DIPs and IFN responses

An important way in which DIPs shape infection dynamics—particularly in IAV infection—is by triggering stronger innate immune responses [12,13]. Replication and transcription products derived from shortened DIP genomes are more potently detected by pattern recognition receptors (PRRs) such as retinoic acid–inducible gene I (RIG–I) than full–length wild type genomes [3,14,15]. Activation of these PRRs initiates signalling pathways that lead to expression of type I and III interferons (IFNs) and various pro–inflammatory cytokines, which are important for dendritic cell activation, fever, and shaping adaptive immunity [16], making DIPs critical actors in virus–host interactions [3]. DIPs have been shown to impact disease progression, act as antiviral and antitumour agents, and interfere with the efficacy of live attenuated vaccines (e.g., IAV [17], measles [18], rubella [19], and others [20]). These features have renewed interest in quantitative understanding of how DIPs alter infection dynamics and innate immunity [9,21].

Limitations of existing models

Several computational studies have explored within–host in vitro infection dynamics, yet critical gaps remain in integrating spatial resolution, immune responses, and viral diversity. Traditional ordinary differential equation (ODE) models, which represent infection and immune processes as changes in average population densities over time, have assumed that IFN reduces viral production by infected cells, decreases the likelihood of infection, or renders uninfected cells refractory to infection [22–24]. However, such models lack spatial information and implicitly assume uniform IFN protection across the tissue, even in cases where DIPs are included [4,25]. A spatial framework for in vitro infection dynamics was introduced by Howat et al. [26], who developed a stochastic, spatially explicit computational model of IFN responses. However, their model assumed instantaneous and global IFN diffusion. Moreover, in the previous model, once triggered, IFN did not decline, and cells that transitioned to the antiviral state remained permanently antiviral. However, others have shown that negative feedback loops can suppress IFN production and potentially revert a cell to a non-antiviral state [27]. In addition, the assumed delay before this transition was very long (95 hours), and the model did not incorporate DIPs, thereby potentially overlooking gradients, gradual activation dynamics, and DIP–IFN interactions. Other models have examined DIP–virus interactions at intracellular or population levels but without immune components such as IFN signalling, limiting their applicability to immune–competent systems [28–32]. Akpinar et al. linked single–cell dynamics to plaque–level outcomes using a spatial cellular automaton, showing how spread depends on initial co–infection with viruses and DIPs [9]; Baltes et al. [33] directly visualised DIP–virus co–transmission, distinguishing virus–only, DIP–only, and co–infected cells through different fluorescent markers; and Liang et al. [34] analysed such plaque images using binarisation and geometric segmentation. While each of these studies highlighted the spatial structure of viral particles spreading, none incorporated IFN responses, leaving open how innate immunity modulates DIP–virus dynamics.

To bridge these gaps, we developed a stochastic, cell–based computational model of in vitro infection dynamics, incorporating DIPs, IFN signalling, and spatial structure (see Fig 1 and Fig A in S1 Appendix for a schematic representation). Our framework is designed to explore how DIP–virus interactions generate heterogeneous plaque structures, how different dispersal routes (cell–to–cell spread, finite–rate diffusion, or rare long–range jumps) influence infection dynamics, and how IFN signalling—whether instantaneous or finite–rate diffusion—modulates immune protection. Our model can naturally reproduce ring–like and patchy plaque morphologies, as observed experimentally. Together, these aspects highlight how spatial structure, viral diversity, and innate immunity combine to shape infection outcomes.

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Fig 1. Schematic of the spatially explicit cell–based model.

The model represents cell interactions and infection dynamics on a hexagonal lattice, capturing spatial organisation and simulating realistic cell–to–cell spread together with IFN effects. Particles are shown as dark green for DIPs and dark red for viruses. Cell states are colour–coded: light red for virus–infected cells, light green for DIP–infected cells, yellow for cells co–infected by both viruses and DIPs, black for dead cells, blue for antiviral cells, grey for susceptible cells, and purple dots represent interferon (IFN). (a) Intracellular stage: each infected cell produces viruses, DIPs, and IFN over time. (b) Initial infection: infected cells release viruses and DIPs. Infected cells ultimately undergo cell death, so releasing particles at cell death captures the overall outcome in the simulation. IFN spreads radially to nearby cells within a finite spatial radius on the hexagonal lattice. (c) Local spread: viruses infect neighbouring susceptible cells. (d) Antiviral state and recovery: dead cells are replaced through regrowth. Figure adapted from Howat et al. [26]. Created in BioRender. Li, Y. (2026) https://BioRender.com/3i0o6bk.

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These multiple components are important because immune responses are inherently heterogeneous due to the structural complexity, diverse cell populations, and spatially varying microenvironments of human organs. For instance, in the lung, alveolar and bronchial regions exhibit distinct immune activities, with alveoli specialised for gas exchange and bronchi acting as physical barriers to infection [35–37]. Similarly, in the liver, during hepatitis B infection, the virus may exploit regions of low immune activity near central veins as “safe zones”, evading immune clearance and underscoring the need to include spatial and immune heterogeneity in infection models [38]. While in vivo complexity motivates the need for a more biologically refined and spatially granular infection model, in vitro systems provide a controlled setting to isolate and model key spatial–immune interactions, helping bridge the gap and guide future experiments.

Application to IAV

IAV is a highly contagious respiratory pathogen that causes seasonal epidemics and occasionally severe pandemics, providing a well–established system in which to study DIP–mediated modulation of infection [16,39]. We parameterised key infection and immune timing parameters—such as virus and DIP burst sizes, IFN delay, and IFN decay—using values derived from published IAV infection experiments [40,41] (these parameter choices are described in detail in the Methods section). With these values, our model captures the interaction between viral diversity and IFN under biologically grounded conditions. During replication, IAV DIPs arise from internal deletions in one of the virus’s eight RNA genome segments due to polymerase template switching. These DelVGs are typically 300–500 nt long, retaining 200 nt from each end of the full–length segment, which ranges from 890 nt (NS) to 2,341 nt (PB1/PB2) in length [42]. They serve as replication templates and are packaged into viruses, with most (in IAV) originating from polymerase–encoding segments [43,44].

Motivating questions

How does IFN spatial behaviour change under different diffusion assumptions—instantaneous versus finite–rate—and how does this influence immune protection? What happens if viruses, including DIPs, are not well–mixed, with some spreading across longer distances (e.g., influenced by convection, cilia movement, or virus particle shape [45]; we will call this “jumping” for simplicity) and generating infection patterns and innate immune responses akin to mucus–mediated dispersal in the respiratory tract? Is a larger DIP output always associated with a stronger IFN response? How do plaque dynamics—such as timing, peak virulence, and infected area—change with or without DIPs or IFN? How can we explain diverse plaque morphologies observed experimentally, including patchy structures, within a unified spatial–immune framework? These questions can be explored using our flexible online RShiny app, which allows users to visualise viral spread, IFN diffusion, and particle movement through dynamic videos; generate time series plots of cell states, virus counts, and IFN levels; and analyse how outcomes vary across different parameter settings (https://shiny-spatial-infection-app-production.up.railway.app/).

Model calibration

Calibration with DIP data in the absence of IFN.

We first included DIPs and disabled IFN signalling to calibrate our model, following the experimental conditions of Baltes et al. [33], who engineered fluorescently labelled DIPs of vesicular stomatitis virus (VSV). Fig 2 compares experimental data with simulation outputs under matched inoculation (DIP–green fluorescent protein (GFP) input of 1) and field size.

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Fig 2. Experimental plaque and matched stochastic simulations at 25 hpi.

Left: raw experimental image from [33] with DIP–GFP input of 1 (single initiating cell). Centre: pre–processed experimental image obtained by tessellating into hexagonal cells and applying automated colour classification, which resolves cell states even when colours are too faint to be distinguished by eye. This processed representation is used to count the number of cells in each state for quantitative comparison with simulations. Surrounding six panels: stochastic realisations under matched inoculation and field size, illustrating variability across runs. Colours: black, susceptible; red, virus–infected; green, DIP–infected; yellow, co–infected. Scale bar: 0.5 mm.

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To enable cell–by–cell quantification, the experimental image at 25 hours post-infection (hpi) (left) was pre–processed by tessellating the field into hexagonal cells and applying automated colour classification. This procedure identifies infection states (virus only, DIP only, or co–infected) even when colours are too faint to be distinguished by eye, yielding a representation from which the number of cells in each category can be counted. The resulting processed image (centre) forms the basis for quantitative comparison with the surrounding six stochastic replicates generated under a fixed parameter set (see Methods for details of parameter calibration).

Parameter values were estimated by scanning plausible ranges for virus and DIP spread (7–35 cells) and burst sizes (50–300 particles per lytic event). Each parameter combination was simulated 30 times, and averages were compared to experimental counts of virus–only, DIP–only, and co–infected cells. The best-fitting set (minimising the discrepancy between simulated and experimental cell counts across all three infection classes; see Table A in S1 Appendix for the selected parameter values) was selected for subsequent analyses.

Ring–like and patchy structures emerge in the absence of IFN.

Our model reproduces the ring–like and patchy plaque morphologies observed experimentally (see Methods and Table A in S1 Appendix for parameter values). These features arise naturally from particle–level stochastic dynamics, without requiring image binarisation or geometric segmentation as in other approaches [34]. Fig 2 illustrates this comparison: the left panel shows the experimental image, the centre panel the pre–processed tessellated representation, and the surrounding six panels representative stochastic simulations.

The central circular region is initially dominated by virus–infected cells (red). Due to the use of maximum–intensity projection, as in the experiment [33], the red signal persists for an extended period, reflecting the long half–life of red fluorescent protein (RFP)/GFP even after lysis and the presence of dead cells in the centre. In one sector of the advancing front, DIPs randomly seed a neighbouring region (green). Where these fronts overlap, a circumferential co–infected band appears (yellow).

The band is annular rather than a local patch, because the central red signal persists under maximum–intensity projection even after virus egress; the overlap therefore wraps around the circular core. An outer green rim forms because DIPs disperse farther than viruses. This mechanism explains the rings in Fig 2 and is consistent with the concentric–ring analysis and localised enrichment described in the experiment [33].

Beyond morphology, the model also captures the temporal dynamics of infection classes (Fig 3). Although variability across stochastic replicates is wide (grey 95% confidence intervals), the mean trajectories closely follow experimental trends, supporting the model’s ability to reproduce both spatial and temporal aspects of DIP–virus interactions. The main discrepancies arise from stochasticity in whether initial DIP foci encounter virus and establish coinfection. When coinfection occurs early, both viruses and DIPs generate large bursts of progeny and sustain spread; when DIPs fail to meet virus, they quickly fade because they cannot replicate on their own.

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Fig 3. Model validation against experimental data from [33] in the absence of IFN.

Cell counts are shown on a logarithmic scale for (top left) virion–infected cells, (top right) DIP–infected cells, (bottom left) co–infected cells, and (bottom right) susceptible cells at four time points (7, 13, 19, and 25 hpi). Solid lines represent experimental data, dashed lines show the mean of stochastic simulations with identical parameters, and grey shading indicates the 95% interval across these simulations.

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Calibration with IFN responses in the absence of DIPs.

After calibrating spatial heterogeneity using the Baltes et al. [33] dataset, we next validated IFN–mediated responses using the experiments of Howat et al. [26], who analysed Herpes simplex virus 1 (HSV–1) infections in Madin-Darby bovine kidney (MDBK) (IFN–competent) and Vero (IFN–deficient) cells [26,46–49]. As their model uses an antiviral delay and effective infection terms rather than explicit IFN or virus half–life parameters, we likewise did not estimate separate IFN or virus half–life terms in this calibration step. We set the antiviral delay time to 95 h, consistent with Howat et al. [26], which ensured that our framework captured IFN activation kinetics (Fig 4; see Methods and Table B in S1 Appendix for parameter values), providing support for the model framework, with good agreement with the experimental data.

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Fig 4. Comparison of model simulations with experimental data from Howat et al. [26].

The percentage of dead cells over time is shown, with simulation outputs (red line, triangles) closely matching experimental measurements (black triangles). Simulations used a time step of 1 h, and the virion infection probability was re–fitted to account for the susceptibility of MDBK cells to HSV infection, giving parameter estimates [0.07, 0.11], [88, 101] h, and [1.2, 1.8]. Experiments were initiated with an inoculum of 50 plaque-forming units (PFU), where the PFU represents a statistical average of plaques expected across repeated assays. Each simulation curve represents the mean of 30 independent realisations. This validates the parameterisation of our framework against the dataset of Howat et al. [26].

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Dynamics of the full DIP–IFN model

Emergent properties of the full model

Intermediate relative DIP yield maximises peak IFN.

To investigate how variation in DIP production affects the spatial dynamics of IFN activation, we varied the relative DIP yield , defined as the DIP:virus output ratio upon lysis of a virus–infected cell. In our model, ranged from 2 to 32, corresponding to DIP burst sizes of 100–1600 PFU/cell, assuming a fixed virus burst size of 50 PFU/cell based on experimental data and the baseline model [22]. We implemented global IFN signalling and restricted virus dispersal to cell–to–cell spread, using parameter values consistent with previous studies [46,50,51]. Simulations were run for 500 hours, with hourly measurements of plaque size, IFN concentration, and infection composition.

We observed a nonmonotonic relationship between and the IFN response, with a clear peak at an intermediate value of , where the IFN concentration reached its maximum (Fig 5, left panel). Beyond this point, further increases in DIP output led to diminished IFN activation. This critical value coincided with the highest number of cells co–infected by both viruses and DIPs, which in our model are the strongest IFN producers—releasing ten times more IFN than virus–only infected cells and twice as much as DIP–only infected cells. At this yield, the virus–only infected population was minimal, while DIP–only infections were widespread. This configuration promoted efficient DIP dissemination, followed by sufficient virus co–infection to generate a large number of double–infected cells.

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Fig 5. IFN dynamics across values of the relative DIP yield .

Left: IFN time series for increasing . The response rises and then declines, with a maximum at approximately (thick red trace). Right: Peak IFN versus across stochastic replicates. Blue points show replicates. The generalised additive model (GAM) fit (red, with 95% confidence band) and the LOESS fit (green, dashed) agree on a non-monotone pattern with an intermediate optimum (vertical dotted line). Simulation times reflect plaque expansion in an idealised in vitro epithelial monolayer.

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To make sure that the observed nonmonotone optimum is not a random outcome of stochastic variability, we further analysed replicate simulations using GAMs with 95% confidence interval and LOESS smoothing (Fig 5, right panel). Both methods consistently recovered an interior maximum in peak IFN across the explored values of the . The exact location of this maximum may shift with the spline dimension and smoothness penalty, but the qualitative pattern is robust: peak IFN is highest at intermediate , rather than increasing monotonically with .

We obtained a similar result under a continuous Gaussian release formulation (Fig E in S1 Appendix): peak IFN still occurred at an intermediate relative DIP yield rather than at the scanned extremes. However, under continuous release, the IFN–yield curve could show additional fine structure, for example a small low-yield shoulder, a local maximum, or a less clearly defined peak, depending on the release-distribution parameters and the number of replicates per condition. Our supplementary analysis suggests that this is likely related to changes in the timing and extent of virus–DIP co-infection over time, while the main pattern remains unchanged. Additional details are provided in the Supplementary Information and in the GitHub repository.

The observed peak arises from the balance between two opposing regimes (Fig 5):

1. (1) At low , DIP production was insufficient to support widespread DIP–only infections or effective co–infection. Consequently, the number of double–infected cells remained low, and total IFN output stayed limited despite virus spread.
2. (2) At high , DIPs spread rapidly, initiating early co–infection and triggering early IFN release. Due to the exponential sensitivity of infection probability P_infection to IFN levels, both DIPs and viruses quickly lost the ability to infect new cells, curtailing further spread and reducing cumulative IFN production.

Thus, an intermediate peak value of marks the most effective balance between particle production, co–infection timing, and IFN–mediated feedback. Values above or below this point disrupt the coordination between DIP seeding and virus co–infection, ultimately leading to reduced IFN activation.

Minimal fractions of free–jump particles strongly enhance spread

To assess sensitivity to long–range transmission (e.g., mucus–mediated dispersal), we simulated infections with free–jump fractions from 1% to 90% in the absence of IFN; the remaining transmission occurred by cell–to–cell spread. As shown in Fig C in S1 Appendix (top left), even 1% free jumps accelerated plaque expansion and altered morphology, with satellite plaques visible by t = 150 h.

Under global IFN signalling, free jumps had little effect because uniform antiviral activation removed any advantage of escaping local immune zones (Fig C in S1 Appendix). In contrast, under local IFN signalling, even 1% free jumps had a strong impact.

Fig 6 shows these outcomes in detail. Despite an earlier and higher antiviral fraction with 1% free jumps (blue curves) than with no jumps (cyan), the dead–cell fraction (red curves) spikes much earlier and reaches peaks comparable to the no–jump IFN range 10 condition (orange). The reason is the response delay : free jumps establish foci beyond the contemporaneous IFN front, allowing damage to accumulate before local antiviral containment is established.

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Fig 6. IFN range and spreading mode jointly shape plaque dynamics.

Thin red and blue curves denote simulations with 1% free–jump transmission for both viruses and DIPs (remaining 99% cell–to–cell). Red gradients (left y–axis) show dead–cell fractions for IFN ranges 1–10, where free jumps generate earlier and higher peaks (arrow, “Peak, 1% jump”). Blue gradients (right y–axis) show antiviral–cell fractions for the same simulations, rising earlier and to higher levels than the no–jump control (labelled “1% jump, Antiviral”). Thick orange (dead) and thick cyan (antiviral) curves indicate IFN range 10 controls without free jumps; the orange curve peaks later (arrow, “Peak, no jump control”) and at similar magnitude to the red curves, while the cyan curve shows a slower antiviral rise (labelled “No jump control”). The three insets (top right) show spatial patterns at t = 120 h: left, IFN range 1 with 1% free jumps yields scattered secondary plaques; middle, IFN range 10 with 1% free jumps forms larger but more contained plaques; right, IFN range 10 with no free jumps produces a single compact plaque. Inset colours: black, susceptible/uninfected; grey, dead; red, virus–infected; green, DIP–infected; yellow, co–infected; blue, antiviral. Simulation times reflect plaque expansion in an idealised in vitro epithelial monolayer.

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Increasing the IFN range provides stronger control: as the range grows, dead–cell peaks (red, orange) are reduced and delayed. The antiviral trajectories (blue, cyan), however, remain similar across ranges because their timing is largely set by . Thus, outcomes depend mainly on how many new foci are seeded outside the current IFN domain rather than on modest differences in IFN radius. Jumps that land beyond the front are particularly consequential, and DIPs tend to jump farther than viruses, increasing the likelihood of such events. Each new focus is rapidly encircled by antiviral cells and then declines, but repeated seeding during the delay accumulates damage.

Caveats and model limitations

Overall model structure

We start with a hexagonal lattice structure to represent the confluent epithelial monolayer, because epithelial cells adhere tightly during in vitro growth (Fig 1; [26,63]). This lattice–based, spatially explicit framework allows us to model individual cell interactions and capture the localised nature of infection, which cannot be approximated by homogeneous mixing or continuum diffusion models [64–67]. Cell connections are weighted by distance on the lattice, while the infection probabilities associated with these connections are updated hourly to capture the changing dynamics. The model defines seven cell states: susceptible, infected by both DIPs and viruses, infected by DIPs only, infected by viruses only, antiviral, dead, and regrowth (see Fig A in S1 Appendix for the schematic of model execution and explicit model transition rules). Simulations extend over several hundred hours to capture plaque expansion across the epithelial monolayer in vitro, rather than the duration of an acute influenza infection in a host.

Initial conditions

At the start of a simulation, all cells are susceptible. The standard grid size is 360 × 360 cells, matching the experimental field size in Howat et al. [26], while reduced 50 × 50 grids are used for small–scale tests. Viruses and DIPs are seeded by assigning initial particle counts to randomly selected cells, with and varying by experimental condition.

Infection probability and IFN response

For A549 cells (which mount a robust IFN response to infection), the probability of infection for both viruses and DIPs is given by

where as adapted from Howat et al. [26], I is the IFN concentration, and  is the suppression factor. The IFN concentration is updated hourly under either local or global signalling.

Guided by experimental observations, we initialised simulations so that virus-only infected cells produce IFN at a baseline level, DIP-only infected cells produce approximately 5-fold more IFN than virus-only infected cells, and virus–DIP co-infected cells produce approximately 10-fold more IFN than virus-only infected cells. These fold differences reflect experimental observations that defective viral genomes are stronger activators of innate immune signalling [3,32]. The absolute IFN production rate can be adjusted in the online model interface.

In the model, infected cells begin producing IFN after a delay following infection. The IFN release time is drawn from a normal distribution with mean 5 h and standard deviation 1 h [68,69]. After this delay, each IFN-producing cell contributes to the total IFN concentration at every simulation step. The IFN concentration is updated according to

where I(t) is the IFN concentration at time t, N_IFN is the number of cells actively producing IFN, is the simulation time step ( h in our simulations), and R is the IFN production rate per cell. IFN concentration is represented as a scaled variable rather than an absolute biochemical concentration, so the baseline IFN production rate is normalised to R = 1 IFN unit per cell per hour [26]. Different infected cell classes produce IFN at different relative rates. Virus-only infected cells produce IFN at the baseline rate (R = 1), DIP-only infected cells produce approximately five times more IFN (5R = 5), and virus–DIP co-infected cells produce approximately ten times more IFN (10R = 10). These fold differences reflect experimental observations that defective viral genomes can induce stronger innate immune signalling. The scale (fold-change) parameter values can be adjusted in the accompanying online app [3,32].

IFN induces an antiviral state in neighbouring cells after a mean delay of h (standard deviation 3 h), with a half–life of 3 h [40,41]. Antiviral cells cannot be infected, creating local barriers to spread. In this setting, the virus is sensitive to the IFN response it provokes.

We implemented two distinct IFN signalling modes:

1. [1] Finite–range/local signalling, where IFN spreads diffusively over a limited radius, creating spatial gradients of protection.
   Under this mode, IFN secreted by infected cells influences neighbouring cells within a finite spatial radius on the hexagonal lattice. The IFN radius determines how far the antiviral signal spreads from each producing cell. This parameter is user-adjustable in the online model interface. In the default configuration used in the simulations presented here, the IFN interaction radius is set to 10 lattice units [70], meaning that IFN can influence all cells within ten lattice distances from the producing cell.
2. [2] Global/instantaneous signalling, where all cells share a uniform IFN concentration at each time step, corresponding to rapid homogenisation in well–mixed environments.
   For Vero cells (which lack an IFN response), with all IFN–related parameters set to zero. Vero cells therefore remain susceptible throughout infection and never enter the antiviral state [26].

Infection cycle and particle release

In the default model, which we use as a simple baseline based on the available data and the calibration in Fig 4 [26], particle release is represented as a combined event that includes both budding over the infection period and burst-like release associated with infected-cell death; the corresponding results are shown in Figs 5 and 6.

Cells infected by viruses or co–infected progress to lysis after an average of 12 h (standard deviation 3 h), releasing progeny. Virus burst size follows a normal distribution with mean 50 PFU per cell, while DIP burst size averages 100 PFU per cell. DIP–only infected cells do not lyse but may convert to the antiviral state. Released particles disperse to neighbouring sites, with local particle density modulating the chance of successful entry.

In this default model, “cell death” represents the combined event of progeny release and subsequent cell death. Influenza virions are primarily released by budding from the cell surface, but infected cells ultimately undergo cell death. The model therefore represents this sequence as a single transition from the infected to the dead state, consistent with the base model tested on experimental data [26]; see Fig 4.

We also examined a continuous Gaussian release formulation, in which particle release is distributed over time; the corresponding results are shown in Figs E and F in S1 Appendix. In the Gaussian formulation, release is centred at 0.5T for each cell’s infection duration T, with standard deviation 0.25T (6.0 h and 3.0 h, respectively, for a mean lysis time of 12.0 h; details are given in the Supplementary Information). These values were used to represent gradual particle release over the infection period, to reflect reports that influenza virus budding occurs over several hours rather than as a single instantaneous event [30,71]. Comparing these two formulations tests whether the main qualitative results depend on how particle release is distributed over time.

For intracellular competition, the DIP-to-virion ratio was defined for each infected cell from the numbers of extracellular DIPs and virions present at that cell at the time of entry. This entry ratio was then used to adjust progeny production at budding. Specifically, DIP amplification was scaled by the parameter , based on [5], such that cells receiving a higher DIP-to-virion ratio produced fewer standard virions and more DIPs.

Cell lysis and regrowth

Cell regrowth occurs when a dead cell is adjacent to a healthy neighbour. Regrowth time follows a normal distribution with mean 24 h (standard deviation 6 h). Regrown cells revert to a susceptible state, allowing repeated infection.

In our framework, progeny particles released at lysis can spread in three distinct ways that mirror in vitro culture conditions: (i) Cell–to–cell spread, which approximates experiments where an agarose or methylcellulose overlay is applied to restrict particles to direct local contacts; (ii) Finite–range dispersal, where particles move over several cell diameters, modelling partial diffusion in semi–restricted environments; and (iii) Unrestricted jumps, where particles disperse freely across the culture dish without an overlay, as in standard liquid medium, allowing stochastic long–range seeding of secondary plaques.

Feedback dynamics

The cycle of infection, lysis, IFN release, antiviral conversion, cell death, and regrowth generates a feedback loop that drives complex spatial and temporal infection dynamics. This structure provides the foundation for model calibration and experimental comparison described in results.