Analysis of a temperature- and rainfall-dependent model for malaria transmission dynamics

Abstract

A new non-autonomous model is designed and used to assess the impact of variability in temperature and rainfall on the transmission dynamics of malaria in a population. In addition to adding age-structure in the host population and the dynamics of immature malaria mosquitoes, a notable feature of the new model is that recovered individuals do not revert to wholly-susceptible class (that is, recovered individuals enjoy reduced susceptibility to new malaria infection). In the absence of disease-induced mortality, the disease-free solution of the model is shown to be globally-asymptotically stable when the associated reproduction ratio is less than unity. The model has at least one positive periodic solution when the reproduction ratio exceeds unity (and the disease persists in the community in this case). Detailed uncertainty and sensitivity analysis, using mean monthly temperature and rainfall data from KwaZulu-Natal province of South Africa, shows that the top three parameters of the model that have the most influence on the disease transmission dynamics are the mosquito carrying capacity, transmission probability per contact for susceptible mosquitoes and human recovery rate. Numerical simulations of the model show that, for the KwaZulu-Natal province, malaria burden increases with increasing mean monthly temperature and rainfall in the ranges ([17–25]°C and [32–110] mm), respectively (and decreases with decreasing mean monthly temperature and rainfall values). In particular, transmission is maximized for mean monthly temperature and rainfall in the ranges [21–25]°C and [95–125] mm. This occurs for a six-month period in KwaZulu-Natal (hence, this study suggests that anti-malaria control efforts should be intensified during this period). It is shown, for the fixed mean monthly temperature of KwaZulu-Natal, that malaria burden decreases whenever the amount of rainfall exceeds a certain threshold value. It is further shown (through sensitivity analysis and numerical simulations) that incorporating host age-structure and reduced susceptibility due to prior malaria infection has marginal effect on the transmission dynamics of the disease.