Model for Interpreting Discordant SARS-CoV-2 Diagnostic Test Results.

We devised a model to interpret discordant SARS-CoV-2 test results. We estimate that, during March 2020-May 2022, a patient in the United States who received a positive rapid antigen test result followed by a negative nucleic acid test result had only a 15.4% (95% CI 0.6%-56.7%) chance of being infected.

Projections of human papillomavirus vaccination and its impact on cervical cancer using the Caputo fractional derivative.

We propose a fractional order model for human papillomavirus (HPV) dynamics, including the effects of vaccination and public health education on developing cervical cancer. First, we discuss the general structure of Caputo fractional derivatives and integrals. Next, we define the fractional HPV model using Caputo derivatives. The model equilibrium quantities, with their stability, are discussed based on the magnitude of the reproduction number. We compute and simulate numerical solutions of the presented fractional model using the Adams-Bashforth-Moulton scheme. Meanwhile, real data sourced from reports from the World Health Organization is used to establish the parameters and compute the basic reproduction number. We present figures of state variables for different fractional orders and the classical integer order. The impacts of vaccination and public health education are discussed through numerical simulations. From the results, we observe that an increase in both vaccination rates and public health education increases the quality of life, and thus, reduces disease burden and suffering in communities. The results also confirm that modeling HPV transmission dynamics using fractional derivatives includes history effects in the model, making the model further insightful and appropriate for studying HPV dynamics.

Modeling the impact of public health education on tungiasis dynamics with saturated treatment: Insight through the Caputo fractional derivative.

Public health education is pivotal in the management and control of infectious and non-infectious diseases. This manuscript presents and analyses a nonlinear fractional model of tungiasis dynamics with the impact of public health education for the first time. The human population is split into five classes depending on their disease status. The infected population is split into two subgroups; infected but unaware and infected but aware. The model focuses on the impacts of public health education, contact and treatment contact on tungiasis transmission dynamics. Notably, public health education is important for containing as well as reducing disease outbreaks in communities. The Caputo fractional derivative is utilised in defining the model governing equations. Model equilibrium points existence and stability are investigated using simple matrix algebra. Model analysis shows that tungiasis is contained when the reproduction number is less than unity. Otherwise, if it is greater than unity, the disease persists and spread in the population. The generalised Adams-Bashforth-Moulton approach is utilised in solving the derived tungiasis model numerically. The impacts of public health education, treatment and contact rate on overall disease dynamics are discussed through numerical simulations. From the simulations, we see that for given fractional order, public health education and treatment increase the quality of life plus reduce equilibrium numbers of tungiasis-infected individuals. We observe that population classes converge quicker to their steady states when α is increased. Thus, we can conclude that the derivative order α captures the role of experience or knowledge that individuals have on the disease's history.

A pharmacokinetic-pharmacodynamic model for chemoprotective agents against malaria.

Chemoprophylactics are a vital tool in the fight against malaria. They can be used to protect populations at risk, such as children younger than the age of 5 in areas of seasonal malaria transmission or pregnant women. Currently approved chemoprophylactics all present challenges. There are either concerns about unacceptable adverse effects such as neuropsychiatric sequalae (mefloquine), risks of hemolysis in patients with G6PD deficiency (8-aminoquinolines such as tafenoquine), or cost and daily dosing (atovaquone-proguanil). Therefore, there is a need to develop new chemoprophylactic agents to provide more affordable therapies with better compliance through improving properties such as pharmacokinetics to allow weekly, preferably monthly, dosing. Here we present a pharmacokinetic-pharmacodynamic (PKPD) model constructed using DSM265 (a dihydroorotate dehydrogenase inhibitor with activity against the liver schizonts of malaria, therefore, a prophylaxis candidate). The PKPD model mimics the parasite lifecycle by describing parasite dynamics and drug activity during the liver and blood stages. A major challenge is the estimation of model parameters, as only blood-stage parasites can be observed once they have reached a threshold. By combining qualitative and quantitative knowledge about the parasite from various sources, it has been shown that it is possible to infer information about liver-stage growth and its initial infection level. Furthermore, by integrating clinical data, the killing effect of the drug on liver- and blood-stage parasites can be included in the PKPD model, and a clinical outcome can be predicted. Despite multiple challenges, the presented model has the potential to help translation from preclinical to late development for new chemoprophylactic candidates.

Pharmacokinetics and Target Attainment of SQ109 in Plasma and Human-Like Tuberculosis Lesions in Rabbits.

SQ109 is a novel well-tolerated drug candidate in clinical development for the treatment of drug-resistant tuberculosis (TB). It is the only inhibitor of the MmpL3 mycolic acid transporter in clinical development. No SQ109-resistant mutant has been directly isolated thus far in vitro, in mice, or in patients, which is tentatively attributed to its multiple targets. It is considered a potential replacement for poorly tolerated components of multidrug-resistant TB regimens. To prioritize SQ109-containing combinations with the best potential for cure and treatment shortening, one must understand its contribution against different bacterial populations in pulmonary lesions. Here, we have characterized the pharmacokinetics of SQ109 in the rabbit model of active TB and its penetration at the sites of disease-lung tissue, cellular and necrotic lesions, and caseum. A two-compartment model with first-order absorption and elimination described the plasma pharmacokinetics. At the human-equivalent dose, parameter estimates fell within the ranges published for preclinical species. Tissue concentrations were modeled using an "effect" compartment, showing high accumulation in lung and cellular lesion areas with penetration coefficients in excess of 1,000 and lower passive diffusion in caseum after 7 daily doses. These results, together with the hydrophobic nature and high nonspecific caseum binding of SQ109, suggest that multiweek dosing would be required to reach steady state in caseum and poorly vascularized compartments, similar to bedaquiline. Linking lesion pharmacokinetics to SQ109 potency in assays against replicating, nonreplicating, and intracellular M. tuberculosis showed SQ109 concentrations markedly above pharmacokinetic-pharmacodynamic targets in lung and cellular lesions throughout the dosing interval.

Dynamics of a fractional order mathematical model for COVID-19 epidemic.

In this work, we formulate and analyze a new mathematical model for COVID-19 epidemic with isolated class in fractional order. This model is described by a system of fractional-order differential equations model and includes five classes, namely, S (susceptible class), E (exposed class), I (infected class), Q (isolated class), and R (recovered class). Dynamics and numerical approximations for the proposed fractional-order model are studied. Firstly, positivity and boundedness of the model are established. Secondly, the basic reproduction number of the model is calculated by using the next generation matrix approach. Then, asymptotic stability of the model is investigated. Lastly, we apply the adaptive predictor-corrector algorithm and fourth-order Runge-Kutta (RK4) method to simulate the proposed model. Consequently, a set of numerical simulations are performed to support the validity of the theoretical results. The numerical simulations indicate that there is a good agreement between theoretical results and numerical ones.

Nonstandard finite difference approach for solving 3-compartment pharmacokinetic models.

Complex nature of the analytical solutions to 3-compartment pharmacokinetic models leads to the discrete approximation of the continuous differential equation been mostly used. In this paper, we applied nonstandard finite difference method to 3-compartment pharmacokinetic models. This method was introduced to compensate for the weaknesses of methods such as the standard finite difference methods, numerical instabilities being a prime example of such. Three-compartment pharmacokinetic model with 2 different routes of administration (IV bolus injection and IV bolus infusion) is considered for simulations. For the case when the system is homogeneous (models arising from IV bolus injection mode of administration), "exact" finite difference scheme is obtained for any step size while in the case of nonhomogeneous (models arising from IV bolus infusion route of administration), scheme that has the same qualitative behavior as the analytical solution for all step sizes is obtained. It was shown computationally that the nonstandard finite difference scheme for 3-compartment pharmacokinetic model with IV bolus mode of administration is exact while 3-compartment pharmacokinetic model with IV infusion is dynamically consistent with the continuous model for all step sizes.

Nonstandard Finite Difference Method Applied to a Linear Pharmacokinetics Model.

We extend the nonstandard finite difference method of solution to the study of pharmacokinetic-pharmacodynamic models. Pharmacokinetic (PK) models are commonly used to predict drug concentrations that drive controlled intravenous (I.V.) transfers (or infusion and oral transfers) while pharmacokinetic and pharmacodynamic (PD) interaction models are used to provide predictions of drug concentrations affecting the response of these clinical drugs. We structure a nonstandard finite difference (NSFD) scheme for the relevant system of equations which models this pharamcokinetic process. We compare the results obtained to standard methods. The scheme is dynamically consistent and reliable in replicating complex dynamic properties of the relevant continuous models for varying step sizes. This study provides assistance in understanding the long-term behavior of the drug in the system, and validation of the efficiency of the nonstandard finite difference scheme as the method of choice.