A model assessing potential benefits of isolation and mass testing on COVID-19: the case of Nigeria

We consider a model with mass testing and isolation mimicking the current policies implemented in Nigeria and use the Nigerian daily cumulative cases to calibrate the model to obtain the optimal mass testing and isolation levels. Mathematical analysis was done and important thresholds such the peak size relation and final size relation were obtained. Global stability analysis of the disease-free equilibrium indicated that COVID-19 can be eradicated provided that $\mathcal{R}_0<1$ and unstable otherwise. Results from simulations revealed that an increase in mass testing and reduction of transmission from isolated individuals are associated with benefits of increasing detected cases, lowering peaks of symptomatic cases, increase in self-isolating cases, decrease in cumulative deaths and decrease in admissions into monitored isolation facilities in the case of Nigeria

Computational and Mathematical Methods to Estimate the Basic Reproduction Number and Final Size for Single-Stage and Multistage Progression Disease Models for Zika with Preventative Measures

We present new mathematical models that include the impact of using selected preventative measures such as insecticide treated nets (ITN) in controlling or ameliorating the spread of the Zika virus. For these models, we derive the basic reproduction number and sharp estimates for the final size relation. We first present a single-stage model which is later extended to a new multistage model for Zika that incorporates more realistic incubation stages for both the humans and vectors. For each of these models, we derive a basic reproduction number and a final size relation estimate. We observe that the basic reproduction number for the multistage model converges to expected values for a standard Zika epidemic model with fixed incubation periods in both hosts and vectors. Finally, we also perform several computational experiments to validate the theoretical results obtained in this work and study the influence of various parameters on the models.