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This study examines the interactions between healthy target cells, infected target cells, virus particles, and immune cells within an HIV model. The model exhibits two equilibrium points: an infection-free equilibrium and an infection equilibrium. Stability analysis shows that the infection-free equilibrium is locally asymptotically stable when R0<1. Further, it is unstable when R0>1. The infection equilibrium is locally asymptotically stable when R0>1. The structural and practical identifiabilities of the within-host model for HIV infection dynamics were investigated using differential algebra techniques and Monte Carlo simulations. The HIV model was structurally identifiable by observing the total uninfected and infected target cells, immune cells, and viral load. Monte Carlo simulations assessed the practical identifiability of parameters. The production rate of target cells (λ), the death rate of healthy target cells (d), the death rate of infected target cells (δ), and the viral production rate by infected cells (π) were practically identifiable. The rate of infection of target cells by the virus (β), the death rate of infected cells by immune cells (Ψ), and antigen-driven proliferation rate of immune cells (b) were not practically identifiable. Practical identifiability was constrained by the noise and sparsity of the data. Analysis shows that increasing the frequency of data collection can significantly improve the identifiability of all parameters. This highlights the importance of optimal data sampling in HIV clinical studies, as it determines the best time points, frequency, and the number of sample points required to accurately capture the dynamics of the HIV infection within a host. 

In this paper we develop a four compartment within-host model of nutrition and HIV. We show that the model has two equilibria: an infection-free equilibrium and infection equilibrium. The infection free equilibrium is locally asymptotically stable when the basic reproduction number $$ \mathcal{R}_0 < 1 $$, and unstable when $$ \mathcal{R}_0 > 1 $$. The infection equilibrium is locally asymptotically stable if $$ \mathcal{R}_0 > 1 $$ and an additional condition holds. We show that the within-host model of HIV and nutrition is structured to reveal its parameters from the observations of viral load, CD4 cell count and total protein data. We then estimate the model parameters for these 3 data sets. We have also studied the practical identifiability of the model parameters by performing Monte Carlo simulations, and found that the rate of clearance of the virus by immunoglobulins is practically unidentifiable, and that the rest of the model parameters are only weakly identifiable given the experimental data. Furthermore, we have studied how the data frequency impacts the practical identifiability of model parameters. 

Understanding the epidemiology of emerging pathogens, such as Usutu virus (USUV) infections, requires systems investigation at each scale involved in the host–virus transmission cycle, from individual bird infections, to bird-to-vector transmissions, and to USUV incidence in bird and vector populations. For new pathogens field data are sparse, and predictions can be aided by the use of laboratory-type inoculation and transmission experiments combined with dynamical mathematical modelling. In this study, we investigated the dynamics of two strains of USUV by constructing mathematical models for the within-host scale, bird-to-vector transmission scale and vector-borne epidemiological scale. We used individual within-host infectious virus data and per cent mosquito infection data to predict USUV incidence in birds and mosquitoes. We addressed the dependence of predictions on model structure, data uncertainty and experimental design. We found that uncertainty in predictions at one scale change predicted results at another scale. We proposedin silicoexperiments that showed that sampling every 12 hours ensures practical identifiability of the within-host scale model. At the same time, we showed that practical identifiability of the transmission scale functions can only be improved under unrealistically high sampling regimes. Instead, we proposed optimal experimental designs and suggested the types of experiments that can ensure identifiability at the transmission scale and, hence, induce robustness in predictions at the epidemiological scale.