An interpretation of COVID-19 in Tokyo using a combination of SIR models

Analytical tool for COVID-19 using an SIR model equivalent to the chain reaction equation of infection

Insights from data analysis of existing cases are important to prevent future outbreaks of coronavirus disease 2019 (COVID-19). Although mathematical models are expected to be useful for this purpose, the adequacy of reproducibility of these models is difficult to confirm because they are based on hypotheses. For example, using the time variation of the parameter of the basic reproduction number for the time variation of complex data on the number of infected persons is a change of expression and does not capture the substance of the problem. We previously showed that the simplest Susceptible, Infected, Recovered (SIR) model alone, without any complex models, exhibits acceptable reproducibility. By clarifying the rationale for this reproducibility, quantifiable characteristics regarding the infection spread, such as the duration of the pandemic and the mechanism of occurrence of several large waves, can be uncovered and this can contribute to countermeasures. Here, we show this method equals the chain reaction equation for infection, allowing the parameters (infection rate, population) of the mathematical models to be extracted from the data. Once a model that reproduces the actual situation is determined, much of the information becomes apparent. As an example, we present three characteristics of the spread of infection effective in controlling COVID-19: the time of onset of infection, the rapidity of the spread, and the time to acquisition of herd immunity. Acquiring this information is likely to increase the predictive accuracy of the model.

Finite-time stability analysis and control of stochastic SIR epidemic model: A study of COVID-19

Finite-time stability analysis is a powerful tool for understanding the long-term behavior of epidemiological models and has been widely used to study the spread of infectious diseases such as COVID-19. In this paper, we present a finite-time stability analysis of a stochastic susceptible-infected-recovered (SIR) epidemic compartmental model with switching signals. The model includes a linear parameter variation (LPV) and switching system that represents the impact of external factors, such as changes in public health policies or seasonal variations, on the transmission rate of the disease. We use the Lyapunov stability theory to examine the long-term behavior of the model and determine conditions under which the disease is likely to die out or persist in the population. By taking advantage of the average dwell time method and Lyapunov functional (LF) method, and using novel inequality techniques the finite-time stability (FTS) criterion in linear matrix inequalities (LMIs) is developed. The finite-time stability of the resultant closed-loop system, with interval and linear parameter variation (LPV), is then guaranteed by state feedback controllers. By analyzing the modified SIR model with these interventions, we are able to examine the efficiency of different control measures and determine the most appropriate response to the COVID-19 pandemic and demonstrate the efficacy of the suggested strategy through simulation results.

An HLD Model for Tomato Bacterial Canker Focusing on Epidemics of the Pathogen Due to Cutting by Infected Scissors

A healthy, latently infected, diseased (HLD) plant model for botanical epidemics was defined for tomato bacterial canker (TBC) caused by the pathogenic plant bacteria, Clavibacter michiganensis subsp. michiganensis (Cmm). To estimate the infection probability parameter, inoculation experiments were conducted in which it was assumed that infection is transferred to healthy plants through contaminated scissors used to cut symptomless infected plants. The approximate concentration of Cmm in symptomless infected plants was 1 × 10⁶ cells/mL, and the probability of infection of healthy tomato plants was approximately 0.75 due to cutting with scissors soaked in a cell suspension of Cmm at 1 × 10⁶ cells/mL. Three different HLD models were developed by changing some parameters, and the D curve calculated by the developed HLD model A was quite similar to the curve of the proportion of diseased plants observed in fields that had a severe disease incidence. Under a simulation of disease incidence using this model, the basic reproduction number (R₀) was 2.6. However, if the infected scissors were disinfected using ethanol, R₀ was estimated as 0.3. The HLD model for TBC can be used to simulate the increasing number of diseased plants and the term of disease incidence.