In the present paper, we introduced a quadratically convergent Newton’s like normal S2 iteration method free from the second derivative for the solution of nonlinear equations permitting 3 f'(x) = 0 at some points in the neighborhood of the root. Our proposed method works well 4 when the Newton method fails. Numerically it has been verified that the Newton’s like normal 5 S-iteration method converges faster than Fang et al. method [A cubically convergent Newton-type 6 method under weak conditions, J. Compute. and Appl. Math., 220 (2008), 409-412]. We studied 7 different aspects of normal S-iteration method. Lastly, fractal patterns support the numerical 8 results and explain the convergence, divergence, and stability of method.

Background: Comorbidities have been frequently reported in COVID-19 patients, which often lead to more severe outcomes. The underlying molecular mechanisms behind these clinical observations have not yet been explained. Herein, we investigated the disease-specific gene expression signatures that may induce susceptibility to SARS-CoV-2 infection. Methods: We studied 30 frequently occurring acute, chronic, or infectious diseases of recent times that have shown comorbidity in one or another respiratory disease(s) caused by pathogenic human infecting coronaviruses, especially SARS-CoV-2. We retrieved array-based gene expression data for each disease and control from relevant datasets. Subsequently, all the datasets were quantile normalized, and log-2 transformed data was used for analysis. Results The expression of ACE2 receptor and host proteases, namely FURIN and TMPRSS2 that are essential for cellular entry of SARS-CoV-2, was upregulated in all six studied subtypes of leukemia (hereafter, referred as leukemia). The expression of ACE2 was also increased in psoriasis, lung cancer, Non-alcoholic fatty liver disease (NAFLD), breast cancer, and pulmonary arterial hypertension patients. The expression of FURIN was higher in psoriasis, NAFLD, lung cancer, and in type II diabetic liver, whereas it was lowered in breast cancer. Similarly, the expression of TMPRSS2 was increased during lung cancer and type II diabetes; it was decreased during psoriasis, NAFLD, lung cancer, breast cancer, and cervical cancer.Furthermore, a heightened expression of genes that are involved in immune response was observed in leukemia patients, as shown by the higher expression of IFNA2, IFNA8, IFNA10, IFNA14, IFNA16, IFNA21, IFNB1, CXCL10, and IL6. The expression of JAK1, STAT1, IL6, and CXCL10 was higher in NAFLD. Besides, JAK1 and STAT1 were upregulated in type II diabetic muscles. In addition, most of the upregulated genes in COVID-19 patients showed a similar trend in leukemia, NAFLD, and psoriasis. Furthermore, SARS-CoV-2, SARS-CoV and MERS CoV, were found to commonly alter two genes, namely, CARBONIC ANHYDRASE 11 and CLUSTERIN.Conclusions: The genes that may confer susceptibility to SARS-CoV-2 infection are mostly upregulated in leukemia patients; hence, leukemia patients are relatively more susceptible to develop COVID-19, followed by other chronic disorders, such as, NAFLD, type II diabetes, psoriasis, and hypertension. This study identifies key genes that are altered in the studied diseases types, which may aid in the infection of SARS-CoV-2 and underlie COVID-19 associated comorbidities.