Background Seasonal influenza poses a significant public health and economic burden, associated with the outcome of infection and resulting complications. The true burden of the disease is difficult to capture due to the wide range of presentation, from asymptomatic cases to non-respiratory complications such as cardiovascular events, and its seasonal variability. An understanding of the magnitude of the true annual incidence of influenza is important to support prevention and control policy development and to evaluate the impact of preventative measures such as vaccination. Methods We use a dynamic disease transmission model, laboratory-confirmed influenza surveillance data, and randomized-controlled trial (RCT) data to quantify the underestimation factor, expansion factor, and symptomatic influenza illnesses in the US and Canada during the 2011-2012 and 2012-2013 influenza seasons. Results Based on 2 case definitions, we estimate between 0.42−3.2% and 0.33−1.2% of symptomatic influenza illnesses were laboratory-confirmed in Canada during the 2011-2012 and 2012-2013 seasons, respectively. In the US, we estimate between 0.08−0.61% and 0.07−0.33% of symptomatic influenza illnesses were laboratory-confirmed in the 2011-2012 and 2012-2013 seasons, respectively. We estimated the symptomatic influenza illnesses in Canada to be 0.32−2.4 million in 2011-2012 and 1.8−8.2 million in 2012-2013. In the US, we estimate the number of symptomatic influenza illnesses to be 4.4−34 million in 2011-2012 and 23−102 million in 2012-2013. Conclusions We illustrate that monitoring a representative group within a population may aid in effectively modelling the transmission of infectious diseases such as influenza. In particular, the utilization of RCTs in models may enhance the accuracy of epidemiological parameter estimation.

We conducted an observational retrospective study on patients hospitalized with COVID-19, during March 05, 2020, to October 28, 2021, and developed an agent-based model to evaluate effectiveness of recommended healthcare resources (hospital beds and ventilators) management strategies during the COVID-19 pandemic in Gauteng, South Africa. We measured the effectiveness of these strategies by calculating the number of deaths prevented by implementing them. We observed differ ences between the epidemic waves. The length of hospital stay (LOS) during the third wave was lower than the first two waves. The median of the LOS was 6.73 days, 6.63 days and 6.78 days for the first, second and third wave, respectively. A combination of public and private sector provided hospital care to COVID-19 patients requiring ward and Intensive Care Units (ICU) beds. The private sector provided 88.4% of High care (HC)/ICU beds and 49.4% of ward beds, 73.9% and 51.4%, 71.8% and 58.3% during the first, second and third wave, respectively. Our simulation results showed that with a high maximum capacity, i.e., 10,000 general and isolation ward beds, 4,000 high care and ICU beds and 1,200 ventilators, increasing the resource capacity allocated to COVID- 19 patients by 25% was enough to maintain bed availability throughout the epidemic waves. With a medium resource capacity (8,500 general and isolation ward beds, 3,000 high care and ICU beds and 1,000 ventilators) a combination of resource management strategies and their timing and criteria were very effective in maintaining bed availability and therefore preventing excess deaths. With a low number of maximum available resources (7,000 general and isolation ward beds, 2,000 high care and ICU beds and 800 ventilators) and a severe epidemic wave, these strategies were effective in maintaining the bed availability and minimizing the number of excess deaths throughout the epidemic wave.

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We formulate a coupled system of renewal equations for the forces of infections in interacting subgroups through a contact network. We use the theory of order-preserving and sub-homogeneous discrete dynamical systems to show the existence and uniqueness of the disease outbreak final sizes in the sub-populations. We illustrate the general theory through a simple SIR model with exponentially and non-exponentially distributed infectious period.

For a variety of tick species, the resistance, behavioural and immunological response of hosts has been reported in the biological literature but its impact on tick population dynamics has not been mathematically formulated and analyzed using dynamical models reflecting the full biological stages of ticks. Here we develop and simulate a delay differential equation model, with a particular focus on resistance resulting in grooming behaviour. We calculate the basic reproduction number using the spectral analysis of delay differential equations with positive feedback, and establish the existence and uniqueness of a positive equilibrium when the basic reproduction number exceeds unit. We also conduct numerical and sensitivity analysis about the dependence of this positive equilibrium on the the parameter relevant to grooming behaviour. We numerically obtain the relationship between grooming behaviour and equilibrium value at different stages.