key: cord-0798347-syuy6m7s authors: Gonzalez, J. A.; Akhtar, Z.; Andrews, D.; Jimenez, S.; Maldonado, L.; Oceguera, T.; Rondon, I.; Sotolongo-Costa, O. title: Combination anti-coronavirus therapies based on nonlinear mathematical models date: 2021-02-23 journal: Chaos DOI: 10.1063/5.0026208 sha: 14c8ccef7fcaf0eb84cb9b83c076cb8b7edb882f doc_id: 798347 cord_uid: syuy6m7s Using nonlinear mathematical models and experimental data from laboratory and clinical studies, we have designed new combination therapies against COVID-19. before that combination therapies can be better than monotherapies. For instance, for some cancer tumors, the immunotherapies do not work at all [3] [4] [5] . We have proposed to use a combination of therapies that could eradicate the cancer completely [3] [4] [5] . In the present paper we will design new therapies based on antiviral agents in combination with other therapeutic approaches. These new therapies should improve patient outcomes. There are several famous equations that have been used to describe cell population growth: exponential, Gompertz, logistic, and power-law equations 6 . In reference 7 , a biophysical justification for the Gompertz's equation was presented. There is a large series of recently found natural systems that present anomalies that violate the standard Boltzmann-Gibbs method. A non-extensive thermostatistics, which contains the Boltzmann-Gibbs as a particle case, was proposed in a series of papers [8] [9] [10] [11] . Nowadays, scientists have produced a large amount of successful applications of the new theory . These are mostly phenomena in complex systems. The mentioned thermodynamic theory contains the non-extensive entropy: where k is a positive constant, w is the total number of possibilities of the system, This expression recovers the Boltzmann-Gibbs entropy, S 1 = −k w i=1 p i ln p i , in the limit q → 1. Parameter q characterizes the degree of non-extensivity of the system. This can be seen in the following rule: where A and B are two independent systems in the sense that P i,j (A+B) = P i (A)P j (B). We could say that parameter (1-q) characterizes the complexity of the system. The case 1 − q ≥ 0 implies that the system is resilient. For example, this condition indicates that the virus infection will lead to a drug-resistant disease. In particular, this disease can become resistant to the attack of the immune system and conventional therapy. The new generalized equation for population growth is the following where X(t) is the growing population, k is certain free parameter, and X ∞ is the asymptotic value of X(t) when t → ∞. We have already remarked that this is a very general model that contains most known growth models 6 . Now, we will show that this model is universal in the sense discussed in Ref. 12, 13 and includes many others classes of models as particulars cases. 14 For early stages of the infection, (4) can be written in the following form 14 (5) , (6) . In this case, the fixed point P I is a stable node, the point P II is a saddle, and the point where X ≈ X ∞ is a stable node (not shown). The blue line is the stable manifold of the saddle point P II . And the red line is the unstable manifold of the mentioned saddle point. The blue line is a global separatrix of the dynamics. All initial conditions that are on the "left" of the blue line will lead to a phase trajectory that tends to a point where X = 0. All initial conditions that are on the "right" of the separatrix will lead to a phase trajectory that tends to the point where X ≈ X ∞ . This picture occurs when q > 1 , bV > af . where α q = kqX∞(q) An analytical solution to equation (4a) can be expressed as where X 0 is the initial condition so that X(t = 0) = X 0 . We can re-write solution (4b) as where r = X X∞(q) This calculation shows that our model represents a universal growth law 12-14 . So even this general class of growth laws are a particular case of equation (4). In the present paper, we will investigate the following dynamical system where X denotes the virus population and Y denotes the population of lymphocytes. Equation (5) describes the reproduction of the virus. The virus is killed when it meets agents of The reproduction of the agents of the immune system is described by the term d(X −eX 2 ), where initially the presence of the virus stimulates the reproduction of Y (t). When virus load is very large, the person is so sick that the reproduction of Y (t) is inhibited. The term −f Y corresponds to the natural death of lymphocytes. The term V represents an external flow of lymphocytes. The term −c 1 (t)X stands for virus-killing process due to different therapies. The term −c 2 (t)Y shows that therapies can also affect other normal cells (including the immune system). The system (5) and (6) is inspired by models of the immune system developed in references 15 and 16 . However, instead of the exponential growth assumed in 15,16 , we are using our growth model given by Eq. (4). First, we will consider the case where q > 1, X ∞ e >> 1, c 1 (t) = 0,c 2 (t) = 0 . Let us define a = qk q−1 . The dynamical system (5)- (6) can have, in principle, four fixed points where 0 < X 3 < 1 2e , Y 3 = a b , where The conditions for the existence of points P II and P III are the following inequalities where The eigenvalues of the Jacobian matrix corresponding to the fixed point P I are If af < V b, the fixed point P I is a stable node and the fixed point P II is a saddle (See figures (1) -(2)) . If af > V b, and h − 1 4e 2 < 0, then the four fixed points exist and are non-negative. Both fixed points P I and P II are now saddles. Between these two points, there is the point P III , which is stable (See Fig. (3) and Fig.(4) )). If af > V b, and h − 1 4e 2 > 0, then there are only two fixed points: point P I which is now unstable and point P IV , which is stable. As a result, most trajectories tend to point P IV (with maximum virus population) . This is not a very favorable situation for the patient. (See Fig. (5 In the neighborhood of point P II , the separatrix of the saddle can be approximated by the straight line Any point corresponding to initial conditions of the Cauchy problem on the right of the separatrix leads to a dynamics where the trajectory approaches the point of maximum virus load (point P IV ). On the other hand, if the initial conditions correspond to a point located on the left of the separatrix, the system will evolve to a stable fixed point. Using (15) , we can calculate the threshold or critical virus population that would lead to a dynamics approaching point P IV : When X ∞ is small, the outcome can be very favorable. For instance, when all the phase trajectories tend to the fixed point P I (X = 0). We can also apply the isocline method in order to further investigate the system. A careful analysis of the behavior of the phase trajectories allows us to conclude that the condition (5) , (6) . In this case, the fixed point P I is unstable, the fixed point P II is still a saddle. Now there is a new fixed point P III that is a stable node (for which X > 0). Now the separatrix is represented with a red line. All the phase trajectories that are on the "left" of the separatrix are approaching the point P III (where X > 0). All the phase trajectories that are on the "right" of the separatrix are approaching the fixed point where X ≈ X ∞ . Note that there are trajectories for which X(t) is monotonically increasing from a small value until it reaches its maximum (Point P III ). There are other trajectories for which X(t) reaches a maximum, and, later, it decreases until it enters the point P III . Conditions bV < af is favorable for the patient. This is a sufficient condition to avoid an uncontrollable rise of the virus population leading to the point P IV . In many cases, it is convenient to re-write the system (5) -(6) as one equation where the only unknown is X(t), In general, it is useful to discuss the dynamics of virus population as a general equation of the following type See Refs 17 for a simple explanation. Equation (20) is equivalent to a Newton's equation for a "fictitious" particle moving in the potential U (X) under the action of nonlinear damping. The potential U (X) can have minima and maxima. So we can conceive the situation where the "fictitious" particle is trapped inside a potential well. The particle needs to jump over a barrier for the virus population to continue increasing. Studying the relative heights of the barriers, we get the condition when this condition is satisfied, the "right" barrier of the potential well is higher than the "left" barrier. This case is more favorable for the patient. A careful analysis shows that the condition is very favorable for the patient. The general meaning of conditions (18), (21) and (22) is that the comparison between the values of d and the product ef can decide the outcome. Let us analyze now the case q ≤ 1. When the point P I will be always unstable. This means that it is almost impossible to reduce the virus population to zero. This finding will play a very important part in the design of new therapies. Let us discuss time-dependent therapy against COVID-19. Let us consider the dynamical system (5)-(6) with time-dependent therapy Using ideas from 6 , we can obtain the following result. If q < 1, it is very difficult to cure the virus disease. If we have a target decay for the virus population X(t) , then c 1 (t) must behave as For instance, if we require the virus population to be reduced following a power law, say X(t) ≈ α/t γ , then the therapy must behave as c 1 (t) = t γ(1−q) . The exponent gamma represents the rate of decay of the virus population. We have designed therapies using the following late-intensification schedules: where c(t) = c 0 is a well-known constant-dose treatment taken by a patient for several days. (See Ref. 4 ). Our logarithmic late-intensification schedule has been very successful (See 5 and references quoted there in). The traditional therapy is changed only slightly. However, the results are spectacular. When q > 1, the parameters of the system and the initial conditions play an important role in the outcome. The virus-host interaction is decisive. There are situations where the immune system by itself can reduce the virus population to zero. Under other circumstances, the virus population will increase to numbers that can threaten the patients survival. If we apply conventional antiviral therapies with c(t) = c 0 in the system (5) and (6) (where c 0 is a constant), for q > 1, the cure can be accelerated 6 . If q ≤ 1, then for any value of c 0 , the virus population is never reduced to zero. The fixed point P I is always unstable. The medical significance of this result can be expressed employing this statement: when q ≤ 1 the disease is resistant to the immune response and the action of conventional therapy. Our analysis shows that for q ≤ 1, the virus can develop resistance both against the attack of the immune system and all conventional monotherapies with constant doses of the medication. All this investigation leads to combination therapies. First, we have to use therapies that change the parameters in such a way that fixed point P I becomes asymptotically stable (a stable node). Then we need to apply therapies that will help the phase trajectory to go to the point P I . The condition q > 1 should be completed with the stability of fixed point P I : and complemented with condition (18) . This means that immuno-therapy is also very important for the development of antiviral therapies. This work can guide physicians to rationally design new drugs or a combination of already existing drugs for the development of antiviral therapies. Condition (23e) shows that the killing ability of the immune system and the external flow of lymphocytes should be stronger than the virus replication and the natural death of immune system agents. Additionally, condition (18) says that the reproduction of the lymphocytes should be stronger than the inhibition of the immune system due to the general health weaknesses created by the disease. The perfect strategy is to use a therapy that can change q so that the fixed P I can be, in principle, stable. Of course, this does not guarantee that the point P I is stable. The condition q > 1 is a necessary condition for the stability of point P I . However, it is not a sufficient condition. Later we need another therapy that will change the other parameters (see section 3) so that the fixed point P I is actually asymptotically stable. This step is probably satisfied with an immuno-therapy. Finally, we need a treatment c(t) that definitely kills the virus, leading the phase trajectory to the fixed point. The ideal candidate for the first task could be a gene-targeted therapy. On the other hand, we believe there are antivirals that can be utilized in order to accomplish this goal. Drug repurposing for SARS-CoV-2 is very important for our world. It can represent an effective drug discovery strategy from existing drugs. It could shorten the time and reduce the cost compared to de novo drug discovery 44 . Phylogenetic analysis of 15 HCoV whole genomes reveal that SARS-CoV-2 shares the highest nucleotide sequence identity with SARS-CoV 44 . A molecular docking study has been published by Abdo Elfiky 45 . The results show the effectiveness of Ribavirin, Remdesivir, Sofobuvir, Galidesivir, and Tenofovir as potent drugs against SARS-CoV-2 since they tightly bind to its RdRp. Additional findings suggest guanosine derivative (IDX-184), Sefosbuvir, and YAK as top seeds for antiviral treatments with high potential to fight SARS-CoV-2 strain specifically. We have reviewed the medical literature on COVID-19 treatments. There is experimental evidence supporting combination therapies However, medical practice has been concentrated mostly on monotherapies. Even when combination therapies have been used, in many cases, the combinations have not been optimized. We believe we can improve the treatment outcomes using our results. Combination of antivirals is the most common therapeutic set. In many cases, the used antivirals were previously developed for other viruses (e.g. SARS, MERS, Ebola, Flu, and HIV). We present a summary of the studies about COVID-19 treatments. Results: There is some scientific evidence that this combination can work 18, 52, 53 Inconsistent results in some completed clinical trials. Therapy 2: Antiflu Arbidol + Anti-HIV antiviral Darunavir. Results: There is some scientific evidence that this combinations can help. 18, 52 Therapy 3: Lopinavir/Ritonavir + Ribavirin. This is an anti-HIV therapy used in SARS. Results: There is some scientific evidence that this combination could work 19 . This is an antiviral that interferes with virus RNA polymerases to inhibit virus replication. Results: Approved by FDA Inconsistent and conflicting results in completed clinical trials. 40, [46] [47] [48] 53, 54 . This is a promising drug. We have estimated the parameters of the model (equations (5) and (6) Often, data about the immune behavior is not explicitly available. So, we use a version of the model that consists of one nonlinear differential equation only for X(t). However, that equation contains the parameters that characterize the immune system. Thus, these parameters can be estimated, too. We have observed several patterns in the virus dynamics First pattern: the viral load increases rapidly and reaches a peak. Then the viral load declines due to the action of a strong immune system. The final viral load cannot be detected. We assume it is zero. (See Fig. (1) ). Second pattern: the viral load increases rapidly and reaches the peak, followed by a plateau. The plateau can be short or long. After the plateau, the viral load declines to zero. (In this case, the dynamics reaches a fixed point. Then, the parameters of the immune system change (e.g. b, V)). Then the fixed point P I is stable again. Third pattern: the viral load increases rapidly and reaches a peak, followed by a plateau with a large value of the virus load. The plateau never ends. The patient dies. The viral load never declines. Fig. (5) . Fourth pattern: the viral load increases rapidly and reaches a peak. Then the viral load declines. The decline is followed by a long plateau. The value of the virus load is much smaller than the peak. However it is far from zero. (See Fig. (3) ) These behaviors can also occur under the action of therapy Let us introduce the units of the variables and parameters In this case, the immune system is so strong that it is able to eradicate the virus by itself. Virus load is approaching zero after 10 days. In this case, the viral load will reach the maximum. Then the virus load will decline. But it will not approach zero. The value of X(t) will be approximately constant for a long time. In the dynamical system this is a stable fixed point. The real data shows a long plateau where 2uv < X < 3uv. The known data does not show an end to this plateau. The cases of patients 2, 4 and 5 from Ref. 65 are very similar to Example 1. The immune system is able to eradicate the virus without external therapy. Example 4 (patient 3 from Ref. 65 ) The viral load reaches a maximum, followed by a plateau. This is an 80 years old man with a very depressed immune system (he had had thyroid cancer). This patient was sick with COVID-19 for 24 days. He was medicated with Remdesivir starting on day 16. The viral load decreased slightly. However, the immune system was too weak. The viral load increases until it reaches the maximum. The immune system is so weak that we can consider that it is not working at all. The viral load will never decrease. The patient died on day 18. The viral load increases very fast and the peak is very high. Common sense would have led physicians to consider this case as critical. However, this patient was treated with a combination therapy. According to the estimated parameters, we believe the treatment changed parameter q. The immune system was working well. The viral load is eradicated. This is seen in the dynamics of the model and in the real clinical data. We have investigated all the data published in Refs . For instance, in Ref. 69 , the authors studied 52 patients. The cases are very similar to the examples and patterns that we have described here. They found mild, severe, critical, and deadly cases. In general, considering all the literature here are interesting points that must be remarked. Some older patients with rapid evolution towards critical disease with multiple organ failure presented a long sustained persistence of SARS-CoV-2. This persistent high viral load is explained by the ability of the SARS-CoV-2 to evade the immune response 65 . SARS-CoV-2 might be able to inhibit immune system signaling pathways, resulting in a malfunctioning of the immune system. In most critical patients, the blood viral load was never eliminated 69 . This can be explained with the stable fixed points of our model. The results of our investigation of the model, the virus kinetics research, and the data from lab experiments and clinical studies 18-69 lead us to the following strategy to cure COVID-19: A combination of antivirals can change the virus reproduction capabilities (parameter k) and drug resistance (parameter q). This can make the fixed point P I stable. A combination of immunotherapies can boost the immune system (parameters (b, d, V ) . The agents of the immune system can reduce the virus load. (See Figs. (1) -(4) ). Even if the point P I is stable and the immune system is working, it is possible that the virus dynamics is not riding a phase trajectory that is approaching the fixed point P I , where X = 0. For instance, if the initial condition is on the "right" of the separatrix of the saddle point P II , then X(t) is not approaching the point X = 0. A virus-killing therapy can change the position of the initial point (X 0 , Y 0 ), in such a way that this point will be on the "left" of the separatrix (See Fig. (1) ). Now there is always a phase trajectory that will drive the viral load, X(t), to the point where X(t) = 0. The particular medications that will be used in every combination are selected from the set of drugs already tested in clinical trials. The ideas discussed in the first 6 sections of the paper lead to the conclusion that we need a combination therapy that contains at least some the following features: (A) A combination of drugs that impair somehow the biophysics of the virus replication, infection and/or treatment resistance. (B) A combination of drugs that enhance the immune system ability to provide enough agents and their capability to fight the virus + anti-inflammatory drugs. (C) A cell-killing therapy. Our paper is not only about mathematical models. We have critically reviewed all the published data about possible medical treatments against COVID-19. We have used a method that we have developed called Complex Systems Investigation to analyze the data. Complex Systems Investigation contains ideas from Nonlinear Dynamical Systems, Inverse Problems, and Experimental Design Mathematics. Our results show that a successful treatment should be a combination of therapies as that shown in Fig. (6) This is just a useful therapeutic plan. We will see later that the role of a cytotoxic therapy sometimes can be played by an immunotherapy or an antiviral. Fig. (6) shows a very general plan. Now we will present several concrete combination therapies. There are certain observations 18 that support the existence of synergism between Remdesivir and monoclonal antibodies. Considering the fact that our investigation leads to a combination of antivirals, immunotherapy, and virus -killing medications, the mentioned synergism help us build the treatment shown in Fig. (12) . The simplest of our designed therapies is shown in Fig. (7) and Figures (8) Sometimes, the data is very fragmented. In some cases, we only know the input, the medications, and the output. For instance, consider a patient with the following estimated parameters before therapy: Evidently, the patient has a bad prognosis. There is no way that this viral load will decrease under natural circumstances. We will apply the therapy shown in Fig. (10) . Our result is the following: The first round (antiviral combination: Remdesivir + EIDD -2801) will produce the parameters: q = 1.9, k = 0.01 (1/day). These are the only parameters that can be changed with the given antivirals. After the immunotherapy (Convalescent plasma + Interferon beta), we get Additionally, the virus-killing medication (Natural Killer Cell Therapy) will reduce the "initial" viral load to the value X 02 < 1.4uv < X crit . Now there is a phase trajectory that can Fig. (1) ). We can cure this patient with fulminant COVID -19 infection!. We believe these results can explain the clinical outcomes observed in references [27] [28] [29] [30] . This is a powerful combination. FIG. 13. This is a next-door therapy. Any hospital should be able to provide this treatment, which could save patients' lives. Regeneron pharmaceuticals has developed monoclonal antibodies to treat MERS. This company is already working on similar antibodies that might work against SARS-CoV-2. Lopinavir/ritonavir + arbidol improved pulmonary computed tomography images 55 . Interferons + Natural killer cells are promising. Interferons can enhance natural killer cells cytotoxicity. Mesenchymal stem cells will act against inflammatory factors (cytokine storms). Carolacton is a MTHFV1 inhibitor. It is a natural bacteria-derived product 55 . This is a good candidate for the first round in the combination therapy (see Fig. (14) ). A candidate for natural killer cell therapy is CYNK-001 37 . The most powerful therapy is shown in Fig. (10) . Probably this therapy should be used in the most severe critical fulminant cases. On the other hand, Fig. (13) shows the next-door therapy. In principle, all elements should be available right now in every American city. Remdesivir is considered the most promising drug for COVID-19 and MERS. However, the clinical trials have produced conflicting results. Sometimes the results are encouraging, sometimes there are no significant benefits at all. Sometimes the people are still dying even taking remdesivir. Our response to this paradox is that remdesivir will work as part of a combination therapy. Our result is that the idea of using remdesivir and some immunotherapies in combination would have profoundly excellent prospects. (See figures (6)- (15)). We have tried to construct the combinations using drugs that have shown proven efficacy in completed clinical trials and/or laboratory experiments 55 . Parameter q can be changed using drugs that change the nature of the virus. Parameter q is related to the nature and structure of the virus. For instance, the drug EIDD-2801 interferes with a key mechanism that allows the SARS- Our research leads to the following solution to these problems: the addition of new drugs to the therapy and the total increase of doses can be administered using late-intensification schedules (e.g. logarithmic or power-law therapies 4-6 . Our stable fixed point with a small but finite virus population explains the following mystery: why a lot of patients who recovered from Coronavirus have retested positive 7 . The existence of a finite minimum of the virus load in order to start an infection (Eq. (16)) explains that there is a threshold value for a person exposure to sick people so that the person becomes infected. Our findings can also inform vaccine development. A vaccine works by training the immune system to recognize and combat viruses. Some precedents.Therapy of HIV is complicated by the fact the HIV genome is incorporated into the host cell genome and can remain there in a dormant state for prolonged periods until it is reactivated. Some scientists believe that it is not possible to actually eradicate the virus completely. Our research shows that this is a very striking example where q ≤ 1 . Following our ideas, it is possible that HIV can be completely eradicated. AZT was the first antiviral agent used for the treatment of HIV and was introduced in 1987. However, it became clear that mono therapy with AZT did not provide durable efficiency and hardly made any dent in the mortality rate. Later, different studies showed that combination therapy with two nucleotide analogues were better than monotherapy with only one. After several experimental breakthoughs, a combination therapy known as HAART (highly active antiretroviral therapy) using two or three agents became available. By combining drugs that are synergistic, non-cross-resistant and no overlapping toxicity, it may be possible to reduce toxicity, improve efficacy and prevent resistance from arising. All the antiviral drugs and therapeutic methods now known were discovered by random search in the laboratory. We believe that using mathematical biophysics it is possible to create a rational approach for the discovery of new antiviral compounds and the design of the optimal combination therapy. • We have developed a mathematical model to describe the SARS-CoV-2 viral dynamics. The model is a nonlinear dynamical system. • We have investigated the dynamical system theoretically and numerically. • We have found conditions for the stability of the fixed point that corresponds to the complete eradication of the virus. • We identified the separatrix that separates the initial conditions that lead to the maximum value of the viral load from the initial conditions that lead to a limited growth of the virus population. • We have studied the global dynamics of the dynamical system. We can predict the evolution of any initial condition. • The fixed point X = 0 is stable when • If the following conditions are satisfied h − 1 4e 2 > 0, (27) then the separatrix does not exist and there are no restrictions to the growth of the viral load. This is a terrible situation. • Furthermore, condition q ≤ 1 means that the virus cannot be eradicated by the immune response or using any conventional monotherapy. • Let us discuss the biological meaning of the following conditions q > 1. In the real-life scenario, conditions (28)- (30) mean that the immune system is working well and the virus infection is not drug resistant. The combination therapy must be able to generate conditions (28)- (30) . • Our study provides explanations to several phenomena that have been observed during the experimental studies of SARS-CoV-2 virus. • We have critically reviewed the experimental and clinical literature about COVID-19. NIAID director had said that remdesivir will become the standard care of COVID-19. The drug shortened the course of illness from an average of 15 days to about 11 days. However, it is clear that the drug is not enough to help patients. The medication is not a cure and it does not act quickly. There is high mortality despite the use of remdesivir. So, remdesivir is not sufficient to cure patients. It seems that remdesivir does not cause an excess of side-effects. Our take is that remdesivir alone is not enough. Many other treatments, given as monotherapies, have failed to provide the promised results. Our conclusion is that we need new scientifically designed combination therapies. Using mathematical models and experimental data from laboratory and clinical studies, we have been able to design new therapies, which, we expect, will cure the patients. (See figures (6)- (15)). The new therapies also should be validated in double-blind, placebo-controlled trials with a large number of patients. The data that supports the findings of this study are available within the article. Functional diversity of helper T lymphocytes Applying predator-prey theory to modelling immunemediated, within-host interspecific parasite interactions Acute or chronic? Within-host models with immune dynamics, and infection outcome Models of the within-host dynamics of persistent mycobacterial infections Are SARS superspreaders cloud adults? Immunology and mathematics: Crossing the divide Virus dynamics: Mathematical principles of immunology and virology Modelling viral and immune system dynamics Superspreading SARS events Modelling within-host evolution of HIV: mutation, competition, and strain replacement Theory of an immune system retrovirus A new theory of cytotoxic T-lymphocyte memory: implications for HIV treatment Mathematical modeling of antigenecity for HIV dynamics Race to find COVID-19 treatments accelerates Dynamic response of cancer under the influence of immunological activity and therapy New combination therapies for cancer using modern statistical mechanics Cancer and nonextensive statistics Modeling tumor growth Generalized statistical mechanics: connection with thermodynamics Introduction to Nonextensive Statistical Mechanics: approaching a complex world Possible generalization of Boltzmann-Gibbs statistics Phase Transitions in Nonextensive Spin Systems A general model for ontogenetic growth Does tumor growth follow a universal law? A generalized q growth model based on nonadditive entropy Course of the immune reaction during the development of a malignant tumor Solitary waves in one-dimensional damped systems Can an anti-HIV combination or other existing drugs outwit the new coronavirus? Role of lopinavir/ritonavir in the treatment of SARS: initial virological and clinical findings Comparative therapeutic efficacy of remdesivir and combination lopinavir, ritonavir, and interferon beta against MERS-CoV" Hydroxychloroquine and azithromycin as a treatment of COVID.19: results of an open-label non-randomized clinical trial Hydroxychloroquine rated most effective therapy by doctors for coronavirus: Global survey". The Washington times (Thuesday Remdesivir and chloroquine effectively inhibit the recently emerged novel coronavirus (2019-nCoV) in vitro Could chloroquine treat coronavirus? The feasibility of convalescent plasma therapy in severe COVID-19 patients: a pilot study Treatment of 5 critically ill patients with COVID-19 with convalescent plasma How blood from coronavirus survivors might save lives A novel treatment approach to the novel coronavirus: an argument for the use of therapeutic plasma exchange for fulminant COVID.19 An orally bioavailable broad-spectrum antiviral inhibits SARS-CoV-2 in human airway epithelial cell cultures and multiple coronaviruses in mice National Health Commission of the People's Republic of China Catching up to coronavirus: Top 60 treatments in developments Vanquishing the virus: 160+ COVID-19 drug and vaccine candidates in development Remdesivir and chloroquine effectively inhibit the recently emerged novel coronavirus (2019-nCoV) in vitro First case of 2019 Novel coronavirus in the United States Transplantation of ACE2-Mesenchymal Stem Cells Improves the Outcome of Patients with COVID-19 Pneumonia How a 100-year-old vaccine for tuberculosis could help fight the novel coronavirus Hydroxychloroquine and ivermectin: A synergistic combination for COVID-19 chemoprophylaxis and treatment? Network-based drug repurposing for novel coronavirus 2019-nCoV/SARS-Cov-2 Ribavirin, Remdesivir, Sofosbuvir, Galidesivir, and Tenofovir against SARS-CoV-2 RNA dependent RNA polymerase (RdRp): A molecular docking study Compassionate Use of Remdesivir for Patients with Severe Covid-19 Early peek at data on Gilead coronavirus drug suggests patients are responding to treatment New data on Gilead´s remdesivir, released by accident, show no benefit for coronavirus patients company still sees reason for hope The FDA-approved drug ivermectin inhibits the replication of SARS-CoV-2 in vitro A human monoclonal antibody blocking SARS-CoV-2 infection Transplantation of ACE2-Mesenchymal Stem Cells Improves the outcome of patients with COVID-19 Pneumonia Triple combination of interferon beta-1b, lopinavir-ritonavir, and ribavirin in the treatment of patients admitted to hospital with COVID-19: an openlabel, randomised, phase 2 trial Financial Times Remdesivir in adults with severe COVID-19: a randomised, doubleblind, placebo-controlled, multicentre trial Baricitinib therapy in COVID19: A pilot study on safety and clinical impact Arbidol combined with LPV/r versus LPV/r alone against corona virus disease 2019 Current status of potential therapeutic candidates for the COVID-19 crisis Remdesivir for the treatment of COVID-19 -Preliminary Report Virological assessment of hospitalized patients with COVID-19 Viral load of SARS-CoV-2 clinical samples Respiratory disease in rhesus macaques inoculated with SARS-CoV-2 Investigation of a COVID-19 outbreak in Germany resulting from a single travel-associated primary case: a case Viral load kinetics of SARS-CoV-2 infection in first two patients in Korea Temporal profiles of viral load in posterior oropharyngeal saliva samples and serum antibody responses during infection by SARS-CoV-2: an observational cohort study Viral load dynamics and disease severity in patients infected with SARS-CoV-2 in Zhejiang province Viral loads and duration of viral shedding in adult patients hospitalized with influenza China: a retrospective cohort study Clinical and virological data of the first cases of COVID-9 in Europe: a case series SARS-CoV-2 viral load in upper respiratory specimens of infected patients Viral shedding and antibody response in 37 patients with East respiratory syndrome coronavirus infection Daily viral kinetics and innate and adaptive immune response assessment in COVID-19: a case series Dynamics of blood viral load is strongly associated with clinical outcomes in coronavirus disease 2019 (COVID-19) patients: a prospective cohort study