Modelling the severity of dual and co-Infection with malaria in populations with persistent and re-emerging Infections.
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Mathematical models have contributed to epidemiological understanding of infectious diseases at all levels, from projections of the magnitude of disease epidemics to the within-host interactions between pathogens and the host’s immune system. The research whose results are outlined in this thesis provide a novel insight into single host-multi pathogen interactions. It constitutes an extensive infectious disease interaction framework constructed for the pathogens and their human and/or vector hosts. Mathematical models in form of coupled differential equations are formulated based on the epidemiology of the interacting species and the transmitting vectors. In some of the studied examples, rather than using differential equations, more recent complex models where stochasticity influences the dynamics and computer simulation needs to be used to generate theory. In each of the study chapters, a specific modelling approach or set of techniques are designed to capture important biological factors of interest to the pathogen under consideration. Particular attention is given throughout the thesis to the development of practical models that are useful both as predictive tools and as a means to understand fundamental epidemiological processes. Diseases considered include malaria, HIV/AIDS, trypanosomiasis (sleeping sickness), Hepatitis E and visceral helminthiasis. Mathematical models describing the dynamics of these diseases when co-infecting with malaria are designed and analyzed. The model for malaria and HIV/AIDS co-infection was designed with HIV-positive immigration and dual protection. Analysis shows that there is no disease-free equilibrium point. Instead, an initial state of infection governed by the infective immigration rate ε exists. A small perturbation around this point approaches global stability if individuals infected with malaria protect themselves against HIV/AIDS during the episode, and if HIV infectives are protected against malaria. Numerical simulation shows that if the prevalence of malaria is high, individuals protect themselves against the disease more than when it is low. In contrast, HIV/AIDS individuals tend not to use protection when there is increased risk of disease transmission. From the model, it is concluded that HIV positive immigrants increase the number of secondary infections as well as the influx of co-infections. In the co-infection of malaria and trypanosomiasis, two mathematical models with and without isolation are formulated. Analysis shows that with strict isolation, the disease-free equilibrium (DFE) is locally asymptotically stable if R0 < 1, and unstable if R0 > 1, but not globally asymptotically stable. Further analysis of the model shows that an endemic equilibrium point exits but not unique due to existence of multiple equilibria of malaria-only, trypanosomiasis-only, or co-existence. Numerical simulation shows that the model exhibits bifurcations and thus cannot attain global stability. When one disease is controlled, results show that the other disease remains endemic in the population where local and global stability are attained under a specific parameter space. In the study of malaria and Hepatitis E, results show that a Hepatitis E outbreak persists in vi presence of malaria. Data was used to determine that R0 for the outbreak was approximately 2. Secondly, the critical level of latrine and borehole coverages needed to eradicate the epidemic was at least 16% and 17% respectively. Results further showed that individuals with malaria were 3.4 more likely to acquire malaria than those without. The critical value of ξ determined in this study agrees with prior studies showing increased susceptibility to other infections for malaria infected individuals . However, this result is speculative and the more important point is the relationship given in Figures 5.4 and 5.6 between co-infection and other model parameters. Immune stimulation and impairment in presence of prophylaxis when malaria and visceral helminthiasis are co-infecting is studied. In absence of immune response, it is found that there is no disease-free equilibrium point, and the antigens invade the blood system if the rate of red cell rupture per invading merozoite is greater than one. If fewer merozoites are released, the initial state of infection is globally asymptotically stable. If more merozoites are released, there exists malaria-only endemic equilibrium point. However, both antigens co-exist if the mean infection burden is greater than one. In this case, there is a threshold value for drug action below which no recovery of host is expected. In presence of immune response, three equilibrium states exist. A model for severity of the co-infection shows that an immune response will be delayed until immunological barrier values for malaria and helminths are exceeded. It is concluded from analytical results that whether the co-infection is sub clinical, acute, chronic or lethal depends on the dose of infection and time taken for immune response. Protection against mosquitoes limits the number of bites by the mosquito per human. In this thesis, a mathematical model where mosquito bites are reduced through DDT house spray was designed. Analysis shows a significant reduction in malaria prevalence. As more people spray, more mosquito are kept away leading to low disease prevalence, and the overall size of the pandemic. If another disease invades the population, the intensity is kept low and co-infections minimal. The main conclusion is that DDT reduces mosquito bites, but consistent house spraying is desirable for the eradication of malaria. One of the greatest effects of malaria is the contribution to high child mortality rates. In this thesis, the effects of how high child mortality rates affect social and economical development are analyzed. The objective is to show that high malaria rates not only kill millions of people each year but have secondary effects as well. A dynamical systems approach was used and it was shown that high child mortality rates lead to high fertility rates and low output per capita. With increasing economic growth, both rates are reduced. The economy then takes off to a sustained growth steady-state equilibrium where child mortality and fertility rates are considerably very low.