Methicillin-resistant Staphylococcus aureus (MRSA) is endemic in many hospital settings, including nursing homes. It is an important nosocomial pathogen that causes mortality and an economic burden to patients, hospitals, and the community. The epidemiology of the bacteria in nursing homes is both hospital- and community-like. Transmission occurs via hands of health care workers (HCWs) and direct contacts among residents during social activities. In this work, mathematical modeling in both deterministic and stochastic frameworks is used to study dissemination of MRSA among residents and HCWs, persistence and prevalence of MRSA in a population, and possible means of controlling the spread of this pathogen in nursing homes. The model predicts that: without strict screening and decolonization of colonized individuals at admission, MRSA may persist; decolonization of colonized residents, improving hand hygiene in both residents and HCWs, reducing the duration of contamination of HCWs, and decreasing the resident∶staff ratio are possible control strategies; the mean time that a resident remains susceptible since admission may be prolonged by screening and decolonization treatment in colonized individuals; in the stochastic framework, the total number of colonized residents varies and may increase when the admission of colonized residents, the duration of colonization, the average number of contacts among residents, or the average number of contacts that each resident requires from HCWs increases; an introduction of a colonized individual into an MRSA-free nursing home has a much higher probability of leading to a major outbreak taking off than an introduction of a contaminated HCW.

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We incorporate a vector-bias term into a malaria-transmission model to account for the greater attractiveness of infectious humans to mosquitoes in terms of differing probabilities that a mosquito arriving at a human at random picks that human depending on whether he is infectious or susceptible. We prove that transcritical bifurcation occurs at the basic reproductive ratio equalling 1 by projecting the flow onto the extended centre manifold. We next study the dynamics of the system when incubation time of malaria parasites in mosquitoes is included, and find that the longer incubation time reduces the prevalence of malaria. Also, we incorporate a random movement of mosquitoes as a diffusion term and a chemically directed movement of mosquitoes to humans expressed in terms of sweat and body odour as a chemotaxis term to study the propagation of infected population to uninfected population. We find that a travelling wave occurs; its speed is calculated numerically and estimated for the lower bound analytically.

Plasmodium vivax (P. vivax) is one of the most important human malaria species that is geographically widely endemic and causes social and economic burden globally. However, its consequences have long been neglected and underestimated as it has been mistakenly considered a benign and inconsequential malaria species as compared to Plasmodium falciparum. One of the important differences between P. falciparum and P. vivax is the formation of P. vivax latent-stage parasites (hypnozoites) that can cause relapses after a course of treatment. In this work, mathematical modeling is employed to investigate how patterns of an incubation period and relapses of P. vivax, variation in treatment, and seasonal abundance of mosquitoes influence the number of humans infected with P. vivax and the mean age at infection of humans in tropical and temperate regions. The model predicts that: (i) the number of humans infected with P. vivax may increase when an incubation period of parasites in humans and a latent period of hypnozoites decreases; (ii) without primaquine, the only licensed drug to prevent relapses, P. vivax may be highly prevalent; (iii) the mean age at infection of humans may increase when a latent period of hypnozoites increases; (iv) the number of infectious humans may peak at a few months before the middle of each dry season and the number of hypnozoite carriers may peak at nearly the middle of each dry season. In addition, glucose-6-phosphate-dehydrogenase (G6PD) deficiency, which is the most common enzyme defect in humans that may provide some protection against P. vivax infection and severity, is taken into account to study its impact on the number of humans infected with P. vivax. Modeling results indicate that the increased number of infected humans may result from a combination of a larger proportion of humans with G6PD deficiency in the population, a lesser protection of G6PD deficiency to P. vivax infection, and a shorter latent period of hypnozoites.