Mathematical Modeling of Mosquito borne Diseases

Abstract

Mosquito-borne diseases are caused by bacteria, viruses or parasites transmitted by mosquitoes. Nearly 700 million people are getting ill from Mosquito-borne diseases and that leads to about one million deaths every year. There are many diseases which are transmitted by mosquitoes e.g. malaria, dengue, zika virus, chickenguniya, west Nile virus etc.. The pathogens of malaria, dengue, zika diseases are transmitted by Aedes aegypti mosquito. Present study is focusing on the study of Mosquito-borne diseases, namely, malaria, dengue, zika virus, disease. We formulate non-linear deterministic models for all three diseases by considering the human and mosquito population and as suming the criss-cross interaction between mosquito and human. Transmission of zika is also possible from human to human. So we have incorporated this human to human transmission in the mathematical model for zika. Our first model on Dengue disease discusses the impact of treatment. The key parameters of the proposed mathematical models are obtained by considering the data from different states of India. Analysis of this model includes computation of basic reproduction number R0, existence of equi librium point, stability analysis, bifurcation analysis and sensitivity analysis. Next we formulate and analyze a mathematical model to study the impact of early case detection on the transmission dynamics of dengue disease. Here we also extend our deterministic model to stochastic model and compare the results of both deterministic and stochastic models. Further, we formulate and analyze one more model for dengue by consider ing the impact of both screening and information. For this model we also formulate optimal control problem and discuss different cost-effective strategies to control the in fection prevalence of this disease. Next we formulate a mathematical model for malaria by considering saturated treatment. Here also we consider data from different states of India and estimate the key parameters. We perform sensitivity analysis of the basic re