A modified mathematical model for malaria transmission under control strategies

Abstract

We study a modified model for malaria transmission. We consider the model proposed by Chiyaka et al in [9] and modify it to include the proportions (i) of infectious humans that enter the human population by immigration; and (ii) of infectious mosquitoes recruited to the mosquitoes population. We believe that these two amendments to the model provide a better approximation of the real dynamics of malaria transmission among heterogeneous populations, given that infectious humans and infectious mosquitoes can also immigrate. We have computed the disease free equilibrium and the reproduction number. We have studied the variation of the reproduction number with the treatment rate κ. By observation of the graphs, we conclude that vaccination can slow the development of malaria in a community, while the treatment may increase the development of the epidemic, unless the therapeutic drugs are those that prevent treated humans to become infectious to mosquitoes. These results are in agreement with those obtained in [9]. We have also varied the rates of infectious humans and infectious mosquitoes that immigrate to the human and mosquitoes populations, respectively. We find that increasing values of the infectious mosquitoes lead to an increase in the values of infectious, infectious vaccinated, and treated humans, and infectious mosquitoes. On the other hand, an increase in the rate of infectious humans, implies greater values of susceptibles, infectious, and treated humans. These results suggest that our model is epidemiologically well-posed.