. This virus has changed the life style and the education system in many countries. As for other viruses, mathematical models have been rated as a useful tool to support the research on COVID-19. In this work, we develop a reaction–diffusion model to describe the within-host dynamics of SARS-CoV-2 in cancer patients. This model studies the interactions between nutrient, healthy epithelial cells, cancer cells, SARS-CoV-2 particles, and immune cells. The model incorporates the spatial mobility of the cells and viruses. The model includes parameters for measuring the effect of lymphopenia on SARS-CoV-2/cancer patients. We verify the basic features of the model’s solutions including the uniqueness, nonnegativity and boundedness. We list all equilibrium points of the proposed model. We show the global stability and the local instability of the most meaningful equilibria. We display some numerical simulations to enhance our theoretical results. The results indicate that diffusion can have a clear effect at the beginning of SARS-CoV-2 infection. Lymphopenia in SARS-CoV-2/cancer patients impairs the immune responses against cancer and SARS-CoV-2, and worsens the health state of patients.

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Oncolytic virotherapy (OVT) is a promising treatment for cancer which can replace or support the traditional treatments like chemotherapy and radiotherapy. Mathematical models have been considered as a powerful tool to develop oncolytic viral treatments and predict the possible outcomes. We study a spatial model for OVT with cytotoxic T lymphocyte immune response and distributed delays. This model is an extended version of the model studied by Wang et al. (Math Biosci 276:19–27, 2016). We study the basic properties of the model including the existence, nonnegativity, and boundedness of solutions. We carefully analyze all equilibrium points and determine the conditions for their existence. We show the global stability of each one of these points by constructing suitable Lyapunov functionals. We use the characteristic equations to confirm the corresponding instability conditions. We carry out some numerical simulations to support the theoretical results and draw some important conclusions. The results show that the distributed delay can have a large impact on the efficacy and amount of OVT. When the immune response is present, the concentration of oncolytic viruses is decreased and the efficiency of treatment is reduced. Changing the diffusion coefficients does not affect the long-time behavior of solutions.

Oncolytic virotherapy (OVT) is a promising therapeutic approach that uses replication-competent viruses to target and kill tumor cells. Alphavirus M1 is a selective oncolytic virus which showed high efficacy against tumor cells. Wang et al. (2016) studied an ordinary differential equation (ODE) model to verify the potent efficacy of M1 virus. Our purpose is to extend their model to include the effect of time delays and anti-tumor immune response. Also, we assume that all elements of the extended model undergo diffusion in a bounded domain. We study the existence, non-negativity and boundedness of solutions in order to verify the well-posedness of the model. We calculate all possible equilibrium points and determine the threshold conditions required for their existence and stability. These points reflect three different fates for OVT: partial success, complete success, or complete failure. We prove the global asymptotic stability of all equilibrium points by constructing suitable Lyapunov functionals, and verify the corresponding instability conditions. We conduct some numerical simulations to confirm the analytical results and show the crucial role of time delays and immune response in the success of OVT.

Antioxidants have numerous applications due to their multiple roles in diminishing harmful effects of oxidative stress. The objective of this work was to highlight the importance of green tea by evaluating the antioxidant activity of the most popular green tea brands in Saudi Arabia, Lipton and Rabea. To our knowledge, no studies have so far been done to estimate the antioxidant activity of these brands. To determine the antioxidant activities of these two brands, 10 mg/ml of each brand was extracted and their total phenolic content (TPC), 2,2-diphenyl-1-picrylhydrazyl (DPPH) radical scavenging activity, hydrogen peroxide scavenging activity, ferric reducing power and ferrous ion chelating effect were measured. The TPC of Lipton tea was 678.7 υg of gallic acid equivalents (GAE)/10mg, whereas in Rabea tea, the TPC was 647.1 υg GAE/10mg. The presence study indicated that there were no significant differences in total phenolic contents and the percentage inhibition as shown in DPPH and H2O2 assays among Lipton and Rabea green teas. Moreover, it was found that all assays have exhibited high antioxidant activity in both green teas. In conclusion, our study showed evidence for evenness and stability of the antioxidant activity of the two commercial green teas available in the markets of Saudi Arabia. Continued researches are needed to further the current knowledge on the health-promoting effects of this popular beverage using different supplements by different mechanisms.

Malaria is one of the most dangerous diseases that threatens people’s lives around the world. In this paper, we study a reaction-diffusion model for the within-host dynamics of malaria infection with an antibody immune response. The model is given by a system of partial differential equations (PDEs) to describe the blood-stage of malaria life cycle. It addresses the interactions between uninfected red blood cells, antibodies, and three types of infected red blood cells, namely ring-infected red blood cells, trophozoite-infected red blood cells and schizont-infected red blood cells. Moreover, the model contains a parameter to measure the efficacy of isoleucine starvation and its effect on the growth of malaria parasites. We show the basic properties of the model. We compute all equilibria and derive the thresholds from the conditions of existence of malaria equilibrium points. We prove the global stability of all equilibrium points based on choosing suitable Lyapunov functionals. We use the characteristic equations to verify the local instability of equilibrium points. We finally execute numerical simulations to validate the theoretical results and highlight some important observations. The results indicate that isoleucine starvation can have a critical impact on the stability of equilibrium points. When the efficacy of isoleucine starvation is high, it switches the system from the infection state to the malaria-free state. The presence of an antibody immune response does not lead to the elimination of malaria infection, but it suppresses the growth of malaria parasites and increases the amount of healthy red blood cells.

Oncolytic virotherapy is a promising cancer treatment that uses replication-competent viruses to target and kill tumor cells. Oncolytic alphavirus M1 is a naturally occurring virus which showed high selectivity and potent efficacy in human cancers. Our purpose in this paper is to propose and analyze a model of oncolytic M1 virotherapy with spatial effects and anti-tumor immune response. We investigate the non-negativity and boundedness of solutions for the modified model. We calculate all possible equilibrium points and determine the threshold conditions needed for their existence. One of the equilibria represents the success of the treatment, while the others represent a partial success or a complete fail. We study the global stability of the corresponding equilibrium points by constructing suitable Lyapunov functionals. We also provide the instability conditions of the equilibrium points. We perform some numerical simulations in order to verify the effect of the immune response on oncolytic virotherapy. Our results indicate that the immune response may weaken the effectiveness of oncolytic virotherapy and control the tumor.