Mathematical Modeling of Neisseria meningitidis: A Case Study of Nigeria

Bacterial meningitis remains one of the deadliest infectious diseases in the African meningitis belt. It is defined as an acute inflammation of the meninges, the protective membranes that cover the brain and spinal cord. This deadly disease has different serogroups with geographical distribution and epidemic potential varying amongst each serogroup. To date, six of these serogroups have been identified as causative agents of epidemics. The effect of this disease cannot be ignored due to its high morbidity and mortality; however, vaccination has played a major role in preventing the spread of the disease in the population. The work presented here was therefore designed to study the effect of constant and pulse vaccination in controlling the disease in the population using a non-impulsive model and an impulsive models. The two models were analyzed qualitatively to determine the conditions for eradicating the disease. Numerical simulation of the non-impulsive model showed that meningitis can be effectively controlled in the population using an imperfect vaccine with an efficacy greater than 75% and high vaccine coverage rate of at least 85%. For the impulsive model, we obtain the disease-free periodic solution, and the model is locally asymptotically stable when the threshold quantity, Rp, is less than one. Furthermore, numerical simulations showed that the final infected population size is lower when applying the impulsive vaccination strategy compared with the scenario without vaccination. Thus, the disease burden in the population decreases with increasing vaccination pulses. Lastly, we present a deterministic model to study the dynamics of the co-infection of multiple strains (serogroup A and serogroup C) in the presence of vaccination. For the scenario in which we set the transmission probability of a strain to zero, our results show that the co-infection model exhibits competitive exclusion (a strain driving the other strain into extinction when both are at endemic equilibrium). However, for the scenario in which we set the transmission probability of one strain greater than that of the other (transmission probability of neither strain is equal to zero), we observed a trade-off mechanism that enables co-existence of the two strains. In this case, regardless of the greatest reproduction number value of each strain, the strain with the highest transmission probability in co-infected individuals will dominate in the population without driving the other strain into extinction. We further analyzed and simulated the model without co-infection. The model exhibit competitive exclusion when R0A R0C 1 (strain A drives out strain C) or when R0C R0A 1 (strain C drives out strain A). Additionally, our results show that when the two strains have the same reproduction number at their endemic state, the two strains will co-exist but the dominance of a strain will depend on the initial size of its population

Qualitative Analysis of a Dengue Fever Model

In this paper, a deterministic mathematical model of the Dengue virus with a nonlinear incidence function in a population is presented and rigorously analysed. The model incorporates control measures at the aquatic and adult stages of the vector (mosquito). The stability of the system is analysed for the disease-free equilibrium and the existence of endemic equilibria under certain conditions. The local stability of the Dengue-free equilibrium is investigated via the threshold parameter (reproduction number) that was obtained using the next-generation matrix techniques. The Routh–Hurwitz criterion, along with Descartes’ rule of signs change, established the local asymptotically stability of the model whenever R0<1 and was unstable otherwise. The comparison theorem was used to establish the global asymptomatically stability of the model

Research capacity. Enabling the genomic revolution in Africa.

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