key: cord-0826076-465tsmmn
authors: Makhoul, Monia; Abu-Hijleh, Farah; Ayoub, Houssein H.; Seedat, Shaheen; Chemaitelly, Hiam; Abu-Raddad, Laith J.
title: Modeling the population-level impact of treatment on COVID-19 disease and SARS-CoV-2 transmission
date: 2022-04-16
journal: Epidemics
DOI: 10.1016/j.epidem.2022.100567
sha: 864a40d2d5407ee859a6abfc8558434189d609c8
doc_id: 826076
cord_uid: 465tsmmn

Different COVID-19 treatment candidates are under development, and some are becoming available including two promising drugs from Merck and Pfizer. This study provides conceptual frameworks for the effects of three types of treatments, both therapeutic and prophylactic, and to investigate their population-level impact, to inform drug development, licensure, decision-making, and implementation. Different drug efficacies were assessed using an age-structured mathematical model describing SARS-CoV-2 transmission and disease progression, with application to the United States as an illustrative example. Severe and critical infection treatment reduces progression to COVID-19 severe and critical disease and death with small number of treatments needed to avert one disease or death. Post-exposure prophylaxis treatment had a large impact on flattening the epidemic curve, with large reductions in infection, disease, and death, but the impact was strongly age dependent. Pre-exposure prophylaxis treatment had the best impact and effectiveness, with immense reductions in infection, disease, and death, driven by the robust control of infection transmission. Effectiveness of both pre-exposure and post-exposure prophylaxis treatments was disproportionally larger when a larger segment of the population was targeted than a specific age group. Additional downstream potential effects of treatment, beyond the primary outcome, enhance the population-level impact of both treatments. COVID-19 treatments are an important modality in controlling SARS-CoV-2 disease burden. Different types of treatment act synergistically for a larger impact, for these treatments and vaccination.

The pandemic caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection and associated Coronavirus Disease 2019 continue to present a global health challenge 1 , a burden to healthcare systems 2 , and a cause of economic disruption 3 . While vaccination remains the fundamental solution for controlling and containing the pandemic 4 , there are challenges to increasing vaccine coverage 5, 6 , and emergence of variants of concern could reduce vaccine efficacy 7-10 . SARS-CoV-2 treatments may thus offer an additional tool to help control this pandemic and to reduce its disease burden, such as two promising drugs from J o u r n a l P r e -p r o o f Merck and Pfizer [11] [12] [13] . Clinical trials are being conducted to assess efficacy and safety of various types of SARS-CoV-2/COVID-19 treatments, with different mechanisms of action [14] [15] [16] [17] .

Experience with other infectious diseases, such as HIV 18, 19 and hepatitis C virus 20, 21 , have demonstrated the utility of treatment programs as integral components of efforts to reduce infection transmission and associated disease burden.

Assessment of the potential population-level impact of candidate drug treatments through mathematical modeling is a component of drug development, licensure, decision-making, and treatment cost administration, just as it is for vaccines 4, [22] [23] [24] [25] [26] [27] . In particular, modeling can be used to define the drug's key preferred product characteristics, by estimating levels of efficacy and mechanisms of action that are necessary to generate the desired population-level impact and to identify priority populations for optimal effectiveness, thereby providing early guidance to developers, manufacturers, and regulators about candidates that are likely to maximize public health impact and cost-effectiveness, as is typically done for vaccines 24, 28, 29 .

Against this background, the objectives of this study were to provide conceptual frameworks for potential effects of three types of treatments, both therapeutic and/or prophylactic, and to investigate the population-level impact of these treatment types. The overarching goal of the study was to provide scientific evidence that could inform and accelerate drug development and licensure, at a critical time for such development. The modeling was applied to the United States population as a relevant and illustrative example.

Age-structured deterministic compartmental models were constructed, building on our earlier calibrated models 4,30-38 of SARS-CoV-2 transmission dynamics to include effects of potential treatments against this infection. The resulting models were based on current understanding of SARS-CoV-2 natural history and epidemiology and consisted of sets of coupled nonlinear differential equations that stratified the population into compartments according to age group (0-9, 10-19, …, ≥80 years), infection status, infection stage (mild (including also asymptomatic), severe, and critical), COVID-19 disease stage (severe, critical), and treatment status.

Following a latency duration, infected individuals were modeled to develop mild (or asymptomatic) infection followed by recovery, or severe infection followed by severe disease and then recovery, or critical infection followed by critical disease and either recovery or mortality. Recovered individuals were assumed to be protected against reinfection [39] [40] [41] [42] . Mixing between individuals in different age groups was described by an age-mixing matrix that allows a variety of mixing patterns. Assortativeness in mixing was assumed not to vary regardless of the presence or absence of public health restrictions. The degree of assortativeness was based on model fitting in mathematical modeling studies for SARS-CoV-2 infection 33, 34, 36 . All infections were assumed equally infectious regardless of the presence or absence of symptoms.

Detailed descriptions of each treatment model and associated schematic diagram are found in the Supplementary Materials (SM). Models were coded and analyzed using MATLAB R2019a 43 .

Details of model parameters, values, and justifications are in Table S2 .

J o u r n a l P r e -p r o o f

Impacts of three types of potential treatments were investigated: i) severe and critical infection treatment, ii) post-exposure prophylactic treatment, and iii) pre-exposure prophylactic treatment. Table 1 lists these types of treatment and their considered drug efficacies (that is product characteristics of candidate drugs), and Figures S1-S3 provide conceptual and schematic illustrations of their effects and mechanisms of action.

We assumed that severe and critical infection treatment was administered to only persons with severe or critical SARS-CoV-2 infection. Treatment thwarts development of severe or critical COVID-19 disease with drug efficacy SC DE (the primary efficacy outcome for this treatment).

However, those successfully treated were assumed not to have acquired protective immunity against reinfection, as such treatment may interfere with development of natural immunity. For those who progress to critical disease despite treatment, treatment is still beneficial in preventing disease mortality, with efficacy M DE . This treatment thus reduces development of full-blown disease, or reduces disease mortality of those with critical disease.

We further assumed that post-exposure prophylactic treatment was administered to persons who had been exposed to SARS-CoV-2 to prevent further infection progression with efficacy

(the primary efficacy outcome for this treatment). Therefore, the mechanism of action is similar to that of other post-exposure prophylactic treatments, such as those for HIV 44 , influenza 45 , and hepatitis B virus (HBV) 46 . However, those successfully treated were assumed not to acquire protective immunity against reinfection. For those in whom infection progresses despite treatment, treatment is still beneficial in preventing severe or critical disease, with efficacy Pre-exposure prophylactic treatment was assumed to have a mechanism of action similar to that of pre-exposure prophylactic ("PrEP") treatment for HIV 47, 48 or malaria 49 

To provide an example and proof-of-concept of the population-level impact of different treatment types, models were applied generically to a SARS-CoV-2 epidemic in a national population of the size and age structure of the U.S. population. Several scenarios were investigated for drug efficacies of each treatment type. These are summarized in Table 1 . In all scenarios, and to assess optimal treatment potential, treatment was assumed to be scaled up at a fixed rate to reach the targeted coverage of 80% in the specific target population at the end of the epidemic cycle.

Two sets of analyses were conducted for each scenario, one assuming a basic reproduction number 0 3 R  , that is assuming a natural course of infection in the absence of social and physical distancing restrictions 50, 51 , as one purpose of the treatments is to avoid such restrictions, and one assuming 0 1.5 R  , that is in concert with social and physical distancing restrictions.

Since the overall level of SARS-CoV-2 ever infection in the global population remains relatively low 52,53 , baseline analyses were conducted assuming a generic case in which population immunity remains limited (set at 0%) at the onset of treatment interventions. Higher levels of population immunity were investigated in sensitivity analyses. Analyses were also conducted by targeting each treatment type to a specific age group, to investigate the age-dependency of the treatment impact. This was done by targeting the treatment to only one specific age group in the population at a time, while evaluating the impact of this age-targeted treatment in the entire population.

Population-level impact of different types of treatment was assessed by quantifying incidence, cumulative incidence, and reduction in incidence of infections, severe disease cases, critical disease cases, and deaths arising despite treatment, compared to the counter-factual scenario of no treatment. Treatment impact was further assessed by quantifying effectiveness, defined as the number of treatments (treated persons) needed to avert one infection or one adverse disease outcome (ratio of the number of treatments relative to that of averted outcomes). The latter measure is essentially a measure of cost-effectiveness, but with no costs included.

Sensitivity analyses were conducted to assess the impact of different values of the basic reproduction number (3 and 6), proportion of the population ever infected at onset of treatment (20% and 50%), treatment coverage (50% and 80%), and treatment efficacy (50% and 80%).

Treatment effectiveness was also assessed by combining these values to yield the worst-case scenario and best-case scenario for treatment effectiveness. Additional univariable sensitivity analyses were performed to assess the range of outcomes by varying treatment efficacy over five-hundred model runs. In each run, Latin Hypercube sampling 54,55 was applied to select the primary treatment efficacy of each treatment type within ±30% of its baseline value. The resulting distributions for treatment impact across all 500 runs were used to calculate predicted means and ranges of outcomes.

Severe and critical infection treatment at 50% SC DE  reduced the incidence peak of severe disease by 39.5%, critical disease by 39.4%, and mortality by 39.8% ( Figure 1A -C). Numbers of treatments needed to avert one severe disease case, one critical disease case, and one death were 2.5, 9.9, and 31.0, respectively. There was strong age-dependence in treatment effectiveness with fewer treatments needed to avert one death at older age ( Figure 1D ). If, in addition to Additional potential efficacies of this treatment in reducing severe and critical disease ( Table 2 .

The results of the sensitivity analyses in assessing the range of outcomes by varying the primary treatment efficacy of each treatment type are shown in Figure S11 . With the tepid scale-up of vaccination worldwide 56 , vaccine hesitancy 5,6,57 , and the circulation of variants of concern with evidence for lower vaccine efficacy against them 7-10,41,58 , it is possible that this pandemic may last for years, highlighting the need for treatment as an additional strategy to complement vaccination and to reduce disease burden. The emergence of variants of concern with higher infectiousness 7-10,41,58 indicates that 0 R of this infection is probably increasing, leading to a higher threshold for herd immunity 59-62 . Perhaps as much as 90% of the population would have to be immune, thereby complicating efforts to fully control the infection. It seems not likely that vaccine coverage will reach the level needed for herd immunity, or that real-world vaccine effectiveness will ever be high enough, given the expanding number of variants of concern and waning of vaccine protection [8] [9] [10] 64, 65 . This further affirms the need to continue development of novel treatments per the three types modeled in this study.

While treatments are likely to be developed for a specific primary outcome, such as efficacy in reducing COVID-19 severity and mortality or acquisition of infection, they may also have other downstream auxiliary effects (Table 1) , just as for vaccines that can reduce infectiousness and change disease progression, in addition to preventing acquisition of infection 4, 25, 66 . The presence J o u r n a l P r e -p r o o f of these additional effects is supported by our growing knowledge of the natural history and immunology of this infection 67 . In the present study, we investigated the impact of such additional effects (note, for example, Figure 1 and Figures S5 and S8) . Their large impact suggests that the population-level impact of each treatment could be even higher than expected, considering only the primary treatment outcome. This further supports the role of treatment as an important approach to confronting this pandemic.

One finding of this study is that treatment coverage is an important factor in its impact, with disproportionally larger impact for higher coverage-the indirect effects on onward transmission are larger the more closely the population approaches the threshold of 0 1 R  . Treatment effectiveness was optimized when a larger segment of the population was targeted than when treatment was restricted to a specific age group. For instance, only 1.6 pre-exposure prophylactic treatments would be needed to avert one infection if this treatment achieves coverage of 80% in the wider population, but ≥2 treatments would be needed by targeting only a specific age group ( Figure 5 ).

The impact of treatment was investigated for a generic population to provide a "proof-ofconcept" for the population-level impact of investigated types of treatment. Actual impact, however, can also depend on the epidemic phase in each country. The conceptual frameworks and modeling tools provided here can be applied to generate specific predictions for specific countries, factoring the actual epidemic phase at any given time.

Model estimations are contingent on the validity and generalizability of input data and parameters. While we used available evidence for SARS-CoV-2 natural history and J o u r n a l P r e -p r o o f epidemiology, our understanding of its epidemiology is still evolving. We provided a conceptual framework for the potential effects of each type of treatment, but actual effects of each specific treatment will be clarified only after each drug product is developed and tested. Development of novel treatments may not also necessarily translate into broad use, as costs and logistics could be barriers to benefits from any novel COVID-19 intervention, especially in resource-limited settings. Despite these limitations, the developed models are sufficiently sophisticated to factor different potential effects for each type of treatment, for broad future use and applications, but still parsimonious enough to be tailored to available data.

In The number of treatments that are needed for each age group to avert one A) infection, B) severe disease case, C) critical disease case, and D) death at 50% PostEP DE  in the absence of social and physical distancing restrictions. Results assuming social and physical distancing are found in Figure S7 . Detailed description of these scenarios can be found in Table 1 . Figure S8 . Results assuming social and physical distancing restrictions are found in Figure S9 . Detailed description of these scenarios can be found in Table 1 . Figure S10 . Detailed description of these scenarios can be found in Table 1 . Figure S4 . Detailed description of these scenarios can be found in Table 1. J o u r n a l P r e -p r o o f Figure S5 . Results assuming social and physical distancing restrictions ( 0 3.0 R  reduced to 0 1. 5 R  ) are found in Figure S6 . Detailed description of these scenarios can be found in Table 1. J o u r n a l P r e -p r o o f R  ) are found in Figure S7 . Detailed description of these scenarios can be found in Table 1 .

J o u r n a l P r e -p r o o f Figure S8 . Results assuming social and physical distancing restrictions ( 0 3.0 R  reduced to 0 1.5 R  ) are found in Figure S9 . Detailed description of these scenarios can be found in Table 1 .

J o u r n a l P r e -p r o o f R  ) are found in Figure S10 . Detailed description of these scenarios can be found in Table 1 .

J o u r n a l P r e -p r o o f Table 2 . Sensitivity analyses assessing the effectiveness of three types of SARS-CoV-2 treatments. For each treatment type, effectiveness is assessed at two different values of the basic reproduction number (3 and 6), proportion of the population ever infected at onset of treatment (20% and 50%), treatment coverage (50% and 80%), and treatment efficacy (50% and 80%). Treatment effectiveness is also assessed by combining these values to yield the worst-case scenario and best-case scenario for treatment effectiveness.

a Combination of parameter values to yield the worst-case scenario for treatment effectiveness. b Combination of parameter values to yield the best-case scenario for treatment effectiveness.

M.M. constructed, coded, and parameterized the mathematical model, conducted the analyses and co-wrote the first draft of the paper. F.A. supported model construction and parametrization.

L.J.A. conceived and led the design of the study, construct, and parameterization of the mathematical model, and co-wrote the first draft of the article. All authors contributed to discussion and interpretation of the results and to the writing of the manuscript. All authors have read and approved the final manuscript.

The authors declare no conflict of interests.

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The authors are grateful for support provided by the Biomedical Research Program and the Biostatistics, Epidemiology, and Biomathematics Research Core, both at Weill Cornell Medicine-Qatar. This publication was made possible by extension of models developed through NPRP grant number 9-040-3-008 (Principal investigator: LJA) and NPRP grant number 12S-

The authors declare no competing interests.

All data are available within the manuscript and its supplementary materials. The codes programmed in MATLAB can be obtained by contacting the authors. Figure S4 . Detailed description of these scenarios can be found in Table  1 . Results including additional potential efficacies of 50% SC DE  and 50% P DE  are found in Figure S5 . Results assuming social and physical distancing restrictions are found in Figure S6 . Detailed description of these scenarios can be found in Table 1 .