In this paper, we formulate and study a mathematical model for the dynamics of jigger infestation incorporating public health education using systems of ordinary differential equations and computational simulations. The basic reproduction number R E is obtained and used to determine whether the disease breaks out in the population and results in an endemic equilibrium or dies out eventually corresponding to a disease-free equilibrium. We carried out an analysis of the model and established the conditions for the local and global stabilities of the disease-free and endemic equilibria points. Using the Lyapunov stability theory and LaSalle invariant principle, we found out that the disease-endemic equilibrium point is globally asymptotically stable if R E > 1 and unstable otherwise. Numerical simulations are performed to illustrate our theoretical predictions. Both the analytical and numerical results show public health education is a very effective control measure in eradicating jigger infestation in the endemic communities at large.
The emergence of parasite resistance to antimalarial drugs has contributed significantly to global human mortality and morbidity due to malaria infection. The impacts of multiple-strain malarial parasite infection have further generated a lot of scientific interest. In this paper, we demonstrate, using the epidemiological model, the effects of parasite resistance and competition between the strains on the dynamics and control of Plasmodium falciparum malaria. The analysed model has a trivial equilibrium point which is locally asymptotically stable when the parasite’s effective reproduction number is less than unity. Using contour plots, we observed that the efficacy of antimalarial drugs used, the rate of development of resistance, and the rate of infection by merozoites are the most important parameters in the multiple-strain P. falciparum infection and control model. Although the drug-resistant strain is shown to be less fit, the presence of both strains in the human host has a huge impact on the cost and success of antimalarial treatment. To reduce the emergence of resistant strains, it is vital that only effective antimalarial drugs are administered to patients in hospitals, especially in malaria-endemic regions. Our results emphasize the call for regular and strict surveillance on the use and distribution of antimalarial drugs in health facilities in malaria-endemic countries.
Human malaria remains a major killer disease worldwide, with nearly half (3.2 billion) of the world's population at risk of malaria infection. The infectious protozoan disease is endemic in tropical and subtropical regions, with an estimated 212 million new cases and 429,000 malaria-related deaths in 2015. An in-host mathematical model of Plasmodium falciparum malaria that describes the dynamics and interactions of malaria parasites with the host's liver cells (hepatocytic stage), the red blood cells (erythrocytic stage), and macrophages is reformulated. By a theoretical analysis, an in-host basic reproduction number 0 is derived. The disease-free equilibrium is shown to be locally and globally asymptotically stable. Sensitivity analysis reveals that the erythrocyte invasion rate , the average number of merozoites released per bursting infected erythrocyte , and the proportion of merozoites that cause secondary invasions at the blood phase are the most influential parameters in determining the malaria infection outcomes. Numerical results show that macrophages have a considerable impact in clearing infected red blood cells through phagocytosis. Moreover, the density of infected erythrocytes and hence the severity of malaria are shown to increase with increasing density of merozoites in the blood. Concurrent use of antimalarial drugs and a potential erythrocyte invasion-avoidance vaccine would minimize the density of infected erythrocytes and hence malaria disease severity.
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