Effects of periodic aerosol emission on the transmission dynamics of Neisseria Meningitis A

Abstract

We develop and analyze a deterministic non-autonomous differential equation model for the meningococcal meningitis, the novelty of which lies in the incorporation of the following important facts: the periodic emission of desert aerosols, the biological sequence involved in the meningitis sero A (NmA) infection, and the burden caused by asymptomatic individuals. Though not containing meningococcus, the desert aerosols serve as a catalyst for meningococcal infection. We assess the impact of seasonality of aerosol production on the transmission dynamics of Neisseria meningitis A. Theoretically, we introduce two explicit threshold parameters, R0˜ and R0̂, that bound the basic reproduction number, R0, from below and above, respectively: R0˜≤R0≤R0̂. We prove that meningitis persists uniformly in the population when R0˜>1 and tends to disappear when R0̂<1. We numerically illustrate these results by considering four well-known functions of the concentration of aerosols, namely the minimum, average, maximum and actual time dependent values of the concentration of aerosols. It is shown that there exists a stable periodic solution (limit cycle) when the basic reproduction exceeds the unity, thereby highlighting the complexity of controlling the disease in the presence of periodic emission of aerosols. Two control strategies are incorporated in the model with the aim to reduce or eradicate the disease. These are to water the roads in the dry season and to raise awareness on the risk factor of the regrouping of the population. Numerical simulations show that the first strategy reduces the rate of disease transmission; but using it alone might not eradicate the disease. On the contrary, the sensitization of people to avoid gatherings can on its own drive the disease to extinction after some time when the maximum sensitization efficiency is above the control efficiency threshold β0c. Under this condition, a combination of the two control strategies leads to same conclusion as the second strategy.