3% of the confirmed cases of COVID-19 infection in South Korea are associated with the worship service that was organized on February 9 in the Shincheonji Church of Jesus in Daegu. We aim to evaluate the effects of mass infection in South Korea and assess the preventive control intervention. Method: Using openly available data of daily cumulative confirmed cases and deaths, the basic and effective reproduction numbers was estimated using a modified susceptible-exposed-infectedrecovered-type epidemic model. Results: The basic reproduction number was estimated to be R 0 ¼ 1:77. The effective reproduction number increased approximately 20 times after the mass infections from the 31 st patient, which was confirmed on February 9 in the Shincheonji Church of Jesus, Daegu. However, the effective reproduction number decreased to less than unity after February 28 owing to the implementation of high-level preventive control interventions in South Korea, coupled with voluntary prevention actions by citizens. Conclusion: Preventive action and control intervention were successfully established in South Korea.

In this work, we have developed a Coxian-distributed SEIR model when incorporating an empirical incubation period. We show that the global dynamics are completely determined by a basic reproduction number. An application of the Coxian-distributed SEIR model using data of an empirical incubation period is explored. The model may be useful for resolving the realistic intrinsic parts in classical epidemic models since Coxian distribution approximately converges to any distribution.

Inflammatory bowel disease (IBD) is a disease that causes inflammation throughout the digestive tract. Repeated inflammation and frequent relapses cause intestinal damage and expose the patient to a higher risk. In this work, we proposed an immune therapy model for effective treatment strategy through mathematical modeling for patients with IBD. We evaluated the ability of the patient's immune system to recover during treatment. For this, we defined the interval of healthy individual, and examined the frequency of compartments such as T cells and cytokines considered in the model maintain the normal state. Based on the fact that each patient has a unique immune system, we have shown at the same drug works differently, depending on the individual immune system characteristics for every patient. It is known that IBD is related to an imbalance between pro-and anti-inflammatory cytokines as the cause of the disease. So the ratios of pro-to anti-inflammatory cytokines are used as an indicator of patient's condition and inflammation status in various diseases. We compared the ratios of pro-to anti-inflammatory cytokine according to patient's individual immune system and drugs. Since the effects of biological drugs are highly dependent on the patient's own immune system, it is essential to define the immune system status before selecting and using a biological drug.

Combination therapy with immune checkpoint blockade and ionizing irradiation therapy (IR) generates a synergistic effect to inhibit tumor growth better than either therapy does alone. We modeled the tumor-immune interactions occurring during combined IT and IR based on the published data from Deng et al. The mathematical model considered programmed cell death protein 1 and programmed death ligand 1, to quantify data fitting and global sensitivity of critical parameters. Fitting of data from control, IR and IT samples was conducted to verify the synergistic effect of a combination therapy consisting of IR and IT. Our approach using the model showed that an increase in the expression level of PD-1 and PD-L1 was proportional to tumor growth before therapy, but not after initiating therapy. The high expression level of PD-L1 in T cells may inhibit IT efficacy. After combination therapy begins, the tumor size was also influenced by the ratio of PD-1 to PD-L1. These results highlight that the ratio of PD-1 to PD-L1 in T cells could be considered in combination therapy.

Background Antibody-drug conjugates (ADCs) are intended to bind to specific positive target antigens and eradicate only tumor cells from an intracellular released payload through the lysosomal protease. Payloads, such as MMAE, have the capacity to kill adjacent antigen-negative (Ag–) tumor cells, which is called the bystander-killing effect, as well as directly kill antigen-positive (Ag+) tumor cells. We propose that a dose-response curve should be independently considered to account for target antigen-positive/negative tumor cells. Methods A model was developed to account for the payload in Ag+/Ag– cells and the associated parameters were applied. A tumor growth inhibition (TGI) effect was explored based on an ordinary differential equation (ODE) after substituting the payload concentration in Ag+/Ag– cells into an Emax model, which accounts for the dose-response curve. To observe the bystander-killing effects based on the amount of Ag+/Ag– cells, the Emax model is used independently. TGI models based on ODE are unsuitable for describing the initial delay through a tumor–drug interaction. This was solved using an age-structured model based on the stochastic process. Results β ∈(0,1] is a fraction parameter that determines the proportion of cells that consist of Ag+/Ag– cells. The payload concentration decreases when the ratio of efflux to influx increases. The bystander-killing effect differs with varying amounts of Ag+ cells. The larger β is, the less bystander-killing effect. The decrease of the bystander-killing effect becomes stronger as Ag+ cells become larger than the Ag– cells. Overall, the ratio of efflux to influx, the amount of released payload, and the proportion of Ag+ cells determine the efficacy of the ADC. The tumor inhibition delay through a payload-tumor interaction, which goes through several stages, may be solved using an age-structured model. Conclusions The bystander-killing effect, one of the most important topics of ADCs, has been explored in several studies without the use of modeling. We propose that the bystander-killing effect can be captured through a mathematical model when considering the Ag+ and Ag– cells. In addition, the TGI model based on the age-structure can capture the initial delay through a drug interaction as well as the bystander-killing effect. Electronic supplementary material The online version of this article (10.1186/s12885-019-5336-7) contains supplementary material, which is available to authorized users.