THE EFFECT OF SUSCEPTIBILITY ON THE DYNAMICS OF EPIDEMICS

This is a temporal machine pre-translation slightly post-edited from the original text in this website

 

Current epidemiological models and theories are limited to epidemiological situations in which there is equal, total, and constant susceptibility for all individuals in a population.

The consideration of epidemiological situations in which individuals present a heterogeneous and variable susceptibility over time due to factors such as seasonality and changes in social behavior would significantly impact the way we currently understand epidemics.

Studying the possibility of a heterogeneous and variable susceptibility during the current coronavirus pandemic and its implications when implementing non-pharmaceutical interventions could help to understand epidemics’ dynamics better and optimize decisions to save the greatest number of possible lives in the least harmful possible way.

 

Theories of group immunity and current compartmental models such as the SIR (susceptible-infected-eliminated) and SEIR (susceptible-exposed-infected-eliminated) models are currently used to determine or theoretically predict the dynamics of epidemics of any infectious disease by calculating the reproductive number R.

Based on the mathematical theory of epidemics by Kermack and McKendrick1, these theories are limited to the case where, at the beginning of the epidemic, the entire population is susceptible, and all individuals are equally susceptible to the disease.

Most of the SIR and SEIR models, based on the model developed by Ronald Ross, William Hamer, and others2, are also limited to scenarios in which populations are homogeneously distributed.

According to these models, the basic reproductive number R0 would be determined by the average number of contacts of an individual , the transmissibility or average probability of infection of a susceptible individual during a contact T, and the average infection period τ.

R0 = c̅ * T * τ

Current models are limited to epidemiological situations in which a population is homogeneously susceptible and homogeneously distributed. These models consider that, for a given population, both the average number of contacts  and the transmissibility T are constant over time and, therefore, so will the basic reproductive number R0.

Different populations would have different basic reproductive numbers R0 depending on the variability of factors that affect both the average number of contacts and the transmissibility. These factors could include population density, different social behaviors, and lifestyle.

The current consideration as a constant of the basic reproductive number R0 implies that the effective reproductive number Re would only vary either as a function of the decrease in the proportion of the population without immunity to infection S

Re = R0 * S

or by introducing non-pharmaceutical interventions NPIs that could either reduce the average number of contacts in the population  or the transmissibility T. This reduction in the effective reproductive number Re would return to its original value once the NPIs are lifted.

More recent models consider heterogeneity in susceptibility to infection by the population3 and heterogeneity in the social contacts4. These models hypothesize how the consideration of a heterogeneous distribution in the way contacts are produced, and heterogeneities in population susceptibility could imply lower group immunity thresholds HIT than those theoretically calculated in the models that do not consider the effects of these factors. This is due to a possible heterogeneous decrease in the non-immunized population, producing a more rapid reduction in the susceptible population among the most contagious individuals who are more susceptible to becoming ill / spreading the disease in the early stages of the epidemic.

However, these models that consider heterogeneity in the susceptibility and social contacts among the population continue to consider susceptibility as a constant. This article considers the possible epidemiological situations in which individuals are not totally and equally susceptible to the disease, and the susceptibility is not constant and varies over time.

A heterogeneous susceptibility that varies in time st could mean that the transmissibility or average probability of infection of a susceptible individual during a contact was not constant either Tt.

The consideration, in certain epidemiological situations, of a transmissibility that is not constant and may vary in time Tt would imply certain variations concerning the current theories:

-A variable transmissibility Tt would mean that the reproductive number would, in turn, be variable Rt and different from the initial reproductive number R0.

The reproductive number Rt could decrease below one Rt <1 when there is a significant decrease in a population’s susceptibility st. A decrease in the susceptibility would cause a decrease in the transmissibility Tt that, together with the continuous reduction of the non-immune population, could reduce the Rt below one at any time. This would mean that the epidemic curve can bend without reaching the herd immunity threshold HIT calculated from a constant basic reproductive number R0 and without the introduction of non-pharmaceutical interventions NPIs.

-Measures that decrease the number of contacts  could, in turn, produce an increase in the susceptibility st, and with it in the transmissibility Tt.

Rt = c̅t * Tt * τt

When, as a result of these interventions, there would be an increase in the transmissibility Tt more significant than the reduction in average contacts , the reproductive number Rt would increase. Therefore, opposite to what current models consider, reducing the number of contacts would not inevitably reduce the reproductive number.
 

 

Susceptibility and its effect on transmissibility

 

Current models are limited to epidemiological situations in which where the initial susceptibility of all individuals to infection is considered equal, constant and total (100%), while the susceptibility of immunized individuals is considered non-existent (0%).

This theoretical simplification does not correspond to the empirical observations, where the susceptibility is never total (100%) in individuals without immunity nor non-existent (0%) after immunization. However, depending on the disease’s infection mechanism, this theoretical approach could be more or less far from what has been empirically observed so far.

Certain infections have developed mechanisms throughout evolution that can “trick” or largely elude the action of the immune system and are capable of infecting even perfectly healthy individuals with similar effectiveness. In this type of infection, a weakened immune system does not have to carry a greater risk of infection.

At the other extreme, certain types of infections do not usually affect people with a healthy immune system and good health. This is the case of opportunistic infections OIs. These infections occur almost exclusively and/or are more severe in people with a weak immune system.

Between both extremes, there are infections that, although they can affect all individuals, do so more efficiently and with greater risk in individuals with a weakened immune system or a worse state of health. For this kind of infection, under similar contact circumstances and similar viral loads, the probability of infection and/or the infection’s severity would vary depending on the individual’s susceptibility.

All the factors that could affect this variability in susceptibility are not yet known. These factors could include immunodeficiencies, the presence of comorbidities, age, obesity and a sedentary lifestyle, stress, depression and mental health in general, smoking, alcohol consumption, diet, lack of vitamins such as C and D, cross immunity or exposure to drops and sudden changes in temperature that could affect the stability of proteins that are involved in defense against infections.

Among the factors that can affect the average probability of contagion in case of contact or transmissibility T, could be the type or mode of contact, the viral load5, and the individual susceptibility.

In the current models and theories limited to epidemiological situations in which the susceptibility s is considered homogeneous, constant, and total, the transmissibility T is, in turn, considered constant. This is because it is assumed that social behavior among the population does not vary under normal circumstances and, therefore, neither will the number of contacts, the types of contacts, and the average viral loads.

However, in epidemiological situations in which individuals were not equally susceptible, the average susceptibility could vary over time st. Factors such as vitamin D levels, stress, depression, sedentary lifestyle, obesity, or exposure to sudden drops in temperature vary seasonally in most populations. This could increase the susceptibility in certain seasons of the year and reduce it in others and, with it, the transmissibility, producing a seasonality of the epidemic. A seasonal change in social behaviors, increasing or decreasing the average time of the population in open spaces in the open air, compared to the time spent in poorly ventilated indoor spaces, could also affect transmissibility due to the population’s exposure to higher viral loads.

A decrease or increase in susceptibility that affects the probability of increased risk and severity of the disease would also affect the reproductive number. An increase in severe infections could lead to an increase in the average viral load to which the rest of the population is exposed, which would cause an increase in transmissibility T6 and in the average duration of infection τ.

The imposition of non-pharmaceutical interventions NPIs on a population could also substantially affect individuals’ susceptibility in that population. These interventions could cause increases in sedentarism, obesity, stress, depression and reduce fresh air and sun exposure, affecting vitamin D levels and mental health. High exposure to air under low ventilation conditions with high viral load levels and re-inhalation of excreted air versus fresh air could also increase the susceptibility.

Currently, due to the assumption of a constant susceptibility S, transmissibility T, and duration of infection τ, it is considered that the introduction of non-pharmaceutical NPIs interventions that produce a decrease in the average number of contacts  inevitably entails a decrease in the reproductive number R.

R = c̅ * T * τ

However, when considering situations in which the susceptibility s and, with it, the transmissibility T and the average period of infection duration τ, may vary, the introduction of NPIs that produce a decrease in the average number of contacts could increase the reproductive number of the epidemic. The increase in the transmissibility T and/or duration of infection τ caused by the NPIs could be proportionally greater than the reduction in the number of contacts c̅. In that cases, the epidemic’s reproductive number will also increase.

Considering a variable transmissibility Tt and thus a reproductive number that is also variable Rt would imply that the effective reproductive number could decrease below one Rt <1 (an epidemic in decreasing phase) without the need to reach the herd immunity threshold HIT. A decrease in the reproductive number below one could occur at any stage of the epidemic. The joint effect of a decrease in transmissibility due to variations in susceptibility, whether seasonal or due to changes in social behavior and habits, and the increase of the population that has acquired some immunity could reduce the R below one at any point. The decline in the non-immune population would occur in a heterogeneous manner, decreasing to a greater degree among the more susceptible population.

Currently, susceptibility has been considered in every epidemiological situation as total and similar, both in individuals with a good state of health and in those with a more deteriorated health system. This consideration could have caused an overestimation of transmissibility and an underestimation of the number of contacts to which individuals in the population are exposed in those epidemic situations where susceptibility was variable and heterogeneous.

The usual approach for all kinds of epidemics is to consider theoretical scenarios practically aseptic with only a minimal number of contacts. If any individual is exposed to a contact and the necessary conditions are met, these theories assume that the individual will be infected. The transmissibility in these theoretical scenarios would depend only on the conditions and type of contact, considering all individuals equal and totally susceptible.

However, the opposite scenario appears to be observed for certain infections. Opportunistic agents, which are present in such a widespread way that they could be considered practically universal, attack the organism when the immune system and the state of health of an individual stop working correctly.

The number of contacts could be considered almost infinite for this kind of infections, and the average susceptibility close to 0 and extremely heterogeneous. In these situations, the total number of highly susceptible individuals could be more relevant in the total number of cases and their severity than the population’s average susceptibility.

Between both situations, all kinds of intermediate scenarios could be possible. With the same reproductive number R, there could be cases of infections with a very low number of contacts, but very transmissible, infections with a very high number of contacts, but very little transmissible, and infections with very heterogeneous transmissibility in which the reproductive number depends mainly from the highly susceptible portion of the population.

Consideration should also be given to the possibility that the total viral load to which an individual is exposed is much more relevant than the total number of contacts. It may be the case that, at low viral loads, only individuals with high susceptibility have a high probability of infection, whereas if the viral load is high enough, it will increase the probability of infection even in healthy individuals.

In those epidemics in which variations in susceptibility and transmissibility Tt are pronounced, the dynamics of the epidemic could be determined mainly by them, and not so much, as is currently being estimated, by variations in the number of contacts or by the proportion of the immune population. In these cases, measures aimed at reducing susceptibility could have a greater effect in reducing the total mortality of the epidemic than measures aimed at reducing contacts.

Assuming an “all or nothing” susceptibility, considering that the susceptibility is either 100% (S = 1) or 0% (S = 0), allows the consideration of the average susceptibility as an independent variable of the transmissibility or average probability of contagion in case of contact. Current theories consider that in the event of contact with a non-immune individual, the probability of contagion T does not decrease due to a possible lower susceptibility in healthy individuals T * 1 = T. In contact with an immune individual, the probability of contagion is considered null T * 0 = 0.

However, if intermediate susceptibility values are considered, it would not be possible to assume with certainty that the probability of contagion or transmissibility was directly proportional to the susceptibility. Susceptibility should be considered as one of the factors that affect transmissibility in a non-linear way, together with viral load and the kind or type of contact.

In the same way, the susceptibility would not go from 100% to zero after the development of immunological memory by any individual, but the decrease in susceptibility would be the result of the difference between the initial susceptibility, different for each individual, minus the susceptibility once acquired immune memory. After an infectious process or vaccination, the susceptibility would decrease more in those who were more susceptible, and therefore, the susceptibility could decrease in a heterogeneous way.

  

 

 Susceptibility in the coronavirus pandemic caused by SARS-CoV-2

 

The pandemic caused by SARS-CoV-2 and the multiple non-pharmaceutical interventions NPIs imposed worldwide have had and continue to have enormous repercussions for all the planet’s inhabitants.

To better understand the pandemic and save as many lives as possible, it seems necessary to study the possibility of a heterogeneous and variable susceptibility in populations to SARS-CoV2. To study how this would affect the way we understand the dynamics of the Covid-19 epidemics and consider the possible effects of different NPIs non-pharmaceutical measures and interventions on population susceptibility and effective reproductive numbers to be able to offer the best possible response.

When considering the assumption of a total, homogeneous and constant susceptibility for SARS-CoV-2 against a possible heterogeneous and variable susceptibility, it should be taken into account that:

 

  • a) The assumption of total, equal and constant susceptibility would imply that a curve with maximum growth would inevitably occur at the beginning of the epidemic that would gradually decrease until the threshold of group immunity was reached.

    Since it is currently considered that in every situation

    Re = R0 * S

    Re
    would reach its maximum value for t0 when 100% of the population does not present immunization.

    R0 = Rmax

    This does not seem to correspond with the empirical observation during the 
    SARS-CoV-2 pandemic, where the infection curve seems to reach its maximum growth after a turning point after the onset.

    A progressive increase in reproductive number until reaching its maximum in the early stages, but not at the beginning, could be explained by a gradual seasonal increase in susceptibility and thus in transmissibility until reaching the maximum when the number of non-immune people is still high.
  • b) The assumption of a total, equal and constant susceptibility would imply that the beginning of the epidemic in a particular population would depend exclusively on the moment of contact of the said population with the infection. The epidemic would begin at the moment when patient 0 or the first contacts occurred in that population. However, during the Covid-19 pandemic, the onset occurred at different moments between both hemispheres’ temperate zones despite globalization in mobility.

    A seasonal variation in susceptibility could explain a different time of onset of epidemics between both hemispheres.
  • c) The assumption of a total, equal and constant susceptibility would imply that the epidemic grows in a single wave until reaching the herd immunity threshold HIT and then recedes.

    However, the epidemics caused by SARS-CoV-2 seem to have occurred in several waves. It appears highly unlikely that the existence of multiple waves can be attributed to the introduction of non-pharmaceutical interventions NPIs since the several waves have occurred equally in diverse territories regardless of the introduction or not of these interventions. No data supports a correlation between reducing the reproductive number and the existence of any NPI, strictness, or moment of its introduction.
    The existence of variable susceptibility could explain the existence of several waves and constant variations in reproductive numbers that do not conform to current models. A variable transmissibility due to a change in susceptibility would imply the existence of a herd immunity threshold HIT that is also variable and dependent on the transmissibility at that time. Such a herd immunity threshold that varies as a function of the seasonal decrease in susceptibility would always be lower than the herd immunity threshold calculated for a totally susceptible population. The reproductive number determines the dynamics of epidemics, and susceptibility could be one of the most important determining factors of the reproductive number. The total number of individuals infected would be irrelevant.
  • d) The epidemic caused by SARS-CoV-2 seems to affect the most susceptible groups, with a clear correlation between mortality and factors that affect individuals’ susceptibility in a population, such as age, the existence of comorbidities, deficiencies in Vitamin D, obesity, and other factors.

     

  • e) SARS-CoV-2has a much lower secondary attack rate than other types of infections that could have similar transmission routes, such as measles or smallpox.

    A lower secondary attack rate could be explained by the existence of less efficient routes or modes of infection or by differences in viral loads. However, they could also be explained by differences in individuals’ susceptibility. SARS-CoV-2 could be much less efficient in infecting individuals with a healthy immune system and general health than other infections that present mechanisms that can effectively circumvent the action of a healthy immune system.



Conclusion

 

Current epidemiological models are limited to epidemiological situations in which the susceptibility of individuals in a population to infections is homogeneous, total, and constant.

The consideration of epidemiological situations in which the susceptibility is not homogeneous, total and constant, but heterogeneous and variable, would explain epidemics characterized by:

-A maximum growth different from the initial moment of the epidemic

-An onset moment of the seasonal epidemic independent of the moment of introduction of patient 0 or first contacts with the infection in a population.

-The existence of several seasonal waves and a reproductive number that varied differently from what would be expected due to the reduction of the susceptible population.

-Produce infections that cause disease more frequently and more seriously in individuals with factors that may affect susceptibility.

-They present a lower secondary attack rate than expected compared to other infections with similar contagion modes.

Contrary to what is currently assumed, non-pharmaceutical interventions, such as confinements, limitations to mobility, and masks, could cause an increase in reproductive numbers and excess mortality by causing an increase in transmissibility linked to an increased susceptibility of the population as a consequence of these measures.

With the information currently available, the characteristics of the coronavirus epidemics caused by SARS-CoV-2 could be explained by a heterogeneous and variable population susceptibility.

In order to reduce as much as possible the number of deaths due to the pandemic, it seems necessary to study the possibility of a heterogeneous and variable susceptibility in the SARS-CoV-2 pandemic and the possibility that the non-pharmaceutical interventions imposed so far could cause an increase in this susceptibility that exceeds its effect on the reduction of the number of contacts, thereby increasing the reproductive number and the total number of deaths.

 

 

 

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Raúl Pérez P.G. @corrnotcausa

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