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Accumulating evidence suggests anti-TNF therapy needs to be given trial priority in COVID-19 treatment https://www.thelancet.com/.../PIIS2665-9913(20.../fulltext An inflammatory cytokine signature predicts COVID-19 severity and survival..We propose that serum IL-6 and TNF-α levels should be considered in the management and treatment of patients with COVID-19 to stratify prospective clinical trials, guide resource allocation and inform therapeutic options. https://www.nature.com/articles/s41591-020-1051-9 Patent, papaya leaf extract as tnf-alpha inhibitor https://patents.google.com/patent/US20140065251

Latest Updated (Added, prospect of Carica Papaya Leaf as Interleukin IL-6 Inhibitor) Papaya leaves extract; a possible weapon against Covid-19 M.S. Shukor1 and M.Y. Shukor2 1Snoc International Sdn Bhd, Lot 343, Jalan 7/16 Kawasan Perindustrian Nilai 7, Inland Port, 71800, Negeri Sembilan, Malaysia. 2Department of Biochemistry, Faculty of Biotechnology and Biomolecular Sciences, Universiti Putra Malaysia, UPM 43400 Serdang, Selangor, Malaysia. Covid-19 is now a pandemic affecting humans at a global scale. Researchers are still trying to find a cure and the vaccine to fight this disease. Drug-based cure and vaccine are overwhelmingly virus-specific and newer drugs and vaccines are needed to resist new novel viral infections. A shift towards herbal remedies to fight viral infections is an approach that can be explored especially in poorer countries or when drugs and vaccines are still not available. One of the top herbal remedies that emerges as a prime weapon for viral infection is Carica papaya, where the leaves extract has been tested in clinical environment in patients infected by the dengue virus. In two studies, platelets, white blood cells and neutrophils counts were back to normal after the administration of papaya leaves aqueous extract and the infected patients recovered (Ahmad et al. 2011; Kumar et al. 2015). Further research has demonstrated that papaya leaf extract decrease dengue complication through another route by inhibiting viral production. A study suggests that papaya leaves extract significantly cause the expression of NS1 and envelope proteins to be lowered in DENV-infected THP-1 cells. A significant lowering of the intracellular viral load supports papaya leaves extract antiviral activity (Sharma et al. 2019). In addition, papaya extracts and papaya-associated phytochemicals possibly enhance recovery in dengue infected patients through their anti-inflammatory and immunomodulatory properties (Pandey et al. 2016). A study shows that nine selected ligands from Carica papaya leaves show good binding to viral proteins from dengue, influenza A (H1N9) and chikungunya (Narayanaswamy et al. 2017). As more and more wonderful properties of papaya leaves extract are reported in the literature, researchers began to use the extracted phytochemicals from the plant to combat other viral infections either in vivo, in vitro or in silico. SARS-CoV-2 is the novel virus that causes Covid-19. It has not benefit from the usage of papaya extract to fight its infection, not yet, but there is a growing body of evidences that suggest its probable usage to combat Covid-19. For a start, the anti-inflammatory and immunomodulatory properties of papaya leaves extract can increase an infected person chance of recovering from the infection. The papaya leaves extract is able to reduce the severity of cytokine storm in dengue infection in mice model (Norahmad et al. 2019). Cytokine storm is one of the most important mechanisms that lead to deaths of Covid-19-infected patients (Chen et al. 2020). Cytokine storm occurs when the lungs of infected patients become severely inflamed due to the massive overproduction of a host of mediators such as interleukins, interferons, tumour necrosis factor, macrophage and other factors which are lumped together as cytokines or chemokines. Cytokine storms often lead to infected cells dying through apoptosis and necrosis leading to severe tissue damage and haemorrhages triggering multiple organ failure (Tetro 2020; Chen et al. 2020; Yao et al. 2020). The inflammation of the lungs in the Covid 19 patient is due to the Interleukin IL-6, Sanofi and Regeneron is running a Clinical trial named Kevzara a fully-human monoclonal antibody to block the Interleukin IL-6 receptors. (Sanofil and Regeneron). Clinical trial on the carica papaya leaf extract (CPLE) on the dengue fever found a decrease of 18% on the Interleukin IL-6 of the treated patients with (CPLE) and an increase of 13% in the placebos subgroup (Dipu T. Sathyapalan et al. 2020). This finding shows that CPLE could be used as an inhibitor candidate for the Interleukin IL-6 in reducing the Covid 19 Cytokine Storm. In another study, patients having virus-induced lung damage were given fermented papaya preparation for one month. The researchers observed an increase in salivary IgA and increase in phase II and SOD enzyme expression levels, which are essential antioxidants in the respiratory tract (Marotta et al. 2012). Consumption of papain leaf extract can probably help in fighting Covid-19 infection, but more studies are needed to support this premise. An important step for a start is the in silico docking behavior of potential ligands from papaya leaves extract to the papain-like Covid-19 protease; one of the main targets of Covid-19 antiviral drug screening strategy (Arya et al. 2020; Zhang et al. 2020). Reference Ahmad N, Fazal H, Ayaz M, Abbasi BH, Mohammad I, Fazal L (2011) Dengue fever treatment with Carica papaya leaves extracts. Asian Pacific Journal of Tropical Biomedicine 1, 330–333. doi:10.1016/S2221-1691(11)60055-5. Arya R, Das A, Prashar V, Kumar M (2020) Potential inhibitors against papain-like protease of novel coronavirus (SARS-CoV-2) from FDA approved drugs. doi:10.26434/chemrxiv.11860011.v2. Chen C, Zhang XR, Ju ZY, He WF (2020) [Advances in the research of cytokine storm mechanism induced by Corona Virus Disease 2019 and the corresponding immunotherapies]. Zhonghua Shao Shang Za Zhi = Zhonghua Shaoshang Zazhi = Chinese Journal of Burns 36, E005. doi:10.3760/cma.j.cn501120-20200224-00088. Kumar DrCVMN, Vadlamudi T, Venkatamuni A, Vardhan V, Prasad Y, Ravi U, D.V.R. S (2015) Therapeutic potential of Carica papaya l. leaf extract in treatment of dengue patients. International Journal of Applied Biology and Pharmaceutical Technology 6, 93–98. Marotta F, Naito Y, Jain S, Lorenzetti A, Soresi V, Kumari A, Carrera Bastos P, Tomella C, Yadav H (2012) Is there a potential application of a fermented nutraceutical in acute respiratory illnesses? An in-vivo placebo-controlled, cross-over clinical study in different age groups of healthy subjects. Journal of Biological Regulators and Homeostatic Agents 26, 285–294. Narayanaswamy R, KW L, ME N (2017) Molecular docking analysis of Carica papaya Linn constituents as antiviral agent. International Food Research Journal 24, 1819–1825. Norahmad NA, Mohd Abd Razak MR, Mohmad Misnan N, Md Jelas NH, Sastu UR, Muhammad A, Ho TCD, Jusoh B, Zolkifli NA, Thayan R, Mat Ripen A, Zainol M, Syed Mohamed AF (2019) Effect of freeze-dried Carica papaya leaf juice on inflammatory cytokines production during dengue virus infection in AG129 mice. BMC Complementary and Alternative Medicine 19,. doi:10.1186/s12906-019-2438-3. Pandey S, Cabot PJ, Shaw PN, Hewavitharana AK (2016) Anti-inflammatory and immunomodulatory properties of Carica papaya. Journal of Immunotoxicology 13, 590–602. doi:10.3109/1547691X.2016.1149528. Sanofi & Regeneron https://www.pharmaceutical-technology.com/news/sanofi-regeneron-kevzara-covid-19/ Sharma N, Mishra KP, Chanda S, Bhardwaj V, Tanwar H, Ganju L, Kumar B, Singh SB (2019) Evaluation of anti-dengue activity of Carica papaya aqueous leaf extract and its role in platelet augmentation. Archives of Virology 164, 1095–1110. doi:10.1007/s00705-019-04179-z. Tetro JA (2020) Is COVID-19 receiving ADE from other coronaviruses? Microbes and Infection. doi:10.1016/j.micinf.2020.02.006. Yao X, Ye F, Zhang M, Cui C, Huang B, Niu P, Liu X, Zhao L, Dong E, Song C, Zhan S, Lu R, Li H, Tan W, Liu D (2020) In Vitro Antiviral Activity and Projection of Optimized Dosing Design of Hydroxychloroquine for the Treatment of Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2). Clinical Infectious Diseases: An Official Publication of the Infectious Diseases Society of America. doi:10.1093/cid/ciaa237. Zhang D, Wu K, Zhang X, Deng S, Peng B (2020) In silico screening of Chinese herbal medicines with the potential to directly inhibit 2019 novel coronavirus. Journal of Integrative Medicine 18, 152–158. doi:10.1016/j.joim.2020.02.005. Efficacy & safety of Carica papaya leaf extract (CPLE) in severe thrombocytopenia (≤30,000/μl) in adult dengue – Results of a pilot study Dipu T. Sathyapalan et al 2020, plosone)

More Clinical studies of papaya leaf extract effectiveness combating dengue fever. Ref: Institute for Medical Research, Ministry of Health Malaysia. Publication Details Year : 2013 Journal : Soobitha Subenthiran, Tan Chwee Choon, Kee Chee Cheong, Ravindran Thayan, Mok Boon Teck, Prem Kumar Muniandy, Adlin Afzan, Noor Rain Abdullah and Zakiah Ismail (2013). Carica papaya leaves juice significantly accelerates the rate of increase in platelet count among patients with dengue fever and dengue haemorrhagic fever. Evidance-Based Complementary and Alternative Medicine Volume 2013: 7 pages Abstract : The study was conducted to investigate the platelet increasing property of Carica papaya leaves juice (CPLJ) in patients with dengue fever (DF). An open labeled randomized controlled trial was carried out on 228 patients with DF and dengue haemorrhagic fever (DHF). Approximately half the patients received the juice, for 3 consecutive days while the others remained as controls and received the standard management. Their full blood count was monitored 8 hours for 48 hours. Gene expression studies were conducted on the ALOX 12 and PTAFR genes. The mean increase in platelet counts were compared in both groups using repeated measure ANCOVA. There was a significant increase in mean platelet count observed in the intervention group (P < 0.001) but not in the control group 40 hours since the first dose of CPLJ. Comparison of mean platelet count between intervention and control group showed that mean platelet count in intervention group was significantly higher than control group after 40 and 48 hours of admission (P < 0.01). The ALOX 12 (FC  =  15.00) and PTAFR (FC  =  13.42) genes were highly expressed among those on the juice. It was concluded that CPLJ does significantly increase the platelet count in patients with DF and DHF.

"Papaya extracts may have anti-inflammatory and immunomodulation efficacy - that does not translate to cure of viral disease - esp. coronavirus for which there re no data." Of course there is no data because covid 19 is a novel virus but we do believe it can reduce Cytokine Storm in the covid 19 infection as the end result of viral flu infections by other viruses mostly the same which is the Cytokine storm. Ref: The Influenza a Virus Subtypes H1N1, H1N2 and H3N2 ,HDFx: A Novel Immunomodulator and Potential Fighter Against Cytokine Storms in Viral Flu Infections- Carica Papaya Linn "https://doi.org/10.25141/2472-102X-2017-8.0162 These qualities reduces Cytokine Storm in other viral flu infections, which can be used as candidate to fight the build up of liquid in the lung due to overwhelm immunity cells production because of the presence of covid 19 virus. If we could reduce the Cytokine storm, we could reduce the chance for a person to develop pneumonia or collapsed lungs and giving the immune system ample time to fight the covid 19 virus. If people are using HIV drug to test its efficacy in fighting covid 19, why not we try this cheap and easily available compounds to try it on covid 19. I had experienced it myself twice with dengue fever and one with leptospirosis which I managed to survive after few days drinking the crude blended papaya leaves. I had also asked my sister to drink the papaya leaf extract to reduce her asthma and it works, asthma got something to do with the cytokine storm: Ref: Targeting the "Cytokine Storm" for Therapeutic Benefit DOI: 10.1128/CVI.00636-12 This is how I got the idea to use the papaya leaf extract as candidate to fight covid 19 infection, not directly killing the virus perhaps could prevent its activity that damages the lungs. It is normal in Malaysia for people to drink papaya leaf juice when they get dengue fever and it works. Of course you need clinical tests for it which would cost lots of money, but there is no harm trying something that might work which could perhaps save many lives when there is no other effective anti-viral drugs or vaccines proven to fight covid 19 so far. We are in race to fight a pandemic that might kill millions of people. I am collecting data for its effectiveness and if it works, it can save many lives at low cost with easily reached ingredients. Papaya plants grow in Italy nowadays, perhaps it might beneficial to them today. On its toxicology "'You need to eat 12,000 papaya leaves to get cyanide poisoning' https://www.malaysiakini.com/news/328875

M.S. Shukor1 and M.Y. Shukor2 1Snoc International Sdn Bhd, Lot 343, Jalan 7/16 Kawasan Perindustrian Nilai 7, Inland Port, 71800, Negeri Sembilan, Malaysia. 2Department of Biochemistry, Faculty of Biotechnology and Biomolecular Sciences, Universiti Putra Malaysia, UPM 43400 Serdang, Selangor, Malaysia. Covid-19 is now a pandemic affecting humans at a global scale. Researchers are still trying to find a cure and the vaccine to fight this disease. Drug-based cure and vaccine are overwhelmingly virus-specific and newer drugs and vaccines are needed to resist new novel viral infections. A shift towards herbal remedies to fight viral infections is an approach that can be explored especially in poorer countries or when drugs and vaccines are still not available. One of the top herbal remedies that emerges as a prime weapon for viral infection is Carica papaya, where the leaves extract has been tested in clinical environment in patients infected by the dengue virus. In two studies, platelets, white blood cells and neutrophils counts were back to normal after the administration of papaya leaves aqueous extract and the infected patients recovered (Ahmad et al. 2011; Kumar et al. 2015). Further research has demonstrated that papaya leaf extract decrease dengue complication through another route by inhibiting viral production. A study suggests that papaya leaves extract significantly cause the expression of NS1 and envelope proteins to be lowered in DENV-infected THP-1 cells. A significant lowering of the intracellular viral load supports papaya leaves extract antiviral activity (Sharma et al. 2019). In addition, papaya extracts and papaya-associated phytochemicals possibly enhance recovery in dengue infected patients through their anti-inflammatory and immunomodulatory properties (Pandey et al. 2016). A study shows that nine selected ligands from Carica papaya leaves show good binding to viral proteins from dengue, influenza A (H1N9) and chikungunya (Narayanaswamy et al. 2017). As more and more wonderful properties of papaya leaves extract are reported in the literature, researchers began to use the extracted phytochemicals from the plant to combat other viral infections either in vivo, in vitro or in silico. SARS-CoV-2 is the novel virus that causes Covid-19. It has not benefit from the usage of papaya extract to fight its infection, not yet, but there is a growing body of evidences that suggest its probable usage to combat Covid-19. For a start, the anti-inflammatory and immunomodulatory properties of papaya leaves extract can increase an infected person chance of recovering from the infection. The papaya leaves extract is able to reduce the severity of cytokine storm in dengue infection in mice model (Norahmad et al. 2019). Cytokine storm is one of the most important mechanisms that lead to deaths of Covid-19-infected patients (Chen et al. 2020). Cytokine storm occurs when the lungs of infected patients become severely inflamed due to the massive overproduction of a host of mediators such as interleukins, interferons, tumour necrosis factor, macrophage and other factors which are lumped together as cytokines or chemokines. Cytokine storms often lead to infected cells dying through apoptosis and necrosis leading to severe tissue damage and haemorrhages triggering multiple organ failure (Tetro 2020; Chen et al. 2020; Yao et al. 2020). In another study, patients having virus-induced lung damage were given fermented papaya preparation for one month. The researchers observed an increase in salivary IgA and increase in phase II and SOD enzyme expression levels, which are essential antioxidants in the respiratory tract (Marotta et al. 2012). Consumption of papain leaf extract can probably help in fighting Covid-19 infection, but more studies are needed to support this premise. An important step for a start is the in silico docking behavior of potential ligands from papaya leaves extract to the papain-like Covid-19 protease; one of the main targets of Covid-19 antiviral drug screening strategy (Arya et al. 2020; Zhang et al. 2020). Reference Ahmad N, Fazal H, Ayaz M, Abbasi BH, Mohammad I, Fazal L (2011) Dengue fever treatment with Carica papaya leaves extracts. Asian Pacific Journal of Tropical Biomedicine 1, 330–333. doi:10.1016/S2221-1691(11)60055-5. Arya R, Das A, Prashar V, Kumar M (2020) Potential inhibitors against papain-like protease of novel coronavirus (SARS-CoV-2) from FDA approved drugs. doi:10.26434/chemrxiv.11860011.v2. Chen C, Zhang XR, Ju ZY, He WF (2020) [Advances in the research of cytokine storm mechanism induced by Corona Virus Disease 2019 and the corresponding immunotherapies]. Zhonghua Shao Shang Za Zhi = Zhonghua Shaoshang Zazhi = Chinese Journal of Burns 36, E005. doi:10.3760/cma.j.cn501120-20200224-00088. Kumar DrCVMN, Vadlamudi T, Venkatamuni A, Vardhan V, Prasad Y, Ravi U, D.V.R. S (2015) Therapeutic potential of Carica papaya l. leaf extract in treatment of dengue patients. International Journal of Applied Biology and Pharmaceutical Technology 6, 93–98. Marotta F, Naito Y, Jain S, Lorenzetti A, Soresi V, Kumari A, Carrera Bastos P, Tomella C, Yadav H (2012) Is there a potential application of a fermented nutraceutical in acute respiratory illnesses? An in-vivo placebo-controlled, cross-over clinical study in different age groups of healthy subjects. Journal of Biological Regulators and Homeostatic Agents 26, 285–294. Narayanaswamy R, KW L, ME N (2017) Molecular docking analysis of Carica papaya Linn constituents as antiviral agent. International Food Research Journal 24, 1819–1825. Norahmad NA, Mohd Abd Razak MR, Mohmad Misnan N, Md Jelas NH, Sastu UR, Muhammad A, Ho TCD, Jusoh B, Zolkifli NA, Thayan R, Mat Ripen A, Zainol M, Syed Mohamed AF (2019) Effect of freeze-dried Carica papaya leaf juice on inflammatory cytokines production during dengue virus infection in AG129 mice. BMC Complementary and Alternative Medicine 19,. doi:10.1186/s12906-019-2438-3. Pandey S, Cabot PJ, Shaw PN, Hewavitharana AK (2016) Anti-inflammatory and immunomodulatory properties of Carica papaya. Journal of Immunotoxicology 13, 590–602. doi:10.3109/1547691X.2016.1149528. Sharma N, Mishra KP, Chanda S, Bhardwaj V, Tanwar H, Ganju L, Kumar B, Singh SB (2019) Evaluation of anti-dengue activity of Carica papaya aqueous leaf extract and its role in platelet augmentation. Archives of Virology 164, 1095–1110. doi:10.1007/s00705-019-04179-z. Tetro JA (2020) Is COVID-19 receiving ADE from other coronaviruses? Microbes and Infection. doi:10.1016/j.micinf.2020.02.006. Yao X, Ye F, Zhang M, Cui C, Huang B, Niu P, Liu X, Zhao L, Dong E, Song C, Zhan S, Lu R, Li H, Tan W, Liu D (2020) In Vitro Antiviral Activity and Projection of Optimized Dosing Design of Hydroxychloroquine for the Treatment of Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2). Clinical Infectious Diseases: An Official Publication of the Infectious Diseases Society of America. doi:10.1093/cid/ciaa237. Zhang D, Wu K, Zhang X, Deng S, Peng B (2020) In silico screening of Chinese herbal medicines with the potential to directly inhibit 2019 novel coronavirus. Journal of Integrative Medicine 18, 152–158. doi:10.1016/j.joim.2020.02.005.

x_i is an arithmetic series (e.g x_1, x_2, ...x_n=2,3,..,1000)

This is part of my works. I have formulated a new formulation for sums of power and it works for any numbers (i.e. real & complex arithmetic progression). The generalize equation can generate any power p (it works fine also with complex p). Let the p-th power of an arithmetic series as follows [math]\sum_{i=1}^n x_i^p = x_1^p + x_2^p + x_3^p + \cdots + x_n^p[/math] The general equation for the sum is given as follows [math]\sum^{n}_{i=1} {x_i}^p=\sum^{u}_{m=0}\phi_m s^{2m}\frac{[\sum^{n}_{i=1} x_i] ^{p-2m}}{n^{p-(2m+1)}}[/math] where: [math]p-(2m+1)\ge 1[/math] if p is even and [math]p-(2m+1)\le 1[/math] if p is odd, [math]\phi_m[/math] is a coefficient,[math]\sum^{n}_{i=1} {x_i}[/math] sum of n-th term, [math]u=\frac {p-1}{2}[/math] for odd p and [math]u=\frac {p}{2}[/math] for even p and s is the difference between terms (i.e [math]s=x_{i+1}-x_{i}[/math]). Below are the equations for p=2-7 [math]\\\sum_{i=0}^{n}x_{i}^{2}=\frac{\left [ \sum_{i=0}^{n}x_{i} \right ]^2}{n}+\frac{n(n^2-1)s^2}{12}\\\\\\\sum_{i=0}^{n}x_i^3=\frac{\left [ \sum_{i=0}^{n}x_i \right ]^3}{n^2}+\frac{(n^2-1)s^2\left [ \sum_{i=0}^{n} x_i\right ]}{4}[/math] The value s is the common difference of successive terms in arithmetic progression and [math]\sum_{i=0}^{n}x_i[/math] is the sum of arithmetic terms. The beauty of this equation is that when you set n=2, it describes the Fermat's Last Theorem in a polynomial forms and if you set p to be negative, you can get new form of Riemmann's Zeta Function. Here, you can see how the coefficients are repetitive: [math]\\\sum_{i=0}^{n}x_i^4=\frac{\left [ \sum_{i=0}^{n}x_i \right ]^4}{n^3}+\frac{(n^2-1)s^2\left [ \sum_{i=0}^{n}x_i \right ]^2}{2n}+\frac{n(3n^2-7)(n^2-1)s^4}{240}\\\\\\\sum_{i=0}^{n}x_i^5=\frac{\left [ \sum_{i=0}^{n}x_i \right ]^5}{n^4}+\frac{5(n^2-1)s^2\left [ \sum_{i=0}^{n} x_i\right ]^3}{6n^2}+\frac{(3n^2-7)(n^2-1)s^4\left [ \sum_{i=0}^{n}x_i \right ]}{48}[/math] [math]\\\sum_{i=0}^{n}x_i^6=\frac{\left [ \sum_{i=0}^{n}x_i \right ]^6}{n^5}+\frac{5(n^2-1)s^2\left [ \sum_{i=0}^{n}x_i \right ]^4}{4n^3}+\frac{(3n^2-7)(n^2-1)s^4\left [ \sum_{i=0}^{n}x_i \right ]^2}{16n}+\frac{n(3n^4-18n^2+31) (n^2-1)s^6}{1344}\\\\\\\sum_{i=0}^{n}x_i^7=\frac{\left [ \sum_{i=0}^{n}x_i \right ]^7}{n^6}+\frac{7(n^2-1)s^2\left [ \sum_{i=0}^{n}x_i \right ]^5}{4n^4}+\frac{7(3n^2-7)(n^2-1)s^4\left [ \sum_{i=0}^{n}x_i \right ]^3}{48n^2}+\frac{(3n^4-18n^2+31) (n^2-1)s^6\left [ \sum_{i=0}^{n}x_i \right ]}{192}[/math] Perhaps, by looking at this new formulation, someone could work out an alternative shorter proof for Fermat's Last Theorem.