Abstract

CoVID-19 pandemic due to SARS-CoV-2 virus has been spreading rapidly worldwide since late 2019, and it may become one of the largest pandemic events in modern human history if out of control.  It appears most of the CoVID-19 infection resulted deaths are mainly due to severe hypoxia from dysfunction of the lung, and that could be attributed to host’s immunodysfunctions particularly hyperinflammatory type disorders or allergic reaction.  In this brief review and study, a mathematical model is proposed to correlate the Pathogen Infection Recovery Probability (PIRP) versus Proinflammatory Anti-Pathogen Species (PIAPS) levels, where a maximum PIRP is expected when the PIAPS levels are equal to or around PIAPS equilibrium levels at the pathogen elimination or clearance onset.  Based on this model, rational or effective therapeutic strategies at right stages or timing, with right type of agents (immuno-stimulators or immuno-suppressors), and right dosages, could be designed and implemented that are expected to effectively achieve maximum PIRP or reduce the mortality. 

Keywords: COVID-19, SARS-cov-2, pathogen, proinflammatory anti-pathogen species (PIAPS), optimal PIAPS level, immunodysfunctions, hyperinflammatory disorders, modelling, pathogen infection recovery probability (PIRP), maximum PIRP.

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Introduction

COVID-19 pandemic due to SARS-cov-2 viruses has been spreading around the globe since late 2019 and has resulted in over seven hundred thousand human deaths with over twenty million confirmed infections worldwide1-2. In addition to loss of human life, social and economic losses or effects can be very significant. A number of notable global pandemics occurred in human history can be attributed to pathogen infections3. Though there are differences among different pathogen induced infections, there were certain similarities among all pathogen infections. The pathogens here mainly include but may not be limited to, bacteria, viruses (such as the new SARS-cov-2 virus causing the covid-19 pandemic), or certain other species that can trigger or initiate a host immune system responses resulting in the production (clonal expansion) of anti-pathogen species (APS), particularly a series of proinflammatory anti-pathogen species (PIAPS). PIAPS here mainly refer to “double-edged sword” species such as certain white blood cells (wbcs) or their generated/related species, such as oxidative radical species and antibodies4-6, cytokines7-12, 18-20, etc. “Double-edged sword” refers to certain PIAPS that not only attack the pathogens but also attack host normal cells and tissues4-12, 18-20.

Analysis and Modeling

Pathogen infection modeling could be very useful for understanding the infection mechanisms and processes, and for preventive or therapeutic strategies. However, most of the existing modeling works are mainly focusing on multiple host infection and transmittance statistics over time domain13-17, very few modeling work provide insights on pathogen infection recovery probability (PIRP) over anti-pathogens species (APS), particularly over proinflammatory anti-pathogen species (PIAPS) which is the focus of this study. A pathogen infection in a host may result in pathogen un-controlled growth if the host immune system is too weak, deficient, or dysregulated (including immunoparalysis and a series of immune deficiency syndromes) that could result in sepsis or septic shocks20. In a host with normal immune response system, as illustrated in Figure 1, a pathogen infection at time t0 (end of incubation period) typically trigger a normal and efficient growth (clonal expansion) of immune system generated anti-pathogen species (APS, including PIAPS at an initial level x0 and time t0) and ideally shall result in pathogen being eliminated/cleared at te13. Once the pathogen is eliminated by the APS or PIAPS at te, the APS or PIAPS growth are supposed to cease and either remain at their equilibrium levels xeor decrease (shown by blue solid lines). Certain APS (such as certain pathogen specific antibodies) are expected to remain at their equilibrium levels for certain period of time so the same pathogen infection can be prevented (principle of vaccination), but APS/PIAPS level decrease are normal or expected13-17.

Figure 1. Schematic levels of pathogen (dashed red curve) and host immune system generated anti-pathogen species (APS), including proinflammatory anti-pathogen species (PIAPS), for normal (solid blue curve/line) and abnormal (dashed blue line, reflecting hyperinflammatory disorder) immune response reactions over time.

However, in certain immunodysfunction disorders, particularly certain hyperinflammatory disorders, such as in cytokine release syndromes (CRS) or cytokine storm (CS)4-12, macrophage activation syndromes (MAS) or macrophage-cytokine self-amplifying loop (MCSAL)11, WBS proliferative disorders4, certain PIAPS (e.g., Interleukin-6 or IL-6) can grow out of control or not being efficiently dampened (blue dashed line in Fig. 1) by the host anti-inflammatory species (e.g., IL-10) even after te where the pathogen level may be very low or have been cleared. It has been known that a number of PIAPS attack or damage normal cells resulting in tissue death (gangrene) and multiple organ dysfunctions or failures2, 4-12, 18-20. Based on these and for potential and practical therapeutic strategies, a normal distribution function Y has been proposed to model the Pathogen Infection Recovery Probability (PIRP, or the survivability, counter to the mortality) versus the PIAPS levels x (shown in Figure 2) and is exhibited with equation (1)21:

[-(x-xe)2/α] (1)

Figure 2. Scheme of Pathogen Infection Recovery Probability (PIRP) versus certain Proinflammatory Anti-Pathogen Species (PIAPS) levels based on equation 1.

Where α parameter is proportional to the PIRP distribution peak full width at half maximum (FWHM) that affects the PIAPS level range width around PIRP maximum. During this range,PIAPS levels can significantly elevate PIRP as compared to other PIAPS range where PIRP remains relatively low. Β parameter represents a coupling factor of PIRP versus PIAPS levels, reflecting how significant or effective PIAPS level affects PIRP.

Based on this math model, the PIRP-PIAPS distribution function curve are divided into two stages: 1) Stage I or the PIRP rising stage corresponds to pathogen/APS evolution time period between t0 to te as shown in Figure 1: The PIRP of the pathogen infected host starts to rise as the host normal immune response generated APS (including PIAPS) are growing from initial levels of x0 (x0 can be zero for pathogen specific APS) and eventually approaching at their equilibrium levels xe (blue solid line) where the pathogens are being eliminated or cleared. 2) Stage II or the PIRP descending stage: The PIAPS level may further grow beyond their equilibrium levels xe as represented by the dashed blue line (representing immunodysregulation such as hyperinflammatory disorders)2, 4-12, 18-20, the PIRP descends presumably due to excessive PIAPS start to damage the normal or healthy tissues or organs. Eventually the PIRP descend to a very low level due to heavy damages of cells and tissues that can result in multiple key organ failures2, 7-12, 18-20.

Results and Discussions

Based on this model, the general therapeutic strategies for minimizing mortality is to achieve and/or to sustain maximum PIRP via a two-stage protocol as following: 1) In stage I or the PIRP rising stage between t0 and te, if the host has a normal immune response to the pathogen infection, the host’s APS/PIAPS should grow efficiently toward their equilibrium levels xe where the pathogens are being eliminated or cleared. In this situation and stage, viral elimination focused therapies maybe unnecessary except supportive therapies are needed for the following situations: a) If the host exhibits breath difficulty (dyspnea) or low blood oxygen level due to the immune reaction generated liquids/mucous in the upper respiratory tubes or lungs (lung infections), then mechanical respiration ventilators and/or oxygen therapy may be utilized to prevent potential oxygen deficiency syndromes and related complications (hypoxemia and hypoxia); b) If the pathogen growth is out of control (such as in the cases where the host has any immune deficiency syndromes), than either pathogen inhibitors/suppressors (if available) or APS boosters/enhancers (immuno-stimulators, such as certain WBC therapies, antibody/immunoglobin therapies, interferon therapies, or therapies utilizing plasma and antibodies from the convalescent patients) may be administered to reduce potential viral damage resulted complications, but the immuno-stimulators must be administered at the right time (in stage I before te), right type (APS/PIAPS boosters/enhancers instead of inhibitors/suppressors), and at the right dosages (i.e., APS/PIAPS levels should be carefully monitored and controlled to be equal or close to their equilibrium levels xe). 2) In stage II or the PIRP descending stage after te, when the PIAPS levels are excessive or their growth are out of control (dysregulated), the most critical or essential therapeutic task in the post te period or stage II shall be to promptly terminate or suppress the further growth of the PIAPS levels (also called immuno-suppressing or dampening, and a variety of known anti-inflammatory therapies may be utilized with care) at or nearby their equilibrium levels xe, while pathogen inhibitors/suppressors may not be necessary at this time if the pathogens have been eliminated. In case where the coupling of the host generated APS to the pathogen is very poor, i.e., hyper-inflammation or cytokine storm has occurred but the pathogen level is still high, pathogen suppressors/inhibitors (if available), anti-inflammatory or non-inflammatory APS, as well as PIAPS suppressors may all be administered for this situation and in this stage but with carefully controlled dosages. Certain host immune system self generated anti-inflammatory species (AIS, such as IL-10) may slowly grow to counter the inflammation, but such anti-inflammatory response could be too slow and may eventually reduce the host PIAPS levels well below the equilibrium levels that may result in immunoparalysis20. A number of therapeutic PIAPS control (immunomodulation) efforts have been reported in recent years4-12, however, the timing, type, and dosages of PIAPS suppressors/antagonists must be carefully monitored and controlled and this appears has not yet been systematically investigated, as PIAPS over-suppression or at wrong stage could result in delayed or incomplete pathogen elimination as well as vulnerability of host re-infection or secondary infections and related complications20. Finally, since the host’s mental/psychological status or modes (fear such as claustrophobia, anxiety, distress, depression, etc.) could also enhance host’s catecholamine/adrenaline level which in turn could boost APS/PIAPS levels, macrophage-cytokine self-amplifying loop MCSAL11, and inflammations22, and may result in mode-inflammation self-amplifying loop (MISAL), psychological counselling to the host thus also appear very important to improve host’s PIRP. Precise, fast, convenient, and reliable protocols of measuring and monitoring pathogen and key “Double-edged sword” PIAPS levels are essential not only to validate this model, but to utilize this model and its generated protocols for safe and effective therapeutic treatments of the infected hosts. Both pathogen and key PIAPS (e.g., IL-6) should be targeted as critical biomarkers ASAP.

As an example, in the case of COVID-19, while there appears lack of evidences of organ damages directly due to SARS-cov-2 virus23, excess levels or presences of certain PIAPS such as macrophages, neutrophils, or inflammatory cytokines (such as IL-6) were observed in multiple damaged organs in the autopsies and biopsies of the SARS-cov-2 virus infected hosts18, 24, i.e., the evidences imply the death of covid-19 infected hosts appears to be mainly due to immune-mediated rather than pathogen mediated organ injuries24. Additionally, the fact that the average viral levels of intensive care unit ICU (i.e., critically ill) patients were surprisingly lower than those non-ICU patients also seem to confirm that many ICU patients may have been already in stage II25. Though APS/PIAPS boosters (such as interferon INF-alpha, gamma immunoglobulin, convalescent plasma containing SARS-cov-2 antibodies collected from COVID-19 recovered patients) were recommended for COVID-19 treatments18, based on this proposed model, such treatments should be used only for those hosts with deficient or very weak immune responses and should be administered in stage I. PIAPS suppression via a series of inflammation antagonists, or cytokine elimination via blood purification18 appear useful for controlling CRS but they should be done after te in the stage II, i.e., the PIAPS level control are extremely critical for COVID-19 therapy. Most importantly, the levels (vital loads) of SARS-cov-2 and key PIAPS levels (particularly IL-6, macrophages, neutrophils, or certain immune system generated radicals) at appropriate time intervals need to be measured and monitored precisely and closely in order to monitor and determine the virus growth, virus elimination onset time te and the corresponding PIAPS equilibrium levels xe. For COVID-19 infection, it appears many host’s antibody IgG equilibrium level xeis about four times of its initial level x018. An approach on controlling dysregulated interferon INF-I production in COVID-19 infection19 appears potentially useful for validating or utilizing this model, again the interferon INF-I level surpression should be done after te and the level should not be over suppressed well below xe. Another example where this two-stage model might be applicable is the application of certain anti-oxidants (assuming Vitamin-C and Vitamins-E have such functions), where the anti-oxidant or radical scavengers appear necessary only during stage II, this is because pathogen supressing oxidative radicals may be needed in stage I. Finally, multiple host units can be utilized to obtain average values of all six parameters of this model (t0,, x0, te,xe, α, β) for a particular host group, and the average values could be useful for therapeutic treatments of an individual host that is the same or similar to the members of the group.

Summary

In summary, a normal distribution function containing two stages is proposed to model the Pathogen Infection Recovery Probability (PIRP) versus Proinflammatory Anti-pathogen Species (PIAPS) levels in a pathogen infected host. Based on this model, therapeutic strategies should be based on two stages: In the first stage, medical treatments may not be necessary for most hosts with normal immune responses as PIRP are expected to grow and remain at the maximum due to APS/PIAPS growing to and remaining at the equilibrium levels xe for certain periods, except supportive treatments are needed for oxygen deficiency syndromes. Hosts with weak or deficient anti-pathogen immune responses may need either pathogen suppressors or immuno-stimulators, however, timing, type, and dosages of both pathogen suppressors and immuno-stimulators are critical. In the second or the PIRP descending stage II due to PIAPS excessive or abnormal growth or levels, it is essential to control the PIAPS around their equilibrium levels xe via immuno-suppressors or inflammation antagonists. If pathogen levels are still high in stage II, then non-inflammatory immuno-stimulators may be applied. Again, timing, types, and dosages of therapeutic treatments are extremely critical depending on the PIRP stages and on pathogen/PIAPS levels. Precise and timely monitoring and controls of both pathogen and PIAPS levels are essential in order to fully utilize this model to reduce mortality. Increased survivability or reduced mortality could be potential key outcomes if this model is fully developed, well characterized, and implemented after innovative and carefully designed and controlled clinical trials. For instance, for current COVID-19 infections, immunomodulation via timely and precise monitoring and level controls of key biomarkers (including the virus, IL-6, macrophages and/or neutrophils, oxidative radical species,IL-10, etc) appear essential for clinical therapeutic strategies.

Acknowledgement

The author wishes to thank allergy specialist Dr. Kelly Maples for helpful discussions on cytokines/chemokines related hyper-inflammations in pathogen and food allergies, and to thank his colleague biochemistry professor Dr. Joseph Hall for helpful discussions on pathogen/anti-pathogens. The author also wishes to acknowledge his brother Mr. Honggang Sun on insightful discussions about “Happy Medium” doctrine of the Confucius philosophy that was established in China for thousands of years. The author particularly wishes to acknowledge and thank Dr. Donald Soles (MD, family medical practitioner) who has been busy taking care of many patients (including COVID-19 patients) and also graciously spent time to review and discuss with author on this article. The author wishes to express his deep appreciation and admiration to all medical staff (medical doctors, nurses, etc) worldwide who are risking their own lives trying to save lives of others in the current global humanity’s battle against covid-19!

Conflict of Interest :

The authors declare no any conflict of interest for publishing this article.

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