Dynamics of SI epidemic with a demographic Allee effect.

In this paper, we present an extended SI model of Hilker et al. (2009). In the presented model the birth rate and the death rate are both modeled as quadratic polynomials. This approach provides ample opportunity for taking into account the major contributors to an Allee effect and effectively captures species' differential susceptibility to the Allee effects. It is shown that, the behaviors (persistence or extinction) of the model solutions are characterized by the two essential threshold parameters λ0 and λ1 of the transmissibility λ and a threshold quantity µ(∗) of the disease pathogenicity µ. If λ<λ0, the model is bistable and a disease cannot invade from arbitrarily small introductions into the host population at the carrying capacity, while it persists when λ>λ0 and µ<µ(∗). When λ>λ1 and µ>µ(∗), the disease derives the host population to extinction with origin as the only global attractor. For the special cases of the model, verifiable conditions for host population persistence (with or without infected individuals) and host extinction are derived. Interestingly, we show that if the values of the parameters α and ß of the extended model are restricted, then the two models are similar. Numerical simulations show how the parameter ß affects the dynamics of the model with respect to the host population persistence and extinction.

Comparison of a static cohort model and dynamic transmission model for respiratory syncytial virus intervention programs for infants in England and Wales.

BACKGROUND: A recent study comparing results of multiple cost-effectiveness analyses (CEAs) in a hypothetical population found that monoclonal antibody (mAb) immunoprophylaxis for respiratory syncytial virus (RSV) in infants averted fewer medically attended cases when estimated using dynamic transmission models (DTMs) versus static cohort models (SCMs). We aimed to investigate whether model calibration or parameterization could be the primary driver of inconsistencies between SCM and DTM predictions. METHODS: A recently published DTM evaluating the CEA of infant mAb immunoprophylaxis in England and Wales (EW) was selected as the reference model. We adapted our previously published SCM for US infants to EW by utilizing the same data sources used by the DTM. Both models parameterized mAb efficacy from a randomized clinical trial (RCT) that estimated an average efficacy of 74.5% against all medically attended RSV episodes and 62.1% against RSV hospitalizations. To align model assumptions, we modified the SCM to incorporate waning efficacy. Since the estimated indirect effects from the DTM were small (i.e., approximately 100-fold smaller in magnitude than direct effects), we hypothesized that alignment of model parameters should result in alignment of model predictions. Outputs for model comparison comprised averted hospitalizations and averted GP visits, estimated for seasonal (S) and seasonal-with-catchup (SC) immunization strategies. RESULTS: When we aligned the SCM intervention parameters to DTM intervention parameters, significantly more averted hospitalizations were predicted by the SCM (S: 32.3%; SC: 51.3%) than the DTM (S: 17.8%; SC: 28.6%). The SCM most closely replicated the DTM results when the initial efficacy of the mAb intervention was 62.1%, leading to an average efficacy of 39.3%. Under this parameterization the SCM predicted 17.4% (S) and 27.7% (SC) averted hospitalizations. Results were similar for averted GP visits. CONCLUSIONS: Parameterization of the RSV mAb intervention efficacy is a plausible primary driver of differences between SCM versus DTM model predictions.

Modeling the transmission dynamics of the COVID-19 Pandemic in South Africa.

Since its emergence late in 2019, the COVID-19 pandemic continues to exude major public health and socio-economic burden globally. South Africa is currently the epicenter for the pandemic in Africa. This study is based on the use of a compartmental model to analyze the transmission dynamics of the disease in South Africa. A notable feature of the model is the incorporation of the role of environmental contamination by COVID-infected individuals. The model, which is fitted and parametrized using cumulative mortality data from South Africa, is used to assess the impact of various control and mitigation strategies. Rigorous analysis of the model reveals that its associated continuum of disease-free equilibria is globally-asymptotically stable whenever the control reproduction number is less than unity. The epidemiological implication of this result is that the disease will eventually die out, particularly if control measures are implemented early and for a sustainable period of time. For instance, numerical simulations suggest that if the lockdown measures in South Africa were implemented a week later than the 26 March, 2020 date it was implemented, this will result in the extension of the predicted peak time of the pandemic, and causing about 10% more cumulative deaths. In addition to illustrating the effectiveness of self-isolation in reducing the number of cases, our study emphasizes the importance of surveillance testing and contact tracing of the contacts and confirmed cases in curtailing the pandemic in South Africa.

Global stability analysis of SEIR model with holling type II incidence function.

A deterministic model for the transmission dynamics of a communicable disease is developed and rigorously analysed. The model, consisting of five mutually exclusive compartments representing the human dynamics, has a globally asymptotically stable disease-free equilibrium (DFE) whenever a certain epidemiological threshold, known as the basic reproduction number (ℛ0), is less than unity; in such a case the endemic equilibrium does not exist. On the other hand, when the reproduction number is greater than unity, it is shown, using nonlinear Lyapunov function of Goh-Volterra type, in conjunction with the LaSalle's invariance principle, that the unique endemic equilibrium of the model is globally asymptotically stable under certain conditions. Furthermore, the disease is shown to be uniformly persistent whenever ℛ0 > 1.