Mathematical Study on Impact of Temperature in Malaria Disease Transmission Dynamics

Abstract

Malaria is one of the most common mosquito borne diseases. Temperature is an important factor which affects the life cycle of the mosquitoes and transmission dynamics of the malaria disease. In the present work, we use SEIR compartmental model for the human population and LSEI compartmental model for mosquito population taking temperature dependent parameters. Basic reproduction number, R₀ of the model is computed using Next Generation Matrix Method. Stability of the disease free equilibrium and the existence of the endemic equilibrium point are discussed by basic reproduction number, R₀ . Numerical results are carried out with different temperature levels. It is observed that temperature affects the transmission dynamics of malaria disease significantly.

Introduction

Change of climate mostly affects the transmission dynamics of vector born disease. The disease is transmitted by female Anopheles mosquitoes. It is spreading in almost all tropical and subtropical region of the world. About 3.2 million people are at risk of malaria. In 2015 there were 214 million new cases of malaria and 438000 deaths from malaria. There is not any effective and safe vaccine against malaria till date. Control e orts of malaria are based on the strategies of reducing the mosquitoes, using the anti-malaria drugs and personal protection against mosquito bites. But still million of people are not receiving the services [1].

Climate factors such as temperature, rainfall, humidity, wind and duration of daylight strongly affect the ecological and behavioral features of vector borne diseases [2]. In the late 19th century average global temperature was increased by about 0.5° C - 0.6° C and by 2100 it is estimated that global temperature will rise 1.0° C - 3.5° C [3,4].

Change of climate mostly impact on the transmission of vector borne diseases. For many diseases it is observed that the transmission of disease occurs within the lower end range and upper end range of temperature. These range of temperatures are respectively considered as 14° C- 18° C and 35° C- 40° C [4]. In the context of malaria, the female adult Anopheles mosquitoes feed more frequently in increasing temperature since blood is digested more quickly with higher temperature [8]. Githeko et al. (2015) explained that the mosquitos’ feeds on blood every 4 days at 17° C and with a temperature increased to 25° C it feeds on blood every 2 days. The average lifespan of an adult mosquito is about 21 days and it is rapidly decreasing in 30° C- 32° C temperature [3]. Temperature levels above 34° C have a negative impact on the survival of both vectors and parasites and survival of adults reaches zero at around 400 C temperature [5,6]. Githeko et al. (2015) reported that the development of a gambiae larva stops when the ambient temperature is below 16° C and the temperature below 14° C leads to their deaths. Generally, the availability and productivity of mosquito breeding areas increases by rainfall. Although excess rainfall can rush out the Anopheles breeding areas.

Mathematical model is very useful tool to understand the dynamics of malaria disease transmission. The mathematical model for malaria disease transmission was studied by Ronald Ross in 1911 using SI compartmental model. His work was extended by Macdonald [7,8]. Aron and May described the properties of models defined by Ross-Macdonald. Anderson and May reviewed the model incorporating various parameters [9]. Chitnis et al. analyzed the bifurcation of a malaria model [10]. Mordecai predicted that the optimal temperature for malaria transmission occurs at 25° C [11]. In the present paper we consider SEIR model for human (host) and LSEI model for mosquito (vector) with temperature dependent model parameters.