KINETIC-TYPE REACTIONS: A VERSATILE REACTION-NETWORK FRAMEWORK FOR AIDS DISEASE TRANSMISSION

G. Sonnino^1,2, P. Peeters¹, P. Nardone¹, M.J. Conti³, A. Coppola⁴, G. Tetè⁵, C. Genovesi⁶, G. Barassi⁷ and P. Conti^8,9

¹ Université Libre de Bruxelles (ULB), Brussels, Belgium;
² International SOLVAY Institute for Physics and Chemistry, Brussels, Belgium;
³ Medical School “La Sapienza”, Rome, Italy;
⁴ Private Practice, Studio Armando Coppola, Corso Garibaldi 246, Naples, Italy;
⁵ Department of Human Sciences, “Sustainable Blue Economy and One Health”-XL Cycle, Law, and Economics “Leonardo da Vinci”, UNIDAV, Telematic University, Chieti, Italy;
⁶ Dentistry, Private Practice, Chieti-Pescara, Italy;
⁷ Physiotherapy, Rehabilitation and Reeducation Training Center (CeFiRR), School of Medicine and Health Sciences, University “Gabriele d’Annunzio” of Chieti-Pescara, Chieti, Italy;
⁸ University “Gabriele d’Annunzio” of Chieti/Pescara, Chieti, Italy;
⁹ Tufts University, School of Medicine, Boston, USA.

*Correspondence to:
Giorgio Sonnino,
Université Libre de Bruxelles (ULB),
Brussels, Belgium.
e-mail: giorgio.sonnino@ulb.be

Received: 02 March, 2026 Accepted: 01 September, 2026

ISSN 2279-5855 print / 3103-7364 [online] Copyright 2026 © by Biolife Publisher This publication and/or article is for individual use only and may not be further reproduced without written permission from the copyright holder. Unauthorized reproduction may result in financial and other penalties. Disclosure: All authors report no conflicts of interest relevant to this article.

ABSTRACT

Human immunodeficiency virus (HIV) can cause acquired immune deficiency syndrome (AIDS), compromise the immune system, and damage the central nervous system by activating macrophage cells such as microglia to cause the release of neurotoxic mediators, and synaptic and neuronal damage with neurodegeneration. Its transmission and progression can be studied using reaction networks and kinetic models that describe the interaction between the virus, target cells, and the immune response over time. This study aims to investigate the spread and temporal evolution of HIV by applying the kinetic-type reaction (KTR) formalism as a mechanistic framework for modelling disease transmission and progression. This approach builds on the successful application of KTR to SARS-CoV-2 (Severe Acute Respiratory Syndrome Coronavirus 2) dynamics, while explicitly accounting for the profound biological and epidemiological differences between the two infections. Whereas SARS-CoV-2 is characterized by relatively rapid epidemic dynamics, HIV involves acute and chronic infectious phases, diagnosis, antiretroviral treatment, progression to AIDS, and mortality over widely separated time scales. These features make HIV a particularly relevant test case for assessing the flexibility and general applicability of the KTR framework. Within KTR, the elementary processes governing disease evolution are represented as reaction channels, in analogy with chemical kinetics, and the corresponding dynamical equations are derived from the associated kinetic fluxes. In contrast to purely phenomenological compartmental models, this formulation emphasizes the underlying mechanisms responsible for transitions among biological states and provides a natural framework for incorporating nonlinear interactions, inhibitory effects, treatment, finite transition times, and conservation laws. We first recall how KTR has been employed to describe SARS-CoV-2 infection and its associated processes, including lockdown, quarantine, and hospitalization, with intervention measures represented through inhibitor-like mechanisms and hospital capacity through a Michaelis-Menten-type formulation. We then extend the same formalism to HIV by constructing a reaction network that accounts for susceptible, infected, diagnosed, and treated populations, as well as acute and chronic infection, disease progression, and mortality. Numerical simulations illustrate the resulting HIV dynamics and demonstrate how the KTR framework can accommodate processes operating across markedly different biological time scales. Rather than proposing a universal model for infectious diseases, this work establishes KTR as a general mechanistic modelling strategy and demonstrates its applicability to HIV transmission and progression. More broadly, the results suggest that KTR, and its possible reaction-transport extensions, may provide a versatile framework for investigating other complex multistage biological processes, including cancer-cell invasion and metastatic dissemination.

KEYWORDS: Kinetic-type reaction, infectious-disease modelling, SARS-CoV-2, HIV/AIDS, reaction network, time delay, neuroinflammation, metastasis

*Note: The equations are visible in the manuscript PDF

INTRODUCTION

Human immunodeficiency virus (HIV) is the virus that can cause acquired immune deficiency syndrome (AIDS), an advanced stage of HIV infection when the immune system is severely compromised (1). The reduced immune defenses in AIDS can also lead to the onset of opportunistic infections or certain cancers. HIV compromises the immune system and can damage the central nervous system, especially when the infection is untreated. The virus can reach the central nervous system and cause cognitive impairment, difficulty concentrating, impairments in memory, movement, or behavior, and chronic fatigue syndrome, a serious illness that causes persistent fatigue with marked asthenia (2). HIV can damage the nervous system even without directly infecting neurons; the virus can reach the brain quickly and infect microglia, causing neuroinflammation. Activated microglia produce inflammatory cytokines and other compounds that can damage neuronal function, promote oxidative stress and mitochondrial dysfunction, and alter the function of astrocytes. The release of neurotoxic mediators causes synaptic and neuronal damage that can lead to neurodegeneration. In advanced AIDS, opportunistic infections and tumors can also occur, with the onset or worsening of pre-existing neurodegeneration. Neurodegeneration may be associated with AIDS as a consequence of HIV infection of the central nervous system and may manifest as HIV-associated neurocognitive disorder.

HIV transmission and progression can be studied using reaction networks, in which each step represents a process, and its rate can be described through kinetic parameters. Cell-free HIV infects the target cell, producing new viruses. The speed of these transformations depends on factors such as the amount of virus, the number of target cells, and the immune response. Kinetic models therefore allow us to describe how the amount of virus and infected cells changes over time. A versatile network-based framework for AIDS transmission can be linked to the study of HIV transmission and progression, which can be described using reaction networks, in which each step represents a process whose rate can be determined through kinetic parameters (3). Mathematical modelling has long played a central role in understanding the transmission, persistence, and control of infectious diseases. Classical compartmental approaches, originating from the susceptible-infected-recovered (SIR) paradigm, describe epidemic dynamics by partitioning a population into epidemiologically meaningful states and specifying the transition rates between them (4-7). These models, together with their numerous extensions, remain fundamental tools in mathematical epidemiology. However, as increasingly complex biological and epidemiological processes are considered, a complementary question naturally arises: can the macroscopic evolution equations be derived systematically from a set of elementary processes describing the interactions and transitions among the populations involved? The kinetic-type reaction (KTR) formalism addresses this question by adopting the language and mathematical structure of chemical reaction kinetics. Within this framework, epidemiological or biological populations are regarded as kinetic species, whereas processes such as infection, disease progression, inhibition, treatment, recovery, and mortality are represented as elementary reaction channels. The macroscopic evolution equations then emerge directly from the kinetic fluxes associated with these reactions. This approach was originally introduced for modelling the spread and control of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) (8-10). However, it should be noted that the main transmission routes for HIV and SARS-CoV-2 are different. HIV is transmitted primarily through blood, some body fluids, and sexual contact, while SARS-CoV-2 is transmitted through respiratory droplets and physical proximity. For instance, a simple infection process may be represented as

Eq. [1]

with the corresponding mass-action flux

Eq. [2]

More complex disease dynamics can subsequently be constructed by combining appropriate elementary reaction channels rather than postulating the complete system of evolution equations from the outset. In this way, the structure of the mathematical model remains directly connected to the biological mechanisms that generate the observed population dynamics.

The purpose of this study is to investigate the applicability of the KTR formalism to HIV transmission and disease progression. Our approach builds on previous applications of KTR to SARS-CoV-2, for which the formalism proved capable of describing a range of epidemiological processes and intervention mechanisms. Here, we examine whether the same reaction-based modelling philosophy can be extended to HIV while explicitly accounting for the profound biological and epidemiological differences between the two infections. The objective is therefore not to transfer a SARS-CoV-2 model directly to HIV, but rather to retain the underlying KTR methodology and construct a reaction network appropriate to the specific mechanisms governing HIV transmission and progression.

SARS-CoV-2 and HIV provide two particularly instructive and biologically distinct examples for assessing the flexibility of the KTR framework. SARS-CoV-2 is characterized by comparatively rapid epidemic dynamics, with infection, disease progression, recovery, and mortality generally occurring over relatively short time scales. HIV, by contrast, evolves over much longer and widely separated time scales and involves a sequence of clinically and epidemiologically distinct stages, including acute and chronic infection, diagnosis, antiretroviral treatment, progression to AIDS, and mortality. HIV currently has no definitive cure. Instead, we can talk about people on treatment or with an undetectable viral load. Consequently, the application of KTR to HIV requires a substantially different reaction network capable of representing these multiple stages and their associated transitions.

Mathematical modelling has long contributed to the understanding of HIV transmission and evaluating prevention and treatment strategies (6, 8, 9). Of particular importance is characterizing the temporal evolution of susceptible, infected, diagnosed, and treated populations and the mechanisms responsible for transitions among these states. Such information is essential for understanding how HIV propagates through a population, identifying the factors that influence its persistence, and assessing the potential effects of prevention and therapeutic interventions. At the same time, HIV dynamics remain challenging to describe quantitatively because transmission and disease progression depend on the complex interplay among viral dynamics, treatment effects, epidemiological conditions, and heterogeneous individual behaviour. These characteristics make HIV a valuable test case for the KTR formalism. By expressing infection, diagnosis, treatment, disease progression, and mortality as interconnected reaction channels, the framework provides a systematic route from the underlying biological processes to the corresponding population-level evolution equations. The comparison with the previous SARS-CoV-2 application is therefore intended to demonstrate that the same KTR philosophy can accommodate infectious diseases governed by markedly different biological mechanisms and temporal scales.

The principal aim of this work is thus to establish KTR as a flexible mechanistic strategy for modelling HIV transmission and progression, rather than to propose a universal model applicable without modification to different infectious diseases. Finally, the reaction-network philosophy underlying KTR is not necessarily restricted to infectious-disease dynamics. When combined with spatial transport mechanisms, the same conceptual framework may provide a natural basis for describing other multistage biological processes in which interacting populations undergo local transitions while simultaneously migrating through space. A particularly relevant example is tumour-cell invasion and metastatic dissemination, for which reaction-diffusion and multiscale mathematical models already constitute an important area of mathematical oncology (10). From this broader perspective, the present application to HIV also serves to illustrate the potential of KTR as a general framework for connecting elementary biological mechanisms with macroscopic population dynamics. This brief report introduces the general principles underlying the KTR formalism. We present the main results obtained by applying the KTR framework to HIV transmission and progression within the population, with particular emphasis on its potential relevance for prevention and treatment strategies. We briefly discuss a possible extension of the KTR approach to the study of cancer invasion and present concluding remarks.

THE KINETIC-TYPE REACTION PRINCIPLE

The KTR methodology was initially developed in the context of SARS-CoV-2 epidemic modelling (11,12). Its central idea is to represent the mechanisms responsible for disease evolution as elementary kinetic processes and subsequently derive the macroscopic dynamical equations from the corresponding reaction fluxes. Consider a set of biological populations

Eq. [3]

A generic elementary process can be represented as

Eq. [4]

where n_ir^– and n_ir⁺ denote the populations participating in and produced by reaction r, respectively. Defining the stoichiometric change

Eq. [5]

the deterministic dynamics takes the general form

Eq. [6]

where J__r is the kinetic flux associated with reaction r. For elementary mass-action processes,

Eq. [7]

Eq. [6] highlights the main feature of the KTR construction: the differential equations are consequences of the reaction network rather than the starting point of the model. The framework can be extended naturally to finite transition times. A delayed kinetic flux may depend on a previous state,

Eq. [8]

or, equivalently, transit populations can be introduced to preserve explicit population bookkeeping. Intervention processes may likewise be represented as competing or inhibitor-like reaction channels, while capacity limitations can generate nonlinear saturating kinetics. Conservation laws emerge directly from the stoichiometric structure. If each elementary process only redistributes individuals among the states, the

Eq. [9]

is conserved and

Eq. [10]

KTR therefore provides a modular construction: changing the biological problem amounts primarily to changing the elementary reaction network, rather than abandoning the mathematical framework. This construction is closely related in spirit to chemical reaction-network theory, while retaining an epidemiological interpretation of the kinetic species and reaction rates. An important advantage is its modularity: additional biological mechanisms can be incorporated by introducing new reaction channels without changing the basic modelling principle.

TWO ILLUSTRATIVE APPLICATIONS

SARS-CoV-2

In this subsection, we briefly review the successful application of the KTR formalism to the modelling of SARS-CoV-2 transmission and discuss its effectiveness in describing the associated epidemic dynamics. Building on these results, we apply the same KTR framework to HIV, while accounting for the markedly different biological and epidemiological characteristics of the two infections. Specifically, we investigate the temporal evolution of susceptible, HIV-infected, and treated populations, together with the mechanisms governing HIV transmission and disease progression within the population. The KTR approach was developed for the spread of SARS-CoV-2 in references 11 and 12, following a stochastic KTR formulation developed in reference 13 (11-13). At its simplest level, the infection process is represented by

Eq. [11]

supplemented by recovery and mortality processes. A distinctive feature of the KTR formulation is that containment measures are incorporated as dynamical mechanisms. In particular, lockdown and quarantine can be represented through inhibitor-like reactions that remove susceptible and infected individuals from the actively interacting populations (8,9). Hospital-mediated recovery was described using an analogy with Michaelis-Menten kinetics, with hospital capacity playing a catalyst-like role, while finite recovery and mortality times were introduced explicitly. The resulting model was compared with epidemiological data from Belgium, France, and Germany and reproduced the main features of the observed epidemic evolution, including the development of a second epidemic wave (8). As an example, Figure 1 provides an illustrative numerical solution of the corresponding kinetic equations, illustrating the evolution of the infected population. In particular, the figure compares the theoretical predictions for the number of infected individuals in France with empirical data provided by Santé publique France (8) (Fig.1). The evolution of the other compartments, together with comparisons with experimental data for France and corresponding analyses for other countries, can be found in reference 11 (11). The purpose of this study is not to repeat the detailed epidemiological analysis of references no.8 and 9, but to show how comparatively complex epidemic dynamics emerge from a network of elementary kinetic processes.

Fig. l. Illustrative numerical solution of the KTR model for SARS-CoV-2 dynamics. This figure shows the comparison between the theoretical prediction for French infected people and real data provided by the database Santé Publique France (8).

HIV/AIDS

HIV provides a substantially different test of the KTR philosophy. It is important to emphasize that the use of the same KTR formalism does not imply that HIV and SARS-CoV-2 share the same biological mechanism of transmission. SARS-CoV-2 is transmitted predominantly through exposure to infectious respiratory particles, whereas HIV transmission requires specific exposure to infectious body fluids, occurring principally through sexual transmission, blood exposure (including the sharing of contaminated injection equipment), and vertical transmission. Accordingly, the kinetic interaction S+I à 2I should be interpreted as an effective transmission event rather than as literal physical contact between a susceptible and an infected individual. In the HIV model, the coefficients b_a and b_c therefore incorporate both the frequency of transmission-relevant exposures and the probability of transmission per exposure during the acute and chronic stages, respectively. The elementary reaction notation provides a common mathematical representation of transmission while allowing the underlying biological mechanisms and kinetic parameters to remain disease-specific. Unlike an acute SIR-type infection, untreated HIV infection is characterized by distinct acute and chronic phases and by progression over much longer characteristic time scales. Moreover, antiretroviral therapy profoundly modifies both disease progression and transmission. These features have motivated an extensive literature on mathematical models of HIV transmission and intervention (6,8,9). Within the KTR framework proposed here, the disease history is represented schematically by

Eq. [12]

supplemented by diagnosis and treatment pathways,

Eq. [13]

Transmission itself is represented by

Eq. [14a]

Eq. [14b]

With departments Q and T denoting the diagnosed individuals awaiting effective ART and the individuals receiving effective ART, respectively. A and D stand for the individuals in the AIDS stage and the cumulative AIDS-related deaths, respectively. We emphasize that for HIV, we do not describe b_aSI_a simply as a “contact rate”. It should be interpreted as an effective transmission flux, where b_a incorporates both the frequency of transmission-relevant exposures and the probability of transmission per such exposure. Schematically, b_i ~ c_ip_i where c_ii represents the rate of epidemiologically relevant exposures and p_i the transmission probability per exposure for infection stage i. Thus, J_a^HIV = ba SIa_a should be read as:

Susceptible individuals x Acutely infected individuals x Effective rate of transmission-relevant exposure

This distinction is particularly important because b_a and b_c can differ partly because infectiousness varies substantially across HIV stages.  The characteristic time scales are very different from those of SARS-CoV-2. The acute phase evolves on a scale of weeks, whereas untreated chronic infection and progression may extend over years. These features can be incorporated into KTR through delayed reaction channels or equivalent transit populations. Figure 2 shows the numerical solutions of the dynamical equations governing the above Kinetic Reaction Network [12-14b] (Fig.2). These solutions correspond to the following values of the parameters: β_a=6.72yr ^-1, β_c=1.72yr^-1, γ_a=4.14yr^-1, γ_c=0.125yr^-1, η_a=0.10yr^-1, η_c=025yr^-1, δ=52.0yr^-1, ρ=0.0 (0= stable ART), μ_A=1.0yr^-1, τ_a=0.242 yr, τ_Q=0.25yr, τ_Q=0.25yr, τ_T=0.0192yr, τ_c= 8.0yr, and τ_A = 1.0yr. A detailed analysis of the kinetic reaction network applied to AIDS can be found in reference number 16 (16).

Fig. 2. Illustrative numerical solution of the delayed KTR model for HIV/AIDS of the dynamical equations given in Eq. [16].  These equations correspond to the kinetic reaction network [12-14b]. The markedly separated time scales distinguish the chronic dynamics from the rapid epidemic evolution of SARS-CoV-2.

The basic reproduction number can be obtained by linearizing the infected subsystem about the disease-free equilibrium and applying the next-generation matrix method (14,15). The basic reproduction number R₀ represents the average number of secondary infections generated by a typical infected individual introduced into an otherwise susceptible population. Thus, R₀ > 1 indicates that the infection can invade and spread, whereas R₀ <1 indicates that sustained transmission is not expected. In the present HIV model, R₀ contains the combined contributions to transmission from the acute and chronic untreated infectious stages. It is possible to show that, for a normalized susceptible population and stable effective ART, the kinetic structure leads to a reproduction threshold of the form (16)

Eq. [15]

where parameters g_a, h_a, g_c, and h_c characterize the competing kinetic pathways through which individuals leave the acute and chronic untreated infectious states (16). More precisely,

g_a is the progression rate from acute to chronic HIV infection.

h_a is the diagnosis (or detection) rate during the acute phase.

g_c is the progression rate from acute to chronic HIV infection

h_c is the diagnosis (or detection) rate during the chronic phase.

The disease-free equilibrium (DFE) is the state of the mathematical model in which the infection is absent from the population and the system is at equilibrium. At the disease-free equilibrium of the normalized system, S*=1.

In Eq. [15], the first contribution,

Eq. [16]

represents secondary infections generated during acute untreated infection. The denominator g_a+h_a reflects the competition between progression to chronic infection and diagnosis during the acute phase. The second contribution,

Eq. [17]

represents secondary infections generated during untreated chronic infection. The factor g_a/(g_a+h_a) is the fraction (or, in the competing exponential-rate interpretation, the probability) of acutely infected individuals who progress to the chronic infectious state before being diagnosed. The factor 1/(g_c+h_c) is the corresponding mean residence time in the untreated chronic infectious state. Thus, R₀=R_a+R_c expresses the total transmission potential as the sum of the acute and chronic infectious contributions. Eq. [15] illustrates an important advantage of the kinetic representation: the epidemic threshold can be interpreted as the cumulative yield of different infection pathways, each weighted by its characteristic residence time and competing removal processes. Consequently, the total rates of departure from the acute and chronic untreated infectious compartments are, respectively, [16]

Eq.[18]

The corresponding mean residence times, under the competing-rate approximation, are therefore,

Eq. [19]

BEYOND VIRAL INFECTION: A PERSPECTIVE ON CANCER INVASION

A possible extension of the KTR methodology concerns cancer progression and metastatic dissemination. Mathematical oncology already provides a substantial body of work in which tumor growth, cellular interactions, migration, invasion, and treatment are described using reaction-diffusion, continuum, and multiscale approaches (13,17). Metastasis involves a sequence of biologically distinct processes, including local invasion, intravasation, survival and transport in the circulation, extravasation, and eventual colonization of distant tissues. This multistage structure suggests a possible reaction-network representation in which the different cellular populations are treated as kinetic states. The examples above suggest that KTR need not be restricted to infectious disease. A particularly interesting direction concerns cancer progression and metastatic dissemination. Metastasis is intrinsically a multistage process involving local tumor-cell proliferation, phenotypic changes, invasion of surrounding tissue, intravasation into blood or lymphatic vessels, transport through the circulation, extravasation, and colonization of distant organs. Mathematical models of cancer invasion already demonstrate the importance of combining cell proliferation and interactions with the tumor microenvironment with spatial migration and reaction-diffusion processes. A KTR representation could associate these stages with kinetic populations, for example,

Eq. [20]

where the states may represent, schematically, primary-tumor cells, locally invasive cells, circulating tumour cells, extravasated cells, and established metastatic populations. Unlike the spatially homogeneous epidemic examples considered above, however, metastatic invasion necessarily requires transport. A natural extension would therefore combine KTR with diffusion, chemotaxis, or other migration mechanisms:

Eq. [21]

In this reaction-transport formulation, the KTR terms describe transformations and interactions among cellular states, whereas the spatial operator describes their migration through tissues. Establishing such a model for a specific cancer type would require experimental identification of the relevant cellular states, reaction pathways, spatial mechanisms, and kinetic parameters. We therefore regard Eq. [21] as a perspective for future investigation rather than as a validated model of metastasis.

CONCLUSIONS

The main objective of this study has been to extend the KTR formalism to the modelling of HIV transmission and disease progression, building on its previous successful application to SARS-CoV-2 epidemic dynamics. The underlying principle of KTR is to identify the elementary biological and epidemiological processes governing disease evolution, represent them as kinetic reaction channels, assign appropriate biologically meaningful fluxes, and derive the corresponding macroscopic evolution equations from the resulting reaction network. The applications to SARS-CoV-2 and HIV demonstrate the flexibility of this framework across markedly different epidemiological and biological regimes. In the case of SARS-CoV-2, the relevant reaction network describes comparatively rapid processes involving infection, intervention measures, hospitalization, recovery, and mortality. HIV, by contrast, requires a substantially different and more complex multistage description, encompassing acute and chronic infection, diagnosis, antiretroviral treatment, progression to AIDS, and mortality over widely separated time scales. Thus, although the two infections differ profoundly in their natural history and characteristic time scales, they can be described within the same mathematical framework by appropriately modifying the structure of the underlying reaction network. In particular, the application of KTR to HIV provides a systematic means of describing the temporal evolution of susceptible, infected, diagnosed, and treated populations and of relating these population-level dynamics to the elementary mechanisms responsible for HIV transmission and disease progression. Characterizing these processes is important for improving our understanding of the evolution and persistence of HIV within a population and may provide a useful basis for evaluating prevention, control, and treatment strategies. At the same time, the considerable variability associated with viral dynamics, treatment response, and individual behavior introduces uncertainties that remain challenging to quantify. Within this context, the KTR formalism offers a mechanistically transparent framework in which such effects can be incorporated progressively as additional reaction channels or modifications of the corresponding kinetic fluxes. The significance of the present results therefore lies not only in the specific application to HIV, but also in demonstrating that the same reaction-based mathematical language can accommodate infectious diseases characterized by very different biological mechanisms and temporal scales. KTR should not be regarded as a replacement for established compartmental, stochastic, or reaction–diffusion approaches. Rather, it provides a complementary organizing principle through which complex dynamical models can be constructed systematically from clearly identified elementary processes, while maintaining a direct connection between the mathematical formulation and the underlying biological mechanisms. Finally, the reaction-network philosophy of KTR may have applications beyond infectious-disease epidemiology. Coupling kinetic-type reactions with spatial transport could provide a natural extension for systems in which biological transitions are accompanied by migration, diffusion, or invasion. Cancer-cell invasion and metastatic dissemination represent particularly relevant examples of such multistage processes. From this broader perspective, the present extension from SARS-CoV-2 to HIV provides a further step toward establishing KTR as a versatile mechanistic framework for the mathematical description of complex biological systems.

Conflict of interest

The authors declare that they have no conflict of interest.

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