Modeling the Effect of Binding Kinetics in Spatial Drug Distribution in the Brain.

A 3-dimensional mathematical model is developed to determine the effect of drug binding kinetics on the spatial distribution of a drug within the brain. The key components, namely, transport across the blood-brain barrier (BBB), drug distribution in the brain extracellular fluid (ECF), and drug binding kinetics are coupled with the bidirectional bulk flow of the brain ECF to enhance the visualization of drug concentration in the brain. The model is developed based on the cubical volume of a brain unit, which is a union of three subdomains: the brain ECF, the BBB, and the blood plasma. The model is a set of partial differential equations and the associated initial and boundary conditions through which the drug distribution process in the mentioned subdomains is described. Effects of drug binding kinetics are investigated by varying the binding parameter values for both nonspecific and specific binding sites. All variations of binding parameter values are discussed, and the results show the improved visualization of the effect of binding kinetics in the drug distribution within the brain. For more realistic visualization, we suggest incorporating more brain components that make up the large volume of the brain tissue.

Age-structured model for COVID-19: Effectiveness of social distancing and contact reduction in Kenya.

Coronavirus disease 2019 is caused by severe acute respiratory syndrome coronavirus 2. Kenya reported its first case on March 13, 2020 and by March 16, 2020 she instituted physical distancing strategies to reduce transmission and flatten the epidemic curve. An age-structured compartmental model was developed to assess the impact of the strategies on COVID-19 severity and burden. Contacts between different ages are incorporated via contact matrices. Simulation results show that 45% reduction in contacts for 60-days period resulted to 11.5-13% reduction of infections severity and deaths, while for the 190-days period yielded 18.8-22.7% reduction. The peak of infections in the 60-days mitigation was higher and happened about 2 months after the relaxation of mitigation as compared to that of the 190-days mitigation, which happened a month after mitigations were relaxed. Low numbers of cases in children under 15 years was attributed to high number of asymptomatic cases. High numbers of cases are reported in the 15-29 years and 30-59 years age bands. Two mitigation periods, considered in the study, resulted to reductions in severe and critical cases, attack rates, hospital and ICU bed demands, as well as deaths, with the 190-days period giving higher reductions.

Modeling the Effects of Nonpharmaceutical Interventions on COVID-19 Spread in Kenya.

Mathematical modeling of nonpharmaceutical interventions (NPIs) of coronavirus disease (COVID-19) in Kenya is presented. A susceptible-exposed-infected-recovered (SEIR) compartment model is considered with additional compartments of hospitalized population whose condition is severe or critical and the fatality compartment. The basic reproduction number (R 0) is computed by the next-generation matrix approach and later expressed as a time-dependent function so as to incorporate the NPIs into the model. The resulting system of ordinary differential equations (ODEs) is solved using fourth-order and fifth-order Runge-Kutta methods. Different intervention scenarios are considered, and the results show that implementation of closure of education institutions, curfew, and partial lockdown yields predicted delayed peaks of the overall infections, severe cases, and fatalities and subsequently containment of the pandemic in the country.

SEIR model for COVID-19 dynamics incorporating the environment and social distancing.

OBJECTIVE: Coronavirus disease 2019 (COVID-19) is a pandemic respiratory illness spreading from person-to-person caused by a novel coronavirus and poses a serious public health risk. The goal of this study was to apply a modified susceptible-exposed-infectious-recovered (SEIR) compartmental mathematical model for prediction of COVID-19 epidemic dynamics incorporating pathogen in the environment and interventions. The next generation matrix approach was used to determine the basic reproduction number [Formula: see text]. The model equations are solved numerically using fourth and fifth order Runge-Kutta methods. RESULTS: We found an [Formula: see text] of 2.03, implying that the pandemic will persist in the human population in the absence of strong control measures. Results after simulating various scenarios indicate that disregarding social distancing and hygiene measures can have devastating effects on the human population. The model shows that quarantine of contacts and isolation of cases can help halt the spread on novel coronavirus.

Application of Optimal Control to Influenza Pneumonia Coinfection with Antiviral Resistance.

Influenza and pneumonia independently lead to high morbidity and mortality annually among the human population globally; however, a glaring fact is that influenza pneumonia coinfection is more vicious and it is a threat to public health. Emergence of antiviral resistance is a major impediment in the control of the coinfection. In this paper, a deterministic mathematical model illustrating the transmission dynamics of influenza pneumonia coinfection is formulated having incorporated antiviral resistance. Optimal control theory is then applied to investigate optimal strategies for controlling the coinfection using prevalence reduction and treatment as the system control variables. Pontryagin's maximum principle is used to characterize the optimal control. The derived optimality system is solved numerically using the Runge-Kutta-based forward-backward sweep method. Simulation results reveal that implementation of prevention measures is sufficient to eradicate influenza pneumonia coinfection from a given population. The prevention measures could be social distancing, vaccination, curbing mutation and reassortment, and curbing interspecies movement of the influenza virus.