Modeling the effect of imported malaria on the elimination programme in KwaZulu-Natal province of South Africa.

Introduction: with imported malaria cases in a given population, the question arises as to what extent the local cases are a consequence of the imports or not. We perform a modeling analysis for a specific area, in a region aspiring for malaria-free status. Methods: data on malaria cases over ten years is subjected to a compartmental model which is assumed to be operating close to the equilibrium state. Two of the parameters of the model are fitted to the decadal data. The other parameters in the model are sourced from the literature. The model is utilized to simulate the malaria prevalence with or without imported cases. Results: in any given year the annual average of 460 imported cases, resulted in an end-of-year season malaria prevalence of 257 local active infectious cases, whereas without the imports the malaria prevalence at the end of the season would have been fewer than 10 active infectious cases. We calculate the numerical value of the basic reproduction number for the model, which reveals the extent to which the disease is being eliminated from the population or not. Conclusion: without the imported cases, over the ten seasons of malaria, 2008-2018, the KwaZulu-Natal province would have been malaria-free over at least the last 7 years of the decade indicated. This simple methodology works well even in situations where data is limited.

A population model for the 2017/18 listeriosis outbreak in South Africa.

We introduce a compartmental model of ordinary differential equations for the population dynamics of listeriosis, and we derive a model for analysing a listeriosis outbreak. The model explicitly accommodates neonatal infections. Similarly as is common in cholera modeling, we include a compartment to represent the reservoir of bacteria. We also include a compartment to represent the incubation phase. For the 2017/18 listeriosis outbreak that happened in South Africa, we calculate the time pattern and intensity of the force of infection, and we determine numerical values for some of the parameters in the model. The model is calibrated using South African data, together with existing data in the open literature not necessarily from South Africa. We make projections on the future outlook of the epidemiology of the disease and the possibility of eradication.