Cardiac electrophysiological heterogeneity includes: (i) regional differences in action potential (AP) waveform, (ii) AP waveform differences in cells isolated from a single region, (iii) variability of the contribution of individual ion currents in cells with similar AP durations (APDs). The aim of this study is to assess intra-regional AP waveform differences, to quantify the contribution of specific ion channels to the APD via drug responses and to generate a population of mathematical models to investigate the mechanisms underlying heterogeneity in rabbit ventricular cells. APD in ∼50 isolated cells from subregions of the LV free wall of rabbit hearts were measured using a voltage-sensitive dye. When stimulated at 2 Hz, average APD₉₀ value in cells from the basal epicardial region was 254 ± 25 ms (mean ± standard deviation) in 17 hearts with a mean interquartile range (IQR) of 53 ± 17 ms. Endo-epicardial and apical-basal APD₉₀ differences accounted for ∼10% of the IQR value. Highly variable changes in APD occurred after IK(r) or ICa(L) block that included a sub-population of cells (HR) with an exaggerated (hyper) response to IK(r) inhibition. A set of 4471 AP models matching the experimental APD₉₀ distribution was generated from a larger population of models created by random variation of the maximum conductances (G_max) of 8 key ion channels/exchangers/pumps. This set reproduced the pattern of cell-specific responses to ICa(L) and IK(r) block, including the HR sub-population. The models exhibited a wide range of G_max values with constrained relationships linking ICa(L) with IK(r), ICl, INCX, and INaK. Modelling the measured range of inter-cell APDs required a larger range of key G_max values indicating that ventricular tissue has considerable inter-cell variation in channel/pump/exchanger activity. AP morphology is retained by relationships linking specific ionic conductances. These interrelationships are necessary for stable repolarization despite large inter-cell variation of individual conductances and this explains the variable sensitivity to ion channel block.

A dynamics informed neural networks (DINNs) incorporating the susceptible-exposed-infectious-recovered-vaccinated (SEIRV) model was developed to enhance the understanding of the temporal evolution dynamics of infectious diseases. This work integrates differential equations with deep neural networks to predict time-varying parameters in the SEIRV model. Experimental results based on reported data from China between January 1, and December 1, 2022, demonstrate that the proposed dynamics informed neural networks (DINNs) method can accurately learn the dynamics and predict future states. Our proposed hybrid SEIRV-DNNs model can also be applied to other infectious diseases such as influenza and dengue, with some modifications to the compartments and parameters in the model to accommodate the related control measures. This approach will facilitate improving predictive modeling and optimizing public health intervention strategies.

Tuberculosis (TB) remains a significant global health concern, necessitating effective control strategies. This article presents a mathematical model to evaluate the comparative effectiveness of medical mask usage and case detection in TB control. The model is constructed as a system of ordinary differential equations and incorporates crucial aspects of TB dynamics, including slow–fast progression, medical mask use, case detection, treatment interventions and differentiation between symptomatic and asymptomatic cases. A key objective of TB control is to ensure that the reproduction number,Rc, remains below unity to achieve TB elimination or persistence ifRcexceeds 1. Our mathematical analysis reveals the presence of a transcritical bifurcation when theRc=1signifies a critical juncture in TB control strategies. These results confirm that the effectiveness of case detection in diminishing the endemic population of symptomatic individuals within a TB-endemic equilibrium depends on exceeding a critical threshold value. Furthermore, our model is calibrated using TB yearly case incidence data per 100 000 population from Indonesia, India, Lesotho and Angola. We employed the bootstrap resampling residual approach to assess the uncertainty inherent in our parameter estimates which provides a comprehensive distribution of the parameter values. Despite a declining trend in new incidence, these four countries exhibit a reproduction number greater than 1, indicating persistent TB cases in the presence of ongoing TB control programmes. We employ the partial rank correlation coefficient in conjunction with the Latin hypercube sampling method to conduct a global sensitivity analysis of theRcparameter for each fitted parameter in every country. We find that the medical mask use is more sensitive to reduceRccompared with the case detection implementation. To further gain insight into the necessary control strategy, we formulated an optimal control and studied the cost-effectiveness analysis of our model to investigate the impact of case detection and medical mask use as control measures in TB spread. Cost-effectiveness analysis demonstrates that combining these interventions emerges as the most cost-effective strategy for TB control. Our findings highlight the critical importance of medical masks and their efficacy coupled with case detection in shaping TB control dynamics, elucidating the primary parameter of concern for managing the control reproduction number. We envisage our findings to have implications and be vital for TB control if implemented by policymakers and healthcare practitioners involved in TB control efforts.

A modified version of the SEIR model with the effects of vaccination and inter-state movement is proposed to simulate the spread of COVID-19 in Malaysia. A mathematical analysis of the proposed model was performed to derive the basic reproduction number. To enhance the model’s forecasting capabilities, the model parameters were estimated using the Nelder–Mead simplex method by fitting the model outputs to the observed data. Our results showed a good fit between the model outputs and available data, where the model was then able to perform short-term predictions. In line with the rapid vaccination program, our model predicted that the COVID-19 cases in the country would decrease by the end of August. Furthermore, our findings indicated that relaxing travel restrictions from a highly vaccinated region to a low vaccinated region would result in an epidemic outbreak.

This study used a non-linear SEIR model to analyze the spread of COVID-19 in Malaysia. The model considered vaccines, booster doses, hospitalized cases, and various infectious cases. The model was fitted to real data using MATLAB's ode solver and the particle swarm optimization method. The results revealed that booster vaccines significantly reduced the total number of infected cases by 62% when 70% of the population received them. This model can help policymakers to make crucial decisions to prevent future outbreaks.