Modeling Ebola Virus Dynamics by Colored Petri Nets

We develop techniques to translate deterministic cellular automata models into colored Petri nets based on an example of known cellular automata for modeling and mimicking Ebola virus dynamics. Cellular automata for Ebola virus dynamics use parametric specifications of rules that is peculiarity of the present study. The simulation results completely coincide with known results obtained via dedicated simulator. Having uniform language for models specification brings in advantages for models mutual transformations and simulation.

Fighting cancer with oncolytic viral therapy: identifying threshold parameters for success

We model interactions between cancer cells and free virus during oncolytic viral therapy. One of our main goals is to identify parameter regions which yield treatment failure or success. We show that the tumor size under therapy at a certain time is less than the tumor size without therapy. We determine the minimum tumor size by the therapy and parameter regions under which this minimum is attained. Our analysis shows there are two thresholds for the horizontal transmission rate: a "Control threshold", the threshold above which treatment is efficient, and an "optimum threshold'', the threshold beyond which infection prevalence reaches 100% and the tumor shrinks to its smallest size. Moreover, we explain how changes in the virulence level of the free virus alters the optimum threshold and the minimum tumor size. We identify a threshold for the virulence level of the virus and show how this threshold depends on timescale of virus dynamics. Our results suggests that when timescale of virus dynamics is fast, administration of a more virulent virus leads into more tumor reduction. When viral timescale is slow, a higher virulence will have drawbacks on the results, such as high amplitude oscillations. Furthermore, our numerical observation depicts fast and slow dynamics. Our numerical simulations indicate there exists a two-dimensional globally attracting surface that includes unstable manifold of the interior equilibrium. All solutions with positive initial conditions rapidly approach this two-dimensional attracting surface. In contrast, the trajectories on the attracting surface slowly tend to the periodic solution.

Timeline of SARS-CoV2 spread in Italy: results from an independent serological retesting

The massive emergence of COVID19 cases in the first phase of pandemic within an extremely short period of time suggest that an undetected earlier circulation of SARS-CoV-2 might have occurred, as documented by several papers in different countries, including a few that reported positive cases even earlier the first cases identified in Wuhan. Given the importance of this evidence, an independent evaluation was recommended. Here we report the results of SARS-CoV-2 antibodies blind retesting of blood samples collected in the prepandemic period in Italy, and in control samples collected one year before, by two independent centers. Results suggest the presence of SARS-CoV-2 antibodies in some samples collected in the prepandemic period, though the detection of IgM and/or IgG binding and neutralizing antibodies is strongly dependent on the different serological assays and thresholds employed, while being absent in control samples collected one year before. These findings highlight the importance of harmonizing serological assays for testing SARS-CoV-2 virus spreading and may contribute to a better understanding the future virus dynamics.

Detection of significant antiviral drug effects on COVID-19 with reasonable sample sizes in randomized controlled trials: A modeling study

Background Development of an effective antiviral drug for Coronavirus Disease 2019 (COVID-19) is a global health priority. Although several candidate drugs have been identified through in vitro and in vivo models, consistent and compelling evidence from clinical studies is limited. The lack of evidence from clinical trials may stem in part from the imperfect design of the trials. We investigated how clinical trials for antivirals need to be designed, especially focusing on the sample size in randomized controlled trials. Methods and findings A modeling study was conducted to help understand the reasons behind inconsistent clinical trial findings and to design better clinical trials. We first analyzed longitudinal viral load data for Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) without antiviral treatment by use of a within-host virus dynamics model. The fitted viral load was categorized into 3 different groups by a clustering approach. Comparison of the estimated parameters showed that the 3 distinct groups were characterized by different virus decay rates (p-value < 0.001). The mean decay rates were 1.17 d−1 (95% CI: 1.06 to 1.27 d−1), 0.777 d−1 (0.716 to 0.838 d−1), and 0.450 d−1 (0.378 to 0.522 d−1) for the 3 groups, respectively. Such heterogeneity in virus dynamics could be a confounding variable if it is associated with treatment allocation in compassionate use programs (i.e., observational studies). Subsequently, we mimicked randomized controlled trials of antivirals by simulation. An antiviral effect causing a 95% to 99% reduction in viral replication was added to the model. To be realistic, we assumed that randomization and treatment are initiated with some time lag after symptom onset. Using the duration of virus shedding as an outcome, the sample size to detect a statistically significant mean difference between the treatment and placebo groups (1:1 allocation) was 13,603 and 11,670 (when the antiviral effect was 95% and 99%, respectively) per group if all patients are enrolled regardless of timing of randomization. The sample size was reduced to 584 and 458 (when the antiviral effect was 95% and 99%, respectively) if only patients who are treated within 1 day of symptom onset are enrolled. We confirmed the sample size was similarly reduced when using cumulative viral load in log scale as an outcome. We used a conventional virus dynamics model, which may not fully reflect the detailed mechanisms of viral dynamics of SARS-CoV-2. The model needs to be calibrated in terms of both parameter settings and model structure, which would yield more reliable sample size calculation. Conclusions In this study, we found that estimated association in observational studies can be biased due to large heterogeneity in viral dynamics among infected individuals, and statistically significant effect in randomized controlled trials may be difficult to be detected due to small sample size. The sample size can be dramatically reduced by recruiting patients immediately after developing symptoms. We believe this is the first study investigated the study design of clinical trials for antiviral treatment using the viral dynamics model.