The main purpose of this article is to formulate a deterministic mathematical model for the transmission of malaria that considers two host types in the human population. The first type is called "non-immune" comprising all humans who have never acquired immunity against malaria and the second type is called "semi-immune". Non-immune are divided into susceptible, exposed and infectious and semi-immune are divided into susceptible, exposed, infectious and immune. We obtain an explicit formula for the reproductive number, R(0) which is a function of the weight of the transmission semi-immune-mosquito-semi-immune, R(0a), and the weight of the transmission non-immune-mosquito-non-immune, R(0e). Then, we study the existence of endemic equilibria by using bifurcation analysis. We give a simple criterion when R(0) crosses one for forward and backward bifurcation. We explore the possibility of a control for malaria through a specific sub-group such as non-immune or semi-immune or mosquitoes.

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A metapopulation malaria model is proposed using SI and SIRS models for the vectors and hosts, respectively. Recovered hosts are partially immune to the disease and while they cannot directly become infectious again, they can still transmit the parasite to vectors. The basic reproduction number [Formula: see text] is shown to govern the local stability of the disease free equilibrium but not the global behavior of the system because of the potential occurrence of a backward bifurcation. Using type reproduction numbers, we identify the reservoirs of infection and evaluate the effect of control measures. Applications to the spread to non-endemic areas and the interaction between rural and urban areas are given.

Salmonella is one of the major sources of toxi-infection in humans, most often because of consumption of poultry products. The main reason for this association is the presence in hen flocks of silent carriers, i.e. animals harboring Salmonella without expressing any visible symptoms. Many prophylactic means have been developed to reduce the prevalence of Salmonella carrier-state. While none allows a total reduction of the risk, synergy could result in a drastic reduction of it. Evaluating the risk by modeling would be very useful to estimate such gain in food safety. Here, we propose an individual-based model which describes the spatio-temporal spread of Salmonella within a laying flock and takes into account the host response to bacterial infection. The model includes the individual bacterial load and the animals' ability to reduce it thanks to the immune response, i.e. maximum bacterial dose that the animals may resist without long term carriage and, when carriers, length of bacterial clearance. For model validation, we simulated the Salmonella spread under published experimental conditions. There was a good agreement between simulated and observed published data. This model will thus allow studying the effects, on the spatiotemporal distribution of the bacteria, of both mean and variability of different elements of host response.